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SE 016 926

From Here, Where? A Space Mathematics Supplement forSecondary Levels.National Aeronautics and Space Administration,Washington, D.C.65184p.; Prepared in cooperation with the U.S. Officeof EducationSuperintendent of Documents, Government PrintingOffice, Washington, D.C. 20402 ($1.25)

MF-$0.65 HC-$6.58Curriculum; Instruction; *Instructional Materials;Integrated Activities; *Interdisciplinary Approach;*Mathewatical Applications; Mathematics Education;Problem Solving; *Science Education; *SecondarySchool Mathematics; Space Sciences; TeachingTechniques

A number of space science resource materials andactivities are developed into a useful format for classroompresentation. The application of mathematical properties in makingscientific discoveries is the major emphasis. Each section has adiscussion centered on the men and history behind the discovery ofphysical laws and phenomena relevant to space flight and exploration.The discussion provides interest and stimulation for the suggestedexperiments and problems. This document provides a valuablesupplement for use with secondary school topics such as ratios,logarithms, vectors, analytic geometry and trigonometry. (JP)

MATHEMATICS IN SPACE SCIENCEU S (1EPARIMENT OF HEALTH

EDUCATION & WELFARENATIONAL INSTITUTE OF

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FROM HERE, WHERE?A space mathematics supplement for secondary levels

FROM HERE, WHERE?GETTING INTO SPACESPACE AND WEATHER

SPACE NAVIGATIONTHE RIDDLE OF MATTER AND MOTION

THE MEASURE OF SPACETHE SPACE ENVIRONMENT

GLOSSARY OF TERMS-USED IN THE EXPLORATION OF SPACE

FILMED FROM BEST AVAILABLE COPY

Prepared by the National Aeronautics and Space Administration in cooperation with the U.S. Office of Education

FROM HERE, WHERE?

A source book in spare oriented mathematicsfor secondary levels.

Prepared from materials furnhlied by the NationalAeronautics and Space Administration in cooperationwith the United States Office of Education by aCommittee on Space Science Oriented Mathematics

1965

ERRATA

The printers inadvertently reduced the navigation mapson pages 62 and 65. Therefore, the answers to problems3, 4, and 12b shown on page 123 should be disregarded.

For sale by the Superintendent of Documents, U.S. Government Printing OfficeWashington, D.C., 20402 - Price $1.25

CONTENTS

Chapter IFROM HERE, WHERE? 1

Chapter IIGETTING INTO SPACE 31

Chapter IIISPACE AND WEATHER 41

Chapter IVSPACE NAVIGATIONChapter VTHE RIDDLE OF MATTER AND MOTION 81

Chapter VITHE MEASURE OF SPACE 97

ANSWERS TO CHAPTERS I-VI AND SELECTED BIBLIOGRAPHY 119

SupplementsTHE SPACE ENVIRONMENT 133

GLOSSARY OF TERMS USED IN THE EXPLORATION OF SPACE 161

INTRODUCTIONTo Students and Their Teachers

Throughout history men have looked to the sky. From the motions of the stars andplanets they have charted their travels, planted their crops, set the time of the days and of thescaaams. Today we not only took into spacewe go there.

Every one of us is a part of what is now called the Space Age. As we work and studytogether to make new discoveries, we share not only the benefits but also the responsibilitiesof this new and fascinating knowledge. We are finding that space exploration contributesmuch to making our world a better place in which to live. It has enabled us to predict and tochart the paths of steams, to produce more accurate maps, to improve our communications,and to discover the wonders of the universe which surround us. Every day orbiting satellitesprovide us with new knowledge, but af.1 of this would be impossible without the use ofmathematics.

Mathematics, one of man's oldest "tools,- has become a very important discipline in thisnew age of discovery. Therefore, to assist students and teachers in relating mathematics to thespats program, NASA/Goddard Space Flight. Center and the United States Office of Edu-cation joined efforts and formed a ClAnmittee on Space Science Oriented Mathematics.

Dr. Michael J. Vaccaro, Assistant Director for Administration, Goddard Space FlightCenter is chairman of the Committee, Dr. Patricia M. Spross, Specialist in Mathematics,U.S. Office of Education, is technical director and Mr. Alfred Rosenthal, Public InformationOfficer at the Goddard Center, publication director.

The first project developed by this group was "What's Up There," a ,space science mathe-matics. source book for use in elementary grades. The second pro oct. of the committee hasresulted in this publication designed to supplement the material usuany studied in secondaryschool mathematics classes. The various chapters of this book were written by experiencedteachers in a workshop held at the American University, Washington, D.C., conducted byDr. Chalmers A. Gross,

Editorial consultants for this project were Mr. Harry L. Phillips and Dr. Lauren G. Woodby,specialists in Mathematics, U.S. Office of Education and Mr. Arthur J. McMahon, Consultant,Mathematics Education, Department of Education, Rhode Island.

The author of each chapter felt that he had something special to say to you aboutapplications of mathematics in space science. It is the purpose of this book to arouse yourinterest and curiosity to search further and to make mathematics more meaningful as itrelates to the new era it now serves. HAVE FUN I

PREFACE

Surrounded by a changing world, the teacher of todly must relate new knowledge andnew experiences to his students.

However, there is a gap between teacher needs end available textbook material. Thisproblem is particularly acute in the areas affected by our efforts in the scientific explorationof space due to the exponential growth of scientific and technological information. Untilthe results of this research can be incorporated into textbooks for classroom use, supple-mental material must provide a partial solution to meeting these needs.

This reference book was developed jointly by the U.S. Office of Education; the AmericanUniversity; and the NASA/Goddard Space Flight Center. Its authors are experiencedclassroom teachers who have translated the wealth of space science resource material de-veloped by NASA into a format. useful for classroom presentation.

We hope that this reference book will be an aid in bridging the information gap whichfaces our secondary students and teachers.

MICHAEL J. VACCAROChairman

Committee on Space ScienceOriented Mathematics

vii

.

Chapter 1

FROM HERE, WHEREby

Robert A. MsasseauChurchill Area High SchoolPittsburgh. Pennsylvania

4

ABOUT THIS CHAPTERWhat is science? The beginning and the end of it could be thought of as experience.

Einstein stressed that: "knowledge about reality begins with experience and ends in it." Thewhat of science is less important than how one obtains it, and the how is more meaningfulto the person who does it.

As we learn the scientific method it takes many forms. Sometimes situations confront uswith the need to think originally and we feel that we must reach out for conclusions. When wedo this we add to the storehouse of knowledge and build on the experiences of the past, Indoing it however, we will perhaps find that we disagree with the past. As we study the greatmen of science we will find that this has been true. They were the scholars who knew andunderstood the past, but saw it in a different way. Therefore we need to know where we are,where we have been, and to have some idea of where we are going.

Sometimes we explore a topic individually and alone, at other times working with otherswill help us. The topics in this chapter are presented in such a fashion that you will experienceeach by some form of activity using simple tools like the straight edge, compass, pencil, andprotractor. You will be investigating the mathematics of ratio and proportion, exponents,logarithms, and vectors. Sample each and as you do, think what the great Galileo said manyyears ago: "You cannot teach a man anything, you can only help him to find it withinhimself. . . ."

1

Man is born with an insatiable curiosity concerning his natural environment. Therestraints upon his satisfying this inmate ,curiosity have been the shackles of superstition andmyth, and the lack of proper tools, such as the microscope, telescope, bathysphere and boosterto help, him carry his investigations further and his probes deeper. In today's refined tech-nology,nian is rapidly developing the tools with which he "an explore not only the earth butalso the ceiestial environment around it.

The space program draws on many areas of science . . . physics, astronomy, and theearth sciences. A general spirit of inquiry into the nature of the earth and its relationship tospace draws them all together. The catalyst of space science is mathematics.

Today we stand on the threshold of the Second Age of Discovery. The space-age"Columbus" and "Magellan" are not now known, but somewhere and sometime they wil; besitting in school preparing for an adventure that fer exceeds the greatest of dreams. It maydistract them from their books!

There is reason for teachers and students to look for new answers to age old questions.This booklet suggests experiences which can help you to understand the mathematics of spaceand which can lead you to develop new ideas. There is something here for everyone. Theexperiences will show you how you can apply the mathematics you study to space exploration.Work hard and see what you can find out.

"Space has devoured ether and time; and it seems to be on the point of swallowing up thefield and corpuscles, so that it alone remains as the vehicle of reality. . . ." &mews.

2

4-

CONCENTRICS, CYNICS, AND COPERNICUS

DiscoveryA Never Ending ProcessSpace is the new frontier for research.

The launching of the first man-made satel-lite plunged man headlong into this newlaboratory. Today every American ischallenged with the opportunity to partici-rode in individual research. Those who dotake advantage of the opportunity arerewarded with the thrills of discovery asexperienced by such men as Archimedes,Ptolemy, Copernicus, Galileo, Kepler, andGoddard.

Discovery has many forms and oftenunexpectedly announces its arrival onlywhen we feel defeated after long investi-gations and many observations. Researchin space is an open door to the study ofmathematics and science.

WhaL experiences and observations doyou need today fur the age of tomorrow?We can gain insight into the problem bygoing back into history and visiting someof the men whose discoveries and obser-vations of physical phenomena havehelped mankind to a better understandingof this place we call space.

3

11%

Concentric Circles Have No Alpha orOwego

Let us enter the "time capsule" 14,Thidjourney back into time. Set the controlsfor the second century somewhere inAlexandria, Egypt, for we are about tovisit Claudius Ptolemaeus, better knownas Ptolemy (toe-la-me). Here we see aman pouring over tables of 'data marchingfor answers to queostions and problemsabout the planets and the stars. One ofthe craters On the moon has been namedfor this man.

He seems to he drawing a series of lineswhich have no beginning and no ending.Yes, Ptolemy is drawing circles, one with-in the othera rather strange activity fora grown man

Ptolemy has been called the greatestastronomer of antiquity because his scien-tific investigations improved and extendedthe theories of his predecessors. Yet evenPtolemy has been criticized by our astron-omers of today. They claim that he wasso possessed by blind faith that he wouldfalsify his own observational results to

make them agree with the data furnishedat that time.

The scientific method used by Ptolemywas different from ours. He had noregular experimental research with ac-knowledged standards of judgment. Ob-servational results were not considereddocuments to add to the storehouse ofknowledge. There were few tools. Newtheories were clouded and condemned byfear and superstition . . . and Ptolemy'swork was essentially theoretical.

Much of his work was concentrated onthe planets and their strange motions inthe sky. Of course, everyone living then"just knew" that all of the planets andstars revolved about the Earth. Eudoxusand Aristotle had shown this 1-)y usingconcentric circles and spheres. Eudoxusused twenty-seven concentric sphereswhile Aristotle required fifty-five. Theseconcepts were believed back in 700 B.C.

Solar SystemsLet us take a little closer look at just

what Ptolemy is drawing. It seems thathe is trying to show pictczally how theplanets move through the constellations.For the most part, they move counterclockwise, if one's observation point isPolaris, ow North Star. This is known astheir direct motion; for it is in this direc-tion that the planets revolve about the sun,although Ptolemy did not realize this. Atintervals, which are not the same for thedifferent planets, they turn and seem tomove backward as they are observed fro ._our earth. They retrograde for a w'before resuming the forward motion.1,1eyare said to be stationary at the turns.

The most enduring early plan for solv-ing the problem of the planetary motio7- swas developed by Ptolemy: It was a planof epicycles and was labeled the PtolemaicSolar System as illustrated in figure 1.Note the use of concentric circles.

The epicycles were formulated by himto account for what we call retrogrademotion. The center of the "epicycle circle"was sometimes called the "fictitiousplanet" which was moving on a largercircle called the deferent. The planetitself was theoretically carried on the end

4

116 nays

CHAN HARM ON\ ANEtS

3/8 dk'sSATURN

Figure I. Ptulein, ystein

of a "crank-arm" pivoti- on the fictitiousplanet for its cent,' the diagram noattention is paid t hil,-nsions, the defer-ents being spaced -qual distances.

This scheme .s the result of a verycarefully thou ,pit plan to account forthe observed ions. Remember, suchobservations , .e made without the aidof a telex:

Let us now go back to another time inour capsule and make another visit. Thistime we shall look in on a famous astron-omer for whom one of the most conspic-uous craters on the moon was named. Heis Tycho Brahe (Tie-co Bra-he), a Danishastronomer whose passion for astronomywas shown in his secret nightly studiesand observations. Tycho was convincedof the truth of astrological doctrines, andhe often computed horoscopes. We mustnot criticize him too severely for thisbecause even today, in our modern worldof science, there are people who stillbelieve in fortune-telling.

The time is around 1590 A.D. and wesee Tycho at one of his instrumentsmaking observations of some celestialobject from the observatory which hebuilt and equipped with the finest astro-nomical instruments in existence. Oneshould remember that Tycho's instruments

Ralph A. Wright, Astronomy Charted (4Mason Street, Worcester, Massachusetts, Copy-wright 1948), p. 1.

did not include the telescope which wasstill to be invented. Yet his work as anobserver was meticulous in the extreme.He plotted planet positions night afternight, almost hour after hour. His ac-curacy was phenomenal and he developeda system of averaging the results of hisobservations in order to eliminate, asnearly as possible, any human errors.

it is said that he held his science in suchrespect that he never entered the observa-tory unless he was dressed in the finest.clothes he owned. His overall purpose wasthe correction of the astronomical theorieswhich existed at that time. No effortscomparable to his had been made sincethe days of Ptolemy.

Tycho suggested several modificationsto the Ptolemaic system, He held thatthe Earth was stationary in space, and&so used concentric circles to picture thesolar system. Figure 2 illustrates Tycho'sconcept of the solar system.

Tycho Brahe made a great advance inthe astronomical thought of his (lay. Hestill gave the Earth the honor of beingthe center of the solar system, but accord-ing to his theory, the moon and sun re-volved about the Earth while the otherplanets revolved about the sun. While theplan was not wholly sound, it did take astep in the right direction. One must

5

Figure 2. ,Tycho Brahe's Solar System

remember the dangers involved in dis-agreeing with the then-accepted theory ofthe day. Disagreement with the existingtheories of Tycho's day might have meantbeing burned at the stake. Credit shouldgo to Tycho Brahe for reasoning out onemore advanced step in astronomicalknowledge.' One should'also rememberKing Frederic of Den? lark who made it

2 Ralph A- Wright, Astronomy Charted (4Mason Street, Worcester, Massachusetts, Copy-wright 1948), p. 2.

possible for Tycho to build his observatoryon the small island of Hven, near Copen-hagen in the Ore Sound.

Now it is time for us to leave Tycho'sobservatory and move on to another coun-try in Europe. Our "time capsule" nowtakes us to the city of Thorn in PrussianPoland and the year is 1530. A man namedNicolaus Copernicus is writting a treatisein which he expresses dissatisfaction withthe Ptolemaic system.

The doctrine of Copernicus meant acomplete upheaval in man's concept of theworld which, as the new truth spread, wasto dominate modern thinking ever after.What was called the deferent of Mars orJupiter was now called its "real orbit."He used new- observations (mostly -madeby himself) to derive the orbits for thepresent time with more accurate periodsof revolution, and he computed new tables.Thus he produced a new manual of astron-omy suited to replace Ptolemy in everyrespect. Figure 3 illustrates the. solarsystem as pictured by Copernicus.

Nicolaus Copernicus was another as-tronomer who placed a milestone in man'sprogress through the ages.. The diagram

6

FIXED STARS

Figure 8. The solar system of Copernicus

abovr, will show some errors, yet an ad-vance is clearly seen with the ,sun finallyestablished as the center of the solar sys-tem. It is adapted in part from a theoryof the ancient Pythagoreans. Latercarried forward by Greek and Latinwriters. Copernicus, pondering on these

theories, formulated his "True Helit-,cen-tric System." He retained some ofPtolerny's epicycles and eccentricities thatwere finally eliminated by Kepler, but thefoundation of a central sun, was laid forus to build upon. Fortunately Copernicus'work was not published as "De Revolu-tionibus Orbium Celestium" until the yearafter his death. Bruno, another earlytheoretician, was .burned at the stake inthe year 1600 for affirming his loyalty tothe new theory. Today astronomers con-tinue to advance on the stepping stones heplaced.'!

The fuel gauge on our time capsule in-dicates we must return to our own eraand refuei. This will provide us with arest and a chance to ponder over thestrange visits we have just made.

EARIN

929 MiLi toN

MILES II A U

SOLAR SYSTEM STATISTICSRatio and Proportion

With a knowledge of ratio and propor-tion, you can duplicate Copernicus' illus-tration of our solar system. All that youneed is a reference book giving the meandistances of the planets from the sun, acompass, and a metric ruler. You canthen convert, or change, these distancesinto what is more commonly called astro-nomical units (A.U.) . You will need toknow the following:

mean distance = average distanceperihelion + aphelion

0Earth's mean distance from the sun is

about 92.9 million miles; therefore,

7

1 astronomical unit = 92.9 millionmiles = 1 A.U. (Wz use the Earth'smean distance from the Sun as 1A.U.)

A ratio is the quotient of two numbers,as 2,i or a/b.

A proportion is a sentence equating tworatios, as, 11/2 = or a/ =

Astronomical UnitsSince one astronomical unit equals the

Earth's mean distance from the sun, thenthe planet Saturn's mean distance fromthe sun could be represented in astronomi-cal units as follows:

mean distance of Saturn in milesSincemean distance of Earth in miles

Saturn's distance in A.U,Earth's distance in A.U.

886,200,000 milesand92,900,000 miles

Saturn's distance in A.U.1 A.U.

hence 9,5 A.U.= Saturn's distance in A.U.

Surely there must be an easier way todo this A man named John Ehlert Bodedid it. Let us examine some special num-bers in a series. Start with 0, and then 3,and double every number thereafter begin-ning with three, 0, 3, 6, 12, 24, . . , andso on.

Next, add 4 to each member of the givenset. This gives us

+ 4, 3 + 4, 6 + 4, 12 + 4, 24 + 4, ...INow divide each new element of the set

by 10. Now we are talking about thevalues in a set:(0 +4 3 + 4 6 + 4 12 +4 24 +4

10 , 10 , 10 , 10 , 10 ,

Take a close look at each of the resultingelements of this final set. Do you see any-thing strange? Can you relate them toanything we have discussed so far?

No one has yet come up with a satis-factory explanation of how a man named

3Ralph A. Wright, Astronomy Charted (4Mason Street, Worcester, Massachusetts, Copy-wright 1948).

John Eh left Bode derived these numbers.Textbooks only mention Bode's Law forits use in approximating mean distancesof the planets in astronomical units.

Yes, the resulting elements of our setrepresent, approximately, the mean dis-tances of the planets from the sun inastronomical units. See table 1 below.

Table 1.Bode's law

Planets Bode's Number Add 1(Experimental)Divide by 10

Distances inA.U. (True)

Mercury 0 4 0.4 0.39Venus 7 0.7 0.72Earth 6 10 1.0 1.00Mars 12 16 1.6 1.52Asteroids 24 28 2.8 2.65Jupiter 48 52 5.2 5.20Saturn 96 100 10.0 9.54Uranus 192 196 19.6 19.19Neptune 384 388 38.8 30.07Pluto 78( 772 77.2 39.52

A close agreement with actual distanceis shown in table 1 in the case of the minorplanets. Legend states that GiuseppiPiazzi discovered Ceres, the first asteroid,as a result of applying Bode's Law.Actually, he accidentally discovered 1-heasteroid Ceres on the first night of thenineteenth century.

The Experimental MethodOne should always be able to make com-

parisons when data are used at any time.For example, we should be able to calcu-late how much error there is in Bode'sLaw, if any.

A ratio is used to calculate what iscalled the per cent of error.Note: Per cent of error

!Experimental value True value(True Value

expressed as per cent.The vertical lines in the numerator rep-

resent a symbol meaning that only thepositive or plus value can be used. Thismeans that if the true value is greaterthan the experimental value and wewould get a negative number in the nu-merator, it would always be treated as apositive number. This is usually calledthe "absolute value" of a number.

For example, the percent of error usingUranus would be as follows:

8

Per cent error ='Experimental True'

Trueexpressed as per cent'19.60 19.191

19.190.41

19.192.14% error

Name

Mercury

Venus

Sym-bol

Table 2.Our solar system

Mean Distancefrom Sun

Period ofRevolution

Astrou, MillionUnits Miles

Side-real

Syn-dic

MilesEccen- Meant rieity Diam-

f ('terOrbit in

Mass Den-sity

Periodof

Rota-ion

Stel-lar

Tdatude

atGreat-

estIlrii-

Iiance

EarthMars

JupiterSaturn

Uranus

Neptune

Pluto

Sun

MoonRuler! II. Raker, An ban Action to Asteonomy (Nem York: I). Van Nostrum! COIIIIony, Inc., 1962).

Questions.1. Were there any entries which were not obtainable or else in doubt as to accu-

racy? If so, which ones and give your own reason as to why?2. Are all of the numbers positive? Can you explain your answer at this time?

Note:Answers for this table are supplied in the answer list at the back. (The inclusionof the table with answers is at your discretion.)

A student should now be able to con-struct an accurate picture of the solarsystem as seen by Copernicus using thedata from table 1. A suggestion Would beto use a scale where 1 A.U. = 1 cm.

Make the sketch and then see if youcan answer the following questions.

1. What are concentric circles?

2. Can you give some examples of con-centric circles?

3. Do you know the meaning of geo-centric and helio-centric?

4. Why are there only seven objectslisted in the solar system as picturedby Copernicus?

5. Do you know the Greek alphabet andits use in astronomy? (See any gooddictionary for this.)

977I -806 0-65-2

Ind iv id ua Rcsca Pelt*

Build a table of numbers (table 2) rep-resenting the solar .system as we know ittoday. Use any library references such asencyclopedias or astronomy texts. Thetable should be neat and kept in a note-book for further reference. The columntitle must be defined before any entry isallowed. Table 2 is one example of someimportant data which are used in spaceresearch.

* To the teacherThis table could beplaced on one spare chalkboard in theclassroom or else on heavy cardboard pos-ter type material. The students could workin assigned groups or teams to fill in theneeded information. A certain time allot-ment previously agreed upon by the stu-dents and the teacher for completionusually acts as a high motivation factor

ir the procurement of data. Stress theneed of using many sources to check theaccuracy of the data acquired. Averagescould be used if discrepancies occur.

ORBITS OF THE EARTH ANDMARS

Laboratory experiment:Object: To determine experimentally the

distance travelled by the planetsEarth and Mars as they revolveabout the sun.

Apparatus: 1 Benjamin Franklin half-dollar

1 Abraham Lincoln penny1 piece of twine at least 10

cm. long1 Metric-English ruler1 pencil

Procedure: Measure the radii of thepenny end half-dollar, andallow each one to representrespectively the mean dis-tances of the Earth and Marsfrom the sun in astronomicalunits.

Place the fifty-cent piece cal the paperand draw its circumference. Now placethe penny concentrically within the cir-cumference of the half dollar and drawthis smaller circumference.

Now use the string and ruler to deter-mine the actual circumferences of the twocoins by wrapping the string around eachand measuring the length of string usedeach time. Take your measurements incentimeters and call one centimeter oneastronomical unit. Compare your observa-tions and measurements with those youmay have found in the references youused for Table 2.

Calculate the circumferences of these"orbits" using C = rd where C = circum-ference, r = 3.14, and d = diameter incentimeters.

Secure the best information you canfind whiel gives the distance of the trueorbit in astronomical units. Compare yourexperimental value with this true valuesand determine a percent of error. Makethree trials and then obtain an averagefor discussion purposes.

List your data in a table similar to theones provided below.

Table 3.Earth's orbit

Trials Diameter ExperimentalCircumference

Calcula:ted (true)Circumference

(from areference book)

PercentError

1

2

3

x

10

Trials

3

Diameter

Table .1.Mars' orbit

ExperimentalCircumference

Calculated (true)Circumference

(from areference book)

PercentError

Questions 1. What conclusions can you make concerning your data?2. Was the percent of error high? Why?3. How does your data compare with that of table 2?

SYMBOLIC SHORTHANDAn Application of Set Theory

Have you ever tried to abbreviate namesand places in order to write faster? Math-ematicians do this every day; in fact,almost everyone uses symbols of one kindor another. A symbol is a mark, a sign,or a word that represents an object or anidea. The following are all symbols:

Can you think of any others? Here aresome of the more common symbols ofarithmetic.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9,+ - x

Pigur4 4. Coneeptfitt Nyartrols of arithmetic

Many schools today are using symbolswhich are somewhat new in introducingsets. A set is described as any collectionof distinct objects. An elementary conceptdealing with sets is one of membershipin a particular group. It AGO] be empha-sized that a set is determined by its mem-bers or elements. For example, the set ofstars is the set whose elements are stars,and both planets and common satellites areexcluded from this group or set.

One should remember that two sets areequal if and only if they have the sameelements. The symbol for a set is a brace

11

and the set of stars can be representedas !stars:. Considering the number of starsin the universe, one could describe {stars 1as an infinite *IA since there seems to be aninfinite number of stars in the universe.

When I Heard The Learn'd AstronomerWhen I heard the learned astronomer,When the proofs, the figures, were

ranged in columns before me,When I was shown the charts and

diagrams, to add, diride, andmeasure them,

When I sitting heard the astronomerwhere he lectured with muchapplause in the lecture-room,

How soon unaccountable I became tiredand sick,

Till rising and gliding out I wander'dof by myself.

In the mystical night-air, and fromtime to time,

Look'd up in perfect silence at flu stars.Walt Whitman

When on a moonless night, one observesthe clear field of stars, a too common firstimpression is that there are "millions ofthem." A useful exercise might be todetermine their number by direct count,a task not so difficult as it may sound.'

Laboratory experiment:Title: A Visible Star Count.Objective: To. determine the number of

stars visible on a given night.Apparatus: 1 piece of white pine

1" x 3" x 6"3 nails1 protractorI ruler1 hammerI clear cloudless night

Procedure: Obviously the dome on whichthe stars appear to be ishemispherical. It rises fromthe horizontal circle or planeknown as the horizon to apoint directly above the headof the observer. This point iscalled the zenith. In order tohave a useable horizon it isnecessary to be in open coun-try with no intervening ob-structions.

Next it is advisable to select a 30° arcon the horizon circle. Perhaps the bestway to do this is to have three nails sodriven into a board that by sighting fromone (A) of them to, in turn, the second(13), then the third (C), the two lines ofsight will enclose a 30° angle. (See figure5)

Net arcs must be imagined drawn ver-tically from each horizon circle pointdetermined by the sides of the 300 angle.Each of these vertical arcs must be pro-duced until they meet at the zenith,directly overhead.

This construction (visual) has de-lineated a spherical triangle with one 30°side on the horizon circle, and two 90°sides intersecting at the zenith. Thisspherical triangle then contains one-twelfth of the area of the visible hemi-sphere. Without an inordinate amount oftrouble the stars in this triangle can becounted. Except on very clear nights,

12

Figure, 5. Spherical triangle DBC

there will be only about two hundred ofthem. This indicates that the entire num-ber of stars visible at one time is about2.500 and this is generally about right.

However. people with exceptionallykeen eyesight on exceptionally good nightsfor viewing may be able to see as many as250 in such a spherical triangle, raisingthe maximum number of stars visible atone time by the unaided eye to approxi-mately 3,000.

To the teerher: Have each member ofthe class make three trials and averagetheir individual results. Then calculatea final average for the class and obtaina percent of emir using three thousandas the acceited or true value. Havestudents observe stars in a triangle out-side of the Milky Way. A triangleraised a little from the horizon mayeliminate counting stars in the surfaceor horizon haze.

4 Courtesy of Mr. Carl Heilman, PennsylvaniaState Supervisor of Mathematics.

Table 5.Data for at visible star count

TrialsI

Eiperimental

1

2

3

Accepted

Cosehision:The student should write a conclusion

to the laboratory experiment report andin it tell whether or not he succeeded inachieving the objective of the experimentReasons for error should be listed regard-less of the size of the error. Suggestionscan be included here as to how to improveon accuracy in this experiment.

One might now say that the number ofvisible stars is a subset of the set of stars.In other words,

(visible stars) C (stars).Have you learned the notation used in

connection with sets? Here are some ofthe symbols used.

I iluc E 0 niFigure 6. Symbols

A good student should know the mean-ing of each and be able to use them all.See a mathematics text for the meanings.Alphabets

Mathematicians today need many sym-bols to carry on their work most efficiently.One would think the twenty-six letters inour alphabet would satisfy the need, butthis is not true. The Greek alphabet isalso used. The beginning letters corre-spond with ours:

Table 6.Greek-English letter equivalentsalpita

a-beta- -gamma6-delta. epsilont zeta-etait-theta

ab

deaelb

.iotakappa k

k -lambdaa - -mur- au to

tit-omicron o- pi

p rho f. rhsigma a

taue-upsilon y. u. -phi Ph5-chi di

Psi Psto-0111Tiga 6

13

Percent of Error

Look up the word alphabet in any gooddictionary and then make a table of theGreek alphabet and compare or contrastit with ours. How many letters are therein the Greek alphabet? (You will find thatthe number varies. The alphabet changedover the centuries).

Table 7.Greek alphabet

. alpha,1 beta.., -gamma6- delta

t-- iotakappa

I-lambdaa -mu

p ira0sigmatau

1 upsilon- epsilon r nu _ phi- Beta E - ti r tin

eta -omitron i psi0-theta r- pi ,t, omega

Symbols and StarsAstronomers today identify many stars

using letters from the Greek alphabet.The plan of designating the brighter starsby letters was introduced by Bayer, aBavarian attorney, in 1603. In a generalway, the stars of each constellation aredenoted by small letters of the Greekalphabet either in order of their bright-ness or according to location, and theRoman alphabet is drawn upon forfurther letters. An example is illustratedin Figure 7 and Figure 8.

9.T

ga

E7

Figure 7. ConstAlatiost of Gewisti

STAR IDENTIFICATION

SYMBOL STAR NAIVE

Dubtve

Meralc

Phecda

4 u4sft4Akoth

Meet

Benetnesch

Figure R. Rig Dipper in Urea Major

Figure $ pictures the constellation UrsaMajor more commonly known as the -BigDipper" of the sky. Here the stars arelettered in order of position, On a clearnight you should always be able to seethis constellation if you live in the nc7th-eni hemisphere since the Big Dipper isone of the circumpolar constellations.

Here is another list of symbols whichare becoming more prominent in our spaceage. Astronomers use these to identifythe following:

Table 8.Signs and symbols

THE PLANETS

Mercury

Venus

EarthMars

JupiterSaturnUranus

Neptune

Pluto

9SpringSigns

SummerSigns

AutumnSigns

WinterSigns

CONSTELLATIONS OFAriesTaurusGemini

CancerLeoVirgo

LibraScorpiusSagittarius

CapricornusAquariusPisces

THE ZODIAC

The RamThe BullThe Twins

The CrabThe LionThe Virgin

The ScalesThe ScorpionThe Archer

The He G.AtThe WatEr ?SourerThe Fishes

OUR SUN is usually represented by the symbol 0.

Exposuitts and Logarithm*There are many interesting ideas about

astronomy in the gettioAs which follow.You may find some mathematics withwhich you are unfamiliar. Do not let thatstop you. Refer to a good algebra textand see what you can do.

Work carefully. You may be surprisedat how much you can accomplish.

Symbols are used to represent manydifferent naratneters. Sometimes numbers

14

are used which have a special meaning.Parameters can be described as letters,variables, or constants which denote quan-tities or nNetbers.

Such is the case with numbers whichrepresent exponents. For example, thesmall number 2 as written in 10: meansthat the number 10 (base 10) is to be tamedas a factor two times. In other words.

10: = 10 x 10 = 100(These are our common basv-ten system

numbers.)

By the same mannerI by definition)

104 = 1 104 = 10,00010' = 10 105 = 100,000102 = 100 104 = 1.000.000103 = 1,000 107 = 10,000,000

It is now possible to see that a numberbetween 10 and 100 could be representedby 10" or 101-" or 10124.

The above numbers are read as 10 to the1.1 power, 10 to the 1.3 power, and 10 tothe 1.5 power respectively.

Some specific examples would be:

Table 9.-Exponents and decimalsprim105.415

10'4"10".101.02101.7"102."101.s

=

926303640

= 61= 100= 200

Notice the exponents of the base 10 getlarger as numbers increase from 9 to 200.

Let us change the name of the ex-ponents in Table 9 above. Instead of call-ing 1.556 and 1.602 exponents, let us callthem logarithms. From now on we shallrefer to the exponents above as loga-rithms.

Instead of saying 10 to the 1.556 poweris equal to 36 or 103.1:4 = 36, we shall nowread it as the logarithm of 36 to the base10 is 1.556. Shorthand notation is asfollows: log,,,36 = 1.556.

Now you should try using this newabbreviation or symbol for a power of 10or an exponent of 10.

Fill in any blanks which are missing.

Table 10.-Logarithms

LOGARITHM NUMBER

log,,.9 = 0.954= 1.415

log,,,30 = 1.477log,..36 = 1.556

= 1.602log,61 = 1.785log,100 =log,200 =

15

Table 10 represents a list of criticalnumbers and their logarithms.

The list is said to be critical since it isto be used in the next topic dealing withthe brightness or magnitude of a star andsome of the instruments used to detecttheir presence.

When observations of stars are made.very obvious differences in color andbrightness of stars are seen. If opticalaids are used to supplement direct vision,such differences in color and brightnessbecome noticeable.

Furthermore, the use of even low powerfield glasses, opera glasses, or small tele-scopes %rid serve to demonstrate howmany more stars can be made visible in agiven area of the sky by such aids. Also,it will be noticed that such optical aids donot increase the size of the star's image;they merely intensify its brightness. Thislast comment does not, of course refer tothe planets, which must not be confusedwith the stars.

Since differences in sizes of stars arenot readily apparent, differences in bright-ness serve much better for purposes ofclassification. The unit of brightness ofstars is known as the atelier magnitude.Stellar magnitude is defined by saying thatif two stars so differ in apparent lumi-nosity that one appears 100 times asbright as the other, then they will differby Ave inagnitudes. The magnitude differ-ence is divided into equal steps, such thattwo stars differing by one magnitude willdiffer by a factor of 2.512 which is the fifthroot of 104.

The ratio of brightness between twostars differing by exactly one magnitudeis the number Whose logarithm is 0.4,which is about 2.512. In other words104.4 = 2.512.

Table 11 illustrates the contrast betweenmagnitude and brightness.

Note: (2.512)1 = 2.512(2.512)! = 6.31(2.512)2 = 15.85(2.512)4 = 39.8(2.512)6 = 100.0

Perhaps by noting the exponents of2.512, the student can see why the concept

Table 11.Magnitudes and brightness

Ratio ofMagnitude Brightness

1.0 magnitude 2.5122.0 magnitude 6.313.0 magnitude 15.854.0 magnitude 39.85.0 magnitude 100.0

of magnitude is a function of logarithms.The two stars in the Big Dipper's bowl

next to the handle are of the third magni-tude. The other five stars in the constella-tion are of the second magnitude.

BIG DIPPER

2nd

2nd0

3rd 2nd

Figure 9. Star magnitudes in. the Big Dipper

Table 12.Star magnitudes

Stars Magnitude

rr

/3

8

it

2nd2nd3rd3rd2nd2nd2nd

Second magnitude stars are approxi-mately 21/2 times brighter than the thirdmagnitude stars. The reader should tryto associate these stars with others toapproximate star magnitudes.

By now it should be obvious why theexperiment on a visible star count pro-duced such a relatively low number com-pared to the actual number of starspresent in the universe. The average

16

human eye can only detect stars up to 01,sixth magnitude in brightness. Beyondthe sixth magnitude, an optical instrumentis required for any observation of dimmerobjects.

However, even the optical instrumentsof today's modern science have theirlimitations. The limiting magnitude ofany optical telescope can be calculatedusing this mathematical relationship.

L.M. 8.8 + 5 log, DWhere L.M. = limiting magnitude of atelescope and log, D = the logarithm ofthe measure of the diameter of the lensin the telescope.Hence the limiting magnitude of a

homemade telescope can be calculatedbefore it is built and the person buildingthe telescope can anticipate the magni-tudes of the faintest stars he will have thegood fortune of viewing.

Here again is further indication of theimportance of a knowledge of mathematicsin this space oriented age we are entering.

Sample problem: What is the limitingmagnitude 07.- a In,-ue made 6-inch reflect-ing telescope': (log,6 = 0.778)

Solution: L.M. = 8.8 + 5 log, D= 8.8 + 5 (0.778)= 8.8 + 3.890= 12.690

Answer:This homemade 6-inch tele-scope will enable its maker to view starsof the /2.69 magnitude.

Table 13 is a list of some of the observa-tories in the United States. Can you usethe above information to determine tIleirlimiting magnitudes?

Reflecting telescopes use a concave mir-ror to gather enough light to enable viewersto see objects fainter than the sixth magni-tude. A refracting telescope uses a glasslens to gather light in the same mannerthat a magnifying glass does. The glas.-;lens is called the "objective" lens of thetelescope.

Table 13.Observatories

Observatory Location

Churchill Area H.S. Pittsburgh, Pa.Georgetown University Washington, I). C.11. S. Naval Observatory Washington. I). C.

Allegheny Observatory Pittsburgh. Pa.Lick Observatory Mt. Hamilton, Calif.

*Yerkes Observatory Wilhome Bay, Wis.

Harvard -University Cambridge, Mass.Palomar Mt. Wilson, Calif.

Hale Telescope Mt. Palomar, Calif.

*Largest refracting telescope of its kind in the world.

H. "

1VP-'

4kr.S,

TelescopeLens Diameter

913"

26"

30"

36"

40"

61"

100"

200"

Figure 10. High 8(.11001 (thseratory in th iv; till arra near Pittsburgh Penns yl van ia

17

Two Studeoe Research Projects1. The student is invited to investigate

-quasi-stellars." What are they? Howhave they been detected ? What is thesignificance of their dismery?

One reference is the May 25. 1964 issueof Newsweek.

2. An individual laboratory experimentin photometrythe science of the meas-urement of light intensity.

Title: THE MOON'S MAGNITUDE

Objective: To determine the magnitude(brightness) of a full moon.

Apparatus: 1 plane mirror(highly reflecti ve I

1 standard candle1 meter stick2 blocks of paraffin wax1 piece of cardboard1 1" x 3" x 72" piece of white

pine1 large shoebox

(for shielding purposes)1 block of wood

(support for the mirror)NOTE :The magnitude of a standard

candle at a distance of 1 meter= 14.2.

NO*: the mainstmle of i slim146.4 candle M &Mance el 1 'mem c 14.2

Figure 11. Muskat photometer

Proeviwre: Place a piece ct cardboardbetween two blocks of paraffinand turn one of the blocksso light will fall on its largestside. Notice the difference incontrast or shading when youlook at one block and that theother. Examine Figure 11 and

18

be satisfied that this contrastcan be increased or diminishedby moving the blocks of paraf-fin toward or away from thesource of light.

NOTE TO STUDENT: This phenomenais often described using what is called theinverse square law. The brightness of the

light varies inversely with the quire ofthe distance. An object two feet awayfrom a light receives one fourth as muchlight as an object one foot away.

If the blocks of paraffin are placed onthe board where one block appears to havethe same illumination as the other, thelight striking the blocks are said to havethe same intensity or brightness or illumi-nating pmver.

All other light must be excluded. there-fore, a darkened room is necessary. A

1""

(sample

IllI i

I Moonlight

shoebox may be used as shown in Figure11.

Stellar magnitude can be determined byusing the following proportion.The magnitude of a candle

1 meter2The magnitude of the Moon

S2S,2 = The square of the distance in meters

a candle is from the cardboard whenthe paraffin blocks appear to beequally illuminated.

Place paraffin Maas at positionof equal shading. (Shoe box for shit:kw-nu)

Candle light ,

it

,wpm.. gar.

14- 'Mom

Figare 12. Sample trial

The meter stick measures the distancefrom the candle to the cardboard to be 94cm. This is the eqoivalent of 0.94 m.

Hence

14.2 magnitude X1 m2 (.94m) 2

X --,-- the stellar magnitude of moon.X m'2 = (-14.2 magnitude) (.8$36m2)X ni1 -,- (-12.547 magnitude) (m1)

Since the accepted stellar magnitude ofthe Moon is 12.6, our experiment showsan error of 0.42 percent which is relativelygood considering the crudeness of ourapparatus.

NOTE: The shoe box with slits cut inthe ends was used to shield the paraffinblocks from any sources except those ofthe Moon and candle.

Try to perform this experiment in adark room by catching the Moon's re-flected light through a window. The shoebox will not be needed as a shield underthese conditions.

19

Remember to position the mirror atsuch an angle so as to receive the maxi-mum amount of reflected light.

S, = distance of candle toparaffin blocks.

Table 14.--Student data table

Trial S. S. 2 XPercenterror

1

2

3

Average

Conclusion: Here you should analyzeyour data and give reasons for your re-sults, good or bad. Can you think of abetter way to conduct the experiment toincrease your accuracy?

SOME MATHEMATICALAPPLICATIONS

Vectors and AnglesMost of science today would be impossi-

13Se without numbers and mathematics.Space scientists and engineers often usenumbers with which we are all familiar,such as decimals, fractions, mixed num-bers, exponents, and of course letters torepresent certain quantities. For example,the speed of a plane is given as Mach 2,or the speed of a booster is listed as Mach20. This simply means the craft is trav-elling 2 or 20 times the speed of sound.

Decimals are often used to designatethe brightness of celestial objects in termsof magnitude. The magnitude of the starAntares k the constellation of Scorpiusis 1.2 and the magnitude of Rigel in theconstellation of Orion is 0.3.

All of the numbers mentioned above arequantitative, that is, they represent cer-tain quantities. These numbers are knownas scalar quantities. A scalar is a numberhaving magnitude only and has nothingwhatsoever to do with direction.

There are times whin the scientist mustuse one number to represent both quantityand direction.

A good example of this is in fixing thepositions of points on the circumference ofa circle. A line one unit long pointing eastcan represent a line from inside the centerof the earth to a fixed point on the equator.Another line one unit long pointing duenorth represents a line from the center ofthe earth to the north pole.

North Pole

AEquator

Figure 13. Earth's radii

Vectors are number pairs that have bathmagnitude and direction.

-4Radius OA is called a vector because it

represents both magnitude and direction.

20

-4Vector OA is described as 1 unit East or

1 unit at 0 °.-4

Vector OB is described as 1 unit North or1 unit at 90' .

Now look at an Earth-Sun relationshipagain assuming the Earth's orbital path isnearly circular.

Earth

Figure 14. Vector diagram

OA = 1 A.U. at 0°-4OR = 1 A.U. at 45°

6C = 1 A.U. ; 180°

6-1) = 1 A.U. at 270°Notice that the letter A denotes the

position of the Earth on its orbit while theline OA represents its distance from theSun. The point of the arrow denotes direc-tion in figure 16.

Hence OB is read, "vector OB and repre-sents a magnitude of 1 astronomical u6tat an anfee of 45°".

Now plot or draw the following vectorsusing figure 15 and using data in table 15.

110'100' 90' 80° 7060°

130°

140° 40'

150° 30'

160° 9G 20'

170° 10"

180'

190° 350'

50°

200' P 340'

210' 330

220' k 320'

230° 310'

240° 300'250"' 260 270y 280° 290'

Figure 15. Vector radius

Table 15.VectorsOA = 1 A.U. 240' OD = 1 A.U.OB = 1 A.U. 130° OE = 1 A.U. 135'OC = 1 A.U. 300' OF = 1 A.U. 175^

Notice the vectors used above are equalin magnitude and vary in their direction.One must have the ability to plot vectorsregardless of magnitude and direction. Allthat is needed is a protractor, a compass,and a ruler. The following problem illus-trates an application of vector.

Retrograde MotionWhat is retrograde motion? Can you

explain retrograde motion in a clear, logi-cal manner? The following is an attemptto explain retrograde motion using vec-tors.

The planets were called "Wanderers"due to their strange motions in the celes-tial sphere. Normally the planets movefrom the west to the east in relation tofixed stars when viewed from the Earth.However, there are times when one willappear to be moving from the east to thewest. This phenomena is defined asretrograde motion.

You will need a compass, a protractor,sharp pencils, a 30°, 60°, 90° triangle, anda T-square. The procedure is as follows:1 Tape a plain white piece of paper to a

drawing board or some other smoothsurface such as ' table top or desk top.

2. Use a scale where 11/4" equals 1 A.U.Then 14" will represent the basic orscalar unit of length for our drawing.This means that 1 scalar unit = 0.1A.11. and 10 scalar units = 1 A.U.1 A.U. = 1 astronomical unit = 92.9million miles (approximately)

3. Construct two concentric circles. Thelarger circle should have a radius of 1A.U. or 11/4". The radius of the smallercircle should be .7 A.U. or 7/8". Thelarge circle represents the Earth'sorbit about the sun and the small circlerepresents the orbit of Venus.

4. Fix the position of Earth and Venusso they are 180° apart. See fizure 18.Figure 18 shows the normal movementof the Earth and Venus in a counter-

2/

clockwise path about the sun as viewedfrom Polaris, the north star.

5. Now divide the orbit of the Earth into12 monthly intervals of 30'-' each.Remember the annual period is thetime for one complete revolution abouta fixed point.

Figure 16. Orbite of Earth and Venom

6. Now refer to table 2 page 7 to obtainthe sidereal period of Venus, or thetime for Venus to complete one revolu-tion. We can use a proportion here:

period of Venus 224.7 daysperiod of Earth 365.3 days

Let x = the period of Venus as com-pared to 12 Earth months.

224.7 days12 mo. 365.3 days

(224.7) (12 months)x =365.3

x = 7.4 months (approximately)The annual period of Venus is 7.4 Earthmonths.

7. Now if we divide the orbit of Venusinto 7.4 eoual intervals, each interval

360°would be7 4

, or approximately 48.6°.

per interval.Round this off to 49° and use a pro-tractor to divide Venus' orbit intomonthly intervals of 49° each.

8. Figure 16 should now resemble figure17 below in which the position of theplanets are fixed at monthly intervals.

Tables 16 and 17 give positions of Venusand Earth during one year.

Notice that Venus in Figure 17 completesclose to one and one half orbits while theEarth is completing one cubit. Position E,is the Earth's position in January whenVenus is at superior conjunction at V,.

E is the Earth's position in June andthis corresponds to V. which is the posi-tion of Venus in June.

A line from E, to V, represents the dis-tance frcIn Earth to litmus and the direc-

E 0

Figure 17. Monthly positions of Earth am,Venus

Table 16.Venus positions

Position Angle

V1 00

V, 47V3 98°

V,

-,

147°

196° = 16° + 180°

VI; 245° = 65° + 180°

V, 294° = 24° + 270°7 343° = 63° + 270°

V. 392° = 32° + 360°

Vi. 441° = 81° + 360°

V31 490° = 130° + 360°

V1, 539° = 179° + 360°

22

tion in January. Therefore line E,V, is avector quantity.

EV, = distance and direction of Venusin February, observed from the Earth.

9. Connect the positions of the planetsEarth and Venus with straight lines atE, and V1, and V.', E3 and V, andso on until one year of time has beencompleted. E,V, E3V3, E,V4.are vectors representing the distancesand directions of Venus from Earthas they move in their orbits.

EaFigure 18. Vector dietatteez;

Table 17.Earth positions from Sun

Position Angie

Ei

EY

E3

E,

180°

210°

240°

270°

E11

300°

330°

360°

390°

420°

450°

480°

510°

Each vector represents the magni-tude of distance and the direction ofVenus from Earth at monthly inter-vals. NOTE: (This entire problem hasbeen treated from a heliocentric stand-point. We anurA apply Hipparcus' andPtolemy's geocentric theory at thistime since Venus is being observedfrom Earth.)

10. Each vector has been measured individ-ually and the statistics for each one hasbeen tabulated and entered into a datatable. See Table 18.

We must now plot each vector inturn using a geocentric or earth cen-tered system. After each vector hasbeen plotted in turn, as in Figure 19,the endpoints are joined by a smoothcurve which traces the apparent pathof Venus us viewed from the Earth.Notice the wandering or retrogrademotion in Figure 19.

Table 18.-Vector coordinates

Vector(Distance)Magnitudeon A.U. n Degreesin

EN, 1 1.70 A.U. 0°

E,V, I 1.65 38.5°

EV 1.60 76.0°

E N, 1.50 112.8°

E V 1.33 151.0°

EV 1.18 186.0°

ETV, 0.95 2210°

ENV 0.74 239.7°

E.V 0.50 282.0°

E ,Vi 0.33 292.0°

EV 0.33 280.0°

EINig 0.49 289.0°

E,,,V, 0.73 316.4°

EI.Vi. 0.95 348.4F.

E V,S 1.17 321.0°

E,,,V, 1.36 419.0°

Table 18 gives both magnitudes (dis-tance in A.U.) and directions of Venusfrom the Earth during 16 months.

23

Examine the above data? Can you ar-rive at any conclusions before plottingthese data?

Figure 19. Retrograde 'notion of Venus

The dotted path illustrates the retro-grade motion of Venus using vectors. Theretrograde motion occurs because we areobserving Venus from a planet that isrevolving at a different rate. V, and Vare endpoints.

How many months after superior con-junction does retrograde motion begin?

The student should be able to show thatthe inferior planets retrograde near in-ferior conjunction. In general, a planetretrogrades when it is nearest the Earth.

CHARTING POSITIONS OFPLANETS

Figures 20 and 21, in conjunction withTable 10, enable us to ascert, n quicklythe approximate location of V ,

, Cr , 24- , and '1,1 at any time inthe interval 1400-2400 A.D. (The symbolsstand for six planets in our solar system;naanely, Mercury, Venus, Earth, Mars,Jupiter, and Saturn.) See pages 22-25

In Figure 20 the orbits of the terrestrialplanets, indicated by their symbols, aredrawn to scale but, by necessity, in thesame plane.'

In both figures, the monthly position ofthe Earth is irdicated while the decimals

s Walter liarticy, Highlights of Astronomy,(Chicago: University of Chicago Press, 1935),p. 168.

0, 0.1, 0.2, up to 0.9 designate orbital posi-tions of the remaining planets, the num-bers 0 and 0.5 defining perihelion andaphelion, respectively. The order of thedecimals indicates the direction of themotion, and the arc between the pointsassociated with two successive decimals isthe path described by the planet in 1/10its period of revolution; consequently,given the length of time that has elapsedsince a perihelion passage, it is possibleby means of these markings to locate theobject in either Figure 20 or Figure 21.

The decimal corresponding to theplanet's position at any specified time isobtained from Table 19 by a simple addi-tion of numbers associated with the dayof the month, the month, and the units,tens, and hundreds in the year number.

23.5

15

5

10

An example illustrates the method:Suppose we seek the position of the

planet Venus on February 5, 1931. Theday of the month is 5, the month Febru-ary, the units in the year number are 4,the tens are 3, and the Innidreds are 19.From Table 19 we obtain certain numbersassociated with the aforementioned, whichwe tabulate and sum as follows:

AssociatedNumber

Day of the month 0.01Month FebruaryUnits in year number ___4 .50Tens in year number____3 :76.Hundreds in year

number 19 0.00

5 ?E

15

Total__ __ _1.99

20

This denotes the posi-tion of Venus onFebruary 5, 1934 y isplaced at .99 on orbitof Venus.

15

Figure 20 . Mercury, Venus, Earth, and MarsWalter Ilartky, Highlights of Astronomy (Chicago: The University of Chicago Press, 1935), p. 169.

24

vi

23.5

We disregard the number to the left ofthe decimal point and retain only the deci-mal part, i.e., 0.99. The point correspond-ing to 0.99 on the orbit of Venus in Figure20 represents the position of this planeton February 5, 1934, while the date itselfdetermines the location of the Earth, Itso happens that these two points, alongwith the central point (the Sun), are ina straight line in the order : Sun, Venus,Earth.

Suppose the next date is November 18,1P34. From Table 19 we find for Venus:

S

2

15

op

\10

0

AssociatedNumber

Day of month 18 0.08Month November .94Units in year number___,1 .50Tens in year number____3 .76Hundreds in year

number 19 0.00

Total_ _ _ __2.28

We place Venus on the point corre-sponding to the decimal 0.28 and theEarth on a position corresponding toNovember 18, to discover that these twoplanets are again in a line with the sunbut now the order is Venus, Sun, Earth.

0 5XXIII

XXII.7

.9

15

XXI 20

SXX

XIX

.51XVIII

XVII

XVI

JA

23.5 June

JUPITER 21.

2

15

/ 10

Figure 21

10\0 5 -a_

. Jupiter and Saturn

15

20

Walter Bartky, Highlights of Astronomy (Chicug : The University of Chicago Press, 193. 5 ), p. 170,

25771-1106 0-65 3

23.5

In analogous fashion we find for Mer-cury on March 6, 1934:

AssociatedNumber

Day of month 6 0.06Month March .96Units in year number___4 .61Tens in year number____3 .56Hundreds in year

number 19 0.00

On placing Mercury at 0.19 and theEarth at March 6 in Figure 20, we notethat these two planets are in a line withthe Sun. The conjunction is seen to havebeen inferior, for Mercury lay betweenthe Earth and the Sun. Similarly, Figure20 plus Table 19 informs us that on Janu-

ary 20, 1934, Mercury was at superiorconjunction.

Find Jupiter for May 8, 1917.Orbital motion in Figure 21 of Jupiter

and Saturn is so slight during the courseof a month that we disregard the day ofthe month; and we find for Jupiter:

AssociatedNumber

Month May 0.64Units in year number_ _7 .59Tens in year number____1 .81Hundreds in year

number 19 0.00

Total_ ___2.07

Note above that Jupiter, Sun, and Earthare on a Line in the order named.

Table 19.-Decimals for planetsDay of Month (Gregorian Calendar)

Day ofmonth 1 4 7 10 13 16 19 22 25 28 31

Mercury ___ 0.00 0.03 0.07 0.10 0.14 0.17 0.20 0.23 0.27 0.31 0.34Venus .00 .01 .03 .04 .05 .07 .08 .09 .11 .12 .13Mars 0.00 0.00 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.04

Month

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. 1)ec.

Mercury __ 0.29 0.64 0.96 0.31 0.65 0.00 0.35 0.70 0.06 0.40 0.75 0.09Venus .58 .72 .85 .99 .12 .26 .39 .53 .67 .80 .94 .07Mars .90 .95 .99 .03 .07 .11 .15 .20 .25 .29 .34 .38Jupiter __ _ .61 .62 .62 .63 .64 .65 .65 .66 .66 .67 .68 .68Saturn 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.51 0.51 0.51 0.52 0.52

Year-Units

0 1 2 3 4 5 6 7 8 9

Mercury ___ 0.00 0.15 0.30 0.46 0.61 0.76 0.91 0.06 0.22 0.37Venus .00 .63 .25 .88 .50 .13 .75 .38 .00 .63Mars .00 .53 .06 .59 .13 .66 .19 .72 .25 .78Jupiter .00 .08 .17 .25 .34 .42 .51 .59 .67 .76Saturn 0.00 0.03 0.07 0.10 0.14 0.17 0.20 0.24 0.27 0.31

Walter Ilartky. Highlights of Astronomy (Chicago: University of Chicago Press. 1935). p. 171.

26

Year-Tens

0 1 2 3 4 5 6 7 8 9

Mercury __ 0.00 0.52 0.04 0.56 0.08 0.60 0.12 0.64 0.16 0.68Venus .00 .25 .51 .76 .01 .27 .53 .78 .04 .29Mars .00 .31 .63 .95 .27 .58 .90 .21 .53 .85Jupiter ___ .00 .84 .69 .53 .37 .22 .06 .90 .74 .59Saturn 0.00 0.33 0.68 0.02 0.35 0.70 0.04 0.38 0.72 0.06

Year-Hundreds

14 15. 16 17 18 19 20 21 22 23

Mercury ___ 0.02 0.22 0.41 0.61 0.80 0.00 0.20 0.39 0.59 0.78Venus .29 .82 .36 .91 .45 .00 .55 .09 .64 .18Mars .18 .34 .51 .67 .84 .00 .16 .33 .49 .66Jupiter .85 .28 .71 .14 .57 .00 .43 .86 .29 .72Saturn 0.02 0.42 0.82 0.21 0.61 0.00 0.39 0.79 0.18 0.58

Table 20.-Evening and morning stars

Decimal RightAscention Declination Sun Description

Sun 5145m 17°

Mercury 0.28 7.00 24° Evening StarVenus .56 2 30 13 Morning Star

Mars .20 4 15 12 Morning StarJupiter .52 12 50 -4 Evening StarSaturn 0.66 22 00 -13 Morning Star

THE FUTURENothing is Impossible

Man has not yet built the "time capsule"that will take him into the future. Wemust be content to look into the futurethrough such eyes as those of Copernicus,Newton, and Einstein. These men un-locked the secret of looking into the-futurewith such keys as mathematics andphysics.

The junior high school student of todaywho is keenly interested in the futuremust prepare himself now. History,Biology, Chemistry, Physics, Algebra II,Trigonometry, Advanced Mathematics,

27

English, and French are courses whichrequire much of the student. The studentwho accepts the challenge to work and.study will discover there are no courseswhich are more rewarding..

Scientists are using space probes to lookfar out into space and make observations.To do this, they must answer the questionsof why, when, where, how and who,

1. Why will we send the space probe?2. When should we send the space

probe?3. Where will we send the space probe?4. How will we send the space probe?5. Who will send the space probe?

Problem:Select some future date as the time for

a space probe to a particular member ofthe solar system. Now try to fix the posi-tion of the planet in question at the timeof launching and also its position at timeof interception, using a diagram such asFigure 17. Investigate the laws of Keplerand Newton to determine how muchthrust is needed to achieve the necessaryescape velocities to go and return.

A knowledge of algebra and physicswill assist the student in solving the fol-lowing problem.

Hypot het kw, ProblemA 100 pound spacecraft is to be launched

toward Venus on July 9, 1965, for thepurpose of conducting approximatelyeight experiments.

a. Fix the position of Venus at the timeof launch.

b. How long will it take the spacecraftto get there?

c. Approximately where will Venus beat the time the spacecraft approachesVenus' position?

d. What is the escape velocity requiredto leave Venus and return to Earth?

1 i 11111111111141111i0 .5 1.0 1.5 2.0 2.5

Figure 22. Scale in astronomical units

Sept.

Apr.Mar.

Figure 23. Positions of Earth and Venus

SolutionA. To fix the position of Venus at time of

of launch:Use Figure 20 to locate Venus at time

of launch.Place Earth at the position represent-

ing July 9.Use chart to locate Venus at time of

launch.Aserwriatrd Nuvrther

(approximately)day of month 9 0.04month July 0.39units in year

number 5 0.13tens in year number_ _6 0.53hundreds in year

number 19 0.00

Total_ _ _ _1.09Position Venus at 0.09 on its orbit in

Figure 20.

Draw EV and compare its length to thescale in Figure 15.

E4V = 1.5 A.U.

B. How long will it take the spacecraftto get there?1. Assume the Earth's escape velocity

to be 7 mi/sec. (7 miles per second)2. Since Distance

= velocity X timeDistance = timeVelocity

distance =A.U. 92,900,000 mi

EV

k

= 139,350,000 mi

time = Distancevelocity

time = 139,350,000 mi7 mi/sec

Remember when dividing by fractionsto invert the divisor and multiply.

Equation (6) then becomes

time = 139,350,000 miX

1 sec1 7 mi

time = 19,907,000 sec. (aprox.)

time =

( 1.99 X 107 secX 1 hour

3.6 X 101sectime = 0.555 X 101 hours

= 5.55 X 101 hourstime = 2.31 X 102 days

= 7.7 monthsC. Approximately where will Venus be at

the time the spacecraft nears theplanet?1. Since 7.7 months have lapsed since

the snacecraft was launched, thedate is now March 2, 1965.

AssociatedNumiwr

day of month_ _ _ ..2 0.00month March 0.85units in year

number 5 0.13tens in year

number 6 0.53hundreds in year

number 19 0.00

Total_ _ _ _1.51The new position of Venus is at V, in

figure 23. What conclusions can you drawconcerning the initial problem?

The balance of the problem is left forthe student.

A challenge for the better student :When will be the most favorable time dur-ing the next two years to send a spaceprobe to Mars?

MARS ATLAUNCH

NOV. IS. 1964

40

EARTH AT LAUNCHNOV. IS. 1964

CONCLUSION

AND

PROJECTION

The discussion and study of orbitingbodies have purposely been limited to cir-cular orbits. The circular orbits which svehave discussed have mu eccentricity ofzero, or e = 0.

Further study of Kepler's Laws willreveal the true nature of the orbitingpaths of the planets as they travel aroundthe suu. A study of conic sections willreveal the possible curves or paths asatellite may have. These topics are gen-erally found in high school mathematics,physics, and astronomy courses. Thedifferent paths are described as beingthose of a circle, ellipse, parabola, orhyperbola. Each of these has a pathwhich can be described by an algebraicequation.

The student willing to spend the timeand work will learn of the method used toclassify these different paths or curves.He will learn the meaning of eccentricity.

We have seen old principles become thebasis for nem ideas. Archimedes andGalileo, Einstein and Goddard have givenus the tools with which to write new his-toryYesFrom HERE, WHERE . . .?

LINE Of NOOES (r)

760DAYS

120

\\<,_ PROBEORBIT

160

ZOO ENCOUNTERJULY 14. 1965

PROSE

Figure Z4. TYPical 1984 Mars trajectory

29)30

MA RSORBIT

../1641.016..A.11,1M11101Naligu..1.1114...1

_doe" 'bintm,

I , ,3 1

' k r rq. 1.

_......

, ,.. ,-- - , GODDARD

. '<% f .../ I

, t cs. jj,i

.,,,...

ZIOLKOVSKY N,--...-....,\....., OBERTH 1°)

a

Chapter II

GETTING INTO SPACERobert J. Butterniark

City ChAiraion, High Srhsol Seienrr Prpt$.Alexandria City Public. Sehoolm

Alcratvdria, Virginia

ABOUT THIS CHAPTEROur orbiting spacecraft have enabled us to send the most delicate scientific instruments

into outer space. Linked to the earth-bound scientist via electronic signals, these laboratoriesare providing us daily with new data,. extending our knowledge and horizons.

The advent of the space age was made possible by the development of the rocket engine.It was Dr. Robert H. Goddard, an American, Dr. Hermann Oberth, a German and KonstantinE. Ziolkovsky, a Russian, working independently, who helped to make one of man's oldestdreams come trueand in your life time!

The purpose of this chapter is to answer one common question, "How does a rocket pushitself through outer space?"

You will find it an interesting and challenging subject which will make news about thespace program even more meaningful

30)-

EARLY ROCKETSWe usually consider rockets as products

of the twentieth century. Actually, theinvention of the first rocket is credited tothe Chinese in about the eleventh century.In the year 1232 it is known that rocketswere used during the Mongol siege of theChinese city of Kaifeng. In 1280 anArabian named Hassan Alrammah wrotea manuscript which indicated how to buildrockets. Knowledge of how to make anduse rockets spread rapidly from countryto country. An Italian engineer, Joanesde Fontana, in 1405 wrote a book in whichhe described a rocket car which could be(nod in battle as a battering -rain. In Italyfrom the eighteenth century to the presentday rockets found their rincipaltion as a source of entertaittmeut Thegigantic displays of Italian fireworks havebeen famous throughout tl)e world.

1010

tr- 647Figure 1. Rocketeer

During the latter part of the eighteenthdialitury the British army stationed InThdia was defeated by the Indian rocketcorps. Aftetr this surprising defeat theBritish attempted to build their ownrockets. In this attempt they were suc-cessful due to the efforts of WilliamCongreve. Later Congreve's rockets werecredited with victorious battles againstDenmark, France. and Prussia. "Therockets red glare," seen by Francis ScottKey, author of 'The Star Spangled Ban-ner," during the British attack on FortMcHenry in Baltimore harbor during theWar of 1812 was due to Congreve'srockets. Rockets saw service in the Mexi-can War of 1847, but thereafter artilleryreplaced rockets in warfare due to its great-er accuracy.

After the turn of the century, rocketryhad a

ofrebirth as a result of the

work of three menall working independ-ently, Dr. Robert H. Goddard, an Ameri-can, Dr. Hermann Oberth, a German, andKonstantin E. Ziolkovsky, a Russian.

33

ripare 2.Or. Goddard's first liquid-fuel rocket-19N

In 1903 Ziolkovsky, who was a ochool-teacheZ wrote an article which consideredfor the hWt time the use of rocket propul-sion power to travel to outer space.

In March of 1926 Dr. Goddard launchedthe world's Swat liquid propellant rocketfrom a farm near Auburn, Massachusetts.As a result of this and other early achieve-ments, he is now considered "The Fatherof Modern Rocketry."

As Dr. Goddard worked in the UnitedStates, Dr, tOberth worked independentlyin Germany. In 1937 the German rocketresearch centee in Peenemuende wasestablished. It was in this place that the17-.2 rockets of World War II were built.

Exercise:%%rho are some current scietitiVs in the

field of rocketry? Consult yow latestencyclopedia and yearbooks,

THE ROCKET ENGINEA rocket is a special kind of jet engine.

A jet, which is a fast moving stream of gas,is produced by the burning of the fuel dothe engine. Escaping from the rear, the hatpropels the rocket forward.

The basic difference between the rockeitengine and jet engines is that rocket en-gines carry not only their fuel, but :alsotheir own oxygen or oxidant needed, for

Figure S.

the burning of the fuel. Jet engines mustuse the oxygen found in the air. Thisdifference dearly limits jet engines to alti-tudes where their is an adequate supplyof oxygen. However, rocket engines can goto any altitude, even to outer space wherethere is no oxygen.

To see what one kind of rocket enginelooks like let us look at Figure 4. We cansee that it has a rather simple structure.Basically. a rocket engine consists ofthree major parts, a propellant storagetank, a combustion chamber; and a nozzle.In the combustion chamber the propellants(which include both the fuel and oxidizer)are brought together and allowed to react.As A result of this reaction, heat energyand gas molecules are rapidly releasedthrough the nozzle, propelling the rocketforward. The shape and size of the nozzleare important in a rocket engine becausethey, as well as the propellant, determinethe sp at which the rocket will travel.

The are two general types of rocketengin used today. They are the mono-propellant and the bipropellant rocket en-gines. The monopropellant rocket enginehas only one propellant storage tank. Inthis one tank are kept both the fuel andthe oxidizer which have been carefullypremixed. Figure 4 shows such an engine.The bitiropellant rocket engine has twotanks in which the fuel and oxidizer arestored separately as in Figure 5.

34

PROPELLANTSTORAGETANK

COMBUSTIONCHAMBER

NOZZLE

Figure 4. Monopropettant rocket engine

STORAGETANK

(OXIDIZER)

STORAGE TANK(FUEL)

COMBUSTIONCHAMBER

NOZZLE

Figure 5. Bipropeilant rocket engine

Each type of rocket engine has its ad-vantages and disadvantages. The advan-tage of a monopropellant engine lies in itssimplicity. Its disadvantage lies in thedanger of its operation because the igni-tion of its premixed fuel and oxidizer isdifficult to control.The bipropellant engine is safer to operateand gives a more efficient performanceeven though the fuel and oxidizer must beseparately controlled.

There are two kinds of propellants,solid and liquid. The solid propellants

used in rockets many centuries ago con-sisted chiefly of gunpowder. Today, mostof the large rockets use liquid propellants.Liquid oxidizers include hydrogen per-oxide, nitric acid, and liquid oxygen. Themost common liquid fuels used along withthe liquid oxidizers are alcohol, kerosene,and aniline.

Exercise:In a chemistry textbook find the chem-

ical formulas for aniline, nitric acid,hydrogen peroxide, ethyl alcohol, andmethyl alcohol. What element do all ofthese substances have in common?

Liquid propellants can be used in eithermono- or bipropellant rocket engines.Solid propellants, however, can only beused in monopropellant rockets becausethe fuel and oxidizer must be premixed.

So far you have seen how a rocket en-gine differs from jet engines; you havealso learned about rocket fuels. Let usnow turn our attention to some of themathematics of the way a rocket engine ispropelled, and how the rocket engine'sperformance is measured.

THE MATHEMATICS OFROCKET PROPULSION

The propulsion of a rocket is explainedby Newton's third law of motion whichstates that for every action there is a re-action equal in size and opposite in direc-tion.

Experiment:

Moteria16:

Procedure

Demonstration of Newton'sThird Law of MotionOne pair of roller skatesSeveral bricks or largewooden blocks(a) Put on skates and

stand on level floorwith feet close to-gether holding onebrick or wooden block.

(b) Throw the brick orblock directly forward.

(c) Measure the distancethat you moved notingalso the direction.

35

(d) Repeat steps a, b, andc, but this time throwtwo bricks or blocks insuccession.

(e) Measure the distanceand direction that youmoved this time.

Results: (a) In what direction didyou move after youthrew the objects?

(b) How far did you moveafter you threw onebrick or block?

(c) How far did you moveafter you threw twobricks or blocks insuccession?

Conclusions: (a) The throwing of thebricks or blocks repre-sented the "action"part of Newton's thirdlaw. What was the"reaction"?

(b) How do you accountfor the difference inthe distanee moved inparts (b) and (d) inthe procedure above?

(c) What do you thinkwould happen if youthrew two bricks outat once instead of insuccession? Try it.

Have you ever tried moving rapidlyfrom the back to the front of a small row-boat while it's in the water? If you did,you probably noticed that the boat movedsuddenly in a direction opposite to thedirection in which you were moving. Themovement of the boat was the "reaction"to your movement, which was the "action".This is an example of Newton's third lawof motion. The faster that you move back-ward in the boat, the faster the boat willbe thrust forward in the water. In

Figure 6. Newton's third law

" REACTION "OF

ROCK ET

"ACT t ON "OF

GASES

Figure 7. Simple solid propellant rocket

other words the thrust or "reaction" de-pends in part upon the velocity o speedof the "action."

Does anything else effect the thrust or"reaction"? Yes. The mass of the movingobject also influences the thrust. By themass of an object is meant the heft orbulk of the object, not the weight. Massis a measure of the quantity of the materialpresent. It is independent of weight.Weight is the pull of gravity on mass. Ifthere is no gravity, there is no weight, butthere is mass.

Many people mistakenly believe that arocket is propelled through the air by itsexhaust gases pushing against the outsideair. Nothing could be further from thetruth. If this belief were true, it wouldnot be possible for rockets to travel inouter space, since there is no air againstwhich to push. In fact rockets travel bet-ter where there is no air for there is lessresistance to the rocket's flight.

If the rocket gases do not push againstthe outside air to propel the rocket for-ward. what do they push against? Theysimply push against the rocket and propelit in the opposite direction to which theyare moving. Note the similarity betweenthis situation and that of the rowboctmentioned earlier.

Let us now consider some of the mathe-matics of propulsion of thrust. For calcu-lating the thrust developed in a rocket

36

engine, the following equation could beused :Carl Besserer and Hazel Besserer, Guide to the Space Age (Engle-wood Cliffs, N.J.: PrenticeHall, 1959).

W v ,F k re Pa Aeg

where F -- the thrust in poundsv = the velocity in feet per second

Pe = the pressure of the > ocket gasesat the exit of the nozzle inpounds per square inch

Ae = the area of the exit nozzle insquare inches

Pa = the pressure of the atmospheresurrounding the rocket inpounds per square inch

W = the rate of discharge of the gasor liquid jet in pounds persecond

g = 32.2 feet per second per second(gravitational acceleration).

Using this as a standard thrust equationlet us work a few problems.

Example 1:A rocket gives off exhaust gas at the

rate of 10 lb. per second and at a pressureof 15 lb. per square inch. The gas is mov-ing at a velocity of 1000 feet per second.The area of the exit nozzle is 50 squareinches. What is the thrust of the rocket ifthe pressure of the surrounding atmos-phere is approximately 15 lb. per squareinch?

W vF = + (P. P.) A.g

We know from the problem that the rocketgives off exhaust gas at the rate of 10 lb.per second; therefore, W = 10. The rocketexhaust pressure is given as approximately15 lb. per square inch; therefore, P. = 15.Tt e pressure of the atmosphere is given as

lb. per square inch; therefore, P. = 15.The velocity, v, is given as 1000; g is takenas 32.2; and the area of the exit nozzle, Ais given as 50.

Now by substituting the appropriatevalues in the equation we have:

(10) (1000)F + (15 15) (50)

32.210,000

F + 0*32.2

F = 310.55 lb. thrust

Example 2:A water sprinkler discharges water at

the rate of 1 lb. per second. The velocityof the water as :t leaves the sprinkler is32.2 feet per second. What is the thrustof the sprinkler assuming that the exitpressure of the water is approximately thesame as the pressure of the surroundingatmosphere?

Here again by substituting in the thrustequation we get

(1) (32.2)F + 0*

32.2F = 1 lb. thrust

*Note: This term totals 0 in these prob-lems because P. = Pe; therefore,P.. -- P. = 0. For example, if P.15 and P. = 15, then by substitu-tion 15 15 = 0.

Exercises:A-1. A rocket gives off exhaust gas at the

rate of 100 lb. per second and at apressure of 25 lb. per square inch.The gas is traveling at a velocity of7500 feet per second. The pressureof the surrounding atmosphere is 15lb. per square inch, and the area ofthe exit nozzle is 50 square inches.What will be the thrust of therocket?

37

A -2. Repeat the above exercise but thistime take the pressure in the upperatmosphere to be 1.5 lb. per squareinch. What will be the thrust of therocket now?

A-3. A garden hose discharges water atthe rate of 2 lb. per second. Thevelocity of the water as it leaves thenozzle of the hose /3 60 feet per sec-ond. What is the thrust of the gar-den hose if the exit pressure of thewater- is approximately the same asthe pressure of the atmosphere?

AI. Look up Sir Issac Newton in somereference books. What other contri-butions to science did he make be-sides his laws of motion?

DETERMINING HOW WELL AROCKET ENGINE PERFORMSMathematics is used also in finding out

how well a rocket engine is performing.With regard to the performance of arocket there are several yardsticks forsuch measurement. One is horsepower; an-other is specific impulse; still another ismass ratio.Horsepower

Horsepower is defined as a rate of doingwork equal to 550 foot-pounds per second.Another way of expressing this is that onehorseplwer is equal to the amount ofwork done in one second by moving 550pounds one foot or, conversely, the amountof work done in one second by moving onepound 550 feet. hi space vehicles we canuse miles per hour which is a larger unitthan feet per second. Using this unit wecan redefinvl horsepower as the amount ofwork done in one hour by moving 375pounds one mile, or conversely, by movingone pound 375 miles in one hour. Can youfigure out how we got 375 mile-pounds perhour from 550 foot-pounds per second?Try figuring it out.

Hint:ft. lb.

Xsec.

Xmiles mile-lb.

sec. hour feet hourMathematically, a formula for horse-

power can be writtenThrust (in lb.) X

Speed of Rocket (in m.p.h.)H. P.375

By substituting in this formula it can beseen that if a rocket travels at 375 milesper hour, the horsepower will be equal tothe thrust of the engine.

Thrust x 37511.P.

375H Thrust

What will be the horsepower when therocket is traveling at 750 miles per hour?Substituting again in the formula we get

Thrust X 750H .P.

375H .P. 2 x Thrust

Here, the horsepower is equal to two timesthe thrust. Thus, it can be readily seenthat the horsepower of a rocket enginechanges with the speed at which it istraveling. Conseqrently, horsepower is nota realist& way of measuring a rocket'sperformance. It can only give us a way todescribe it. See Chapter III page 10.

Exercises:11-1. What would be the horsepower of a

rocket engine having a thrust of5000 lb. when it is traveling at aspeed of 750 miles per hour?

11-2. What would be the thrust of a rocketengine while traveling at a speedof 375 miles per hour and developing3000 horsepower?

B-3. A rocket is traveling at the rate of1500 miles per hour, At this speedit is giving off exhaust gas at therate of 150 pounds per second at anexhaust pressure of 15 lb. per squareinch. The gas is traveling at a veloc-ity of 10,000 feet per second. Thesurrounding atmosphere is 10 lb. persquare inch. The area of the exitnozzle is 50 square inches. Whathorsepower is the rocket engine de-veloping? (HINT: Use standardthrust equation first.)

Specific impulseAnother method of measuring rocket

performance is by determining the specificimpulse which is defined as the amouni ofpropellant that has to be burned per secondin order to maintain a thrust of a givenamount. More specifically the specific im-

38

pulse is defined as the thrust a rocket willproduce when the gas is coming out of theexit nozzle at the rate of (e lb. per sec-ond. Mathematically stated

P Wwhere ,,- specific impulse, in seconds

F -- thrust of rocket, in poundsW weight of propellant used per

second

Example .1:What would be the specific impulse of a

rocket engine which has a thrust of 10,000pounds and uses its propellant at the rateof 50 pounds per second?

By substitution in the above formula weget

10,000iry

50:= 200 seconds

Normally, the higher the specific impulsethe more efficient is the rocket engine. Thechemical rocket engines used today havespecific impulses much more efficient, W:ththe advent of newer- propulsion systemshigher specific impulses can be expected.

Fzercises:C-I. What would be the specific impulse

of a rocket engine like the Deltawhich has a thrust of 170,000 lb. anduses its propellant at the rate of 850lb. per second.

C-2. The specific impulse of an engine is275 seconds, and the engine has athrust of 27,500 lb. What would bethe rate at which the propellant willbe used?

C-3. A rocket engine develops 2000 horse-power at 750 miles per hour while-using 4 lb, of propellant per second.What specific impulse does the rocketengine have?(HINT: Combine the horsepower

formula and the specificimpulse formula to elimi-nate the thrust factor.)

Mais MHOStill another method of measuring

rocket performance is by determining- themass ratio. The mass ratio is defined asthe ratio of the total mass of .the rocket attake-off to the mass of the empty rocket atburnout. Mathematically stated

RMM,.

where R Mass ratioAf mass of propellant, in poundsM,. mass of empty rocket, in pounds

It can be seen from this formula thatsince the total mass of the:rocket at take-off consists of the mass of the empty rocketplus the mass of the propellant, thenumerator of the fraction in the formulafor H is larger than the denominator. Rwill, therefore, always be greater than 1.Designers of rockets try to build rocketswhich have mass ratios on the order ofabout 6 to 15.

How do scientists design a rocket havinga high mass ratio? Let us again look atthe formula above. Suppose a rocket isbuilt which when empty weighs 200 lb. andcan carry 800 lb. of propellant at take-off.What would be its mass ratio? By sub-stitution in the formula we find that

800 -1' 200 1000R

200 200R -5

Here then the mass ratio is 5. Supposenow that the scientist is able to build arok-7:et which will weigh only 100 lb. andstill be able to carry 800 lb. of propellant attake-off. What will be the mass ratio ofthis rocket? Again by substitution in theformula we get

800 -1- 100 900R

100 100R -9

Now the mass ratio is 9. Hence, it can beseen that if the rocket can be made lighterbut still able to carry the same mass orpropellant (in this case 800 lb.), the massratio can be increased. Of course there arepractical limits to this rule. A rocket mustbe able to support its own weight as wellas the weight of its propellant during take-off and during its burning period. Scien-tists are today at work trying to find bettermaterials that are able to withstand thetremendous stresses encountered in highspeed rocket travel.

39

Exercises:D-1. A rocket when empty of propellant

weighs 500 11). It carries 1000 lb. ofpropellant at take-off. What is themass ratio?

-1)-2. A rocket has a mass ratio of 10. Theempty rocket weighs -100 lb. Howmuch propellant does it carry attake-off?

D-3. A rocket has a mass ratio of 5. Itcarries 1000 lb. of propellant at take-off. What is the weight of the emptyrocket?

ROCKETRY IN THE FUTUREAt the present time the most common

type of rocket engine is the chemical one.However, scientists are busy developingother types. One concept which looks quitepromising- is the nuclear rocket engine.(see figure 8). In this engine liquid hydro-gen is pumped through the nuclear reactor.As a result of the high temperature inthe reactor, the liquid hydrogen is changedto a gas. This gas is then passed outthrough the rocket nozzle where it pro-vides.the thrust to propel the rocket.

The ion rocket engine is another typeundergoing study. (See Figure 9.) It ispropelled by it jet of ions. (Ions are atomswhich have either a positive or negativeelectrical charge on them.) The ions in theengine would be produced by passing apropellant, such as the element cesium or

PROPELLANT TANKCONTAINING LIQUID

HYDROGEN

NUCLEAR REACTOR

NOZZLE

GASEOUS HYDROGEN

Figure 8. Nuclear rocket engine

rubidium, through an ionizing device, suchas a heated grid. The ions would then beaccelerated to very high speeds by an elec-tric field after which they would be ex-pelled from the rocket, giving the rocketits thrust.

Still another type is the plasma rocketengine. Plasma is a gas which will conductan electric current. This gas is made upof neutral particles, free electrons, par-ticles with positive electric charges, andparticles with negative electric charges.(NOTE: Do not confuse this plasma withblood plasma. They are entirely different.)In this type of engine a powerful electricarc is passed through a gaseous propellant,forming the plasma, which then passesthrough the rocket nozzle. The plasma en-

gine is caPable of very' high specific im-pulses. Even so it presents a problem tothe scientist because it requires a greatdeal of electrical energy to operate it.

An interesting a»d. as yet, a speculativekind of rocket engine is the photon engine.In this engine photons, or light particles.would provide the thrust. \Vhile such en-gines would be capable of very high spe-cific impulses, they would require theradiation of intense beams. of light. Howthis amount of radiation could be obtainedis not now known. This will be another ofmany challenges for present and futurescientists. How well our scientists areable to meet these challenges will deter-mine our future in space.

HEATEDGRID

NEUTRALIZINGGRID

LARGEVOLTAGE

DIFFERENCE

ACCELERATINGGRID

Figure 9. Simplified ion rocket engine

40

HIGHSPEEDIONS

Chapter III

SPACE AND WEATHERPaul H. Keller

Earth Stiettee TeacherWalter Johnson High School

Bethesda, Maryland

ABOUT THIS CHAPTERMathematics is a vital tool of science. Often we do not realize the need to study pure

mathematics. In many eases, however, its application proves to be very interesting. When wesee how necessary mathematics is to space-science, we begin to realize that without it theexploration of space would be impossible. The activities suggested in this booklet will help youto understand this relationship and to bring space-science into your mathematics classroom.

The distance to the Sun is 93,000,000 miles. Light travels at a speed of 186,000 miles asecond. This is 60 X 60 X 186,000 miles an hour. In today's science these are relatively smallnumbers. In computing we cannot manipulate the numerals which describe the measure ofspace with ease. Therefore we have devised a shorter way of expressing very long numerals.It is called scientific notation.

771-806 0-65-44)4

SCIENTIFIC NOTATION

We often refer to these verb- large andvery small numbers as macro and micromeasurements. This is an area in whichit may seem that you are reading a for-eign language and you may not have anyreally good idea of the size (largeness orsmallness) of the numbers. For this rea-son we must understand scientific nota-tion.

Scieniqic NotationIn scientific notation large and small

numbers are written as the product of anumber from I up to 10 and a power of10. (3000 = 3 X

First we must detne some terminology.,bet us use as an example 5x 5 = 52. Inthis expression 5 is called the base andthe small numeral 2 written to the upperright side of the base is called the ex-ponent. The- exponent tells how manytimes the base is used as a factor and isexpressed as the power of the base. Wesee that

7' means 7 is a factor 3 times or7' means 7 X 7 X 7, Thus

10' means 10x 10 X 10 x 10 X 10 and10' is read "10 to the fifth power."We expreSS 10 as 10%

Problems:(MI the problems are numbered.within

the text of the booklet. You may checkyour answers with those given in theback.)

Read each of the following and tellwhat each means;(1) 102 is read " " and means(2)(3) 10` is read " " and means(4)(5) '1Vhat is the value of 102?(6) What is the value of 10'?

A more mechanical way of thinkingabout scientific notation is that the ex-ponent indicates the position of the deci-mal point. If the exponent is positive, itmeans that the number is greater thanone and that the decimal point must be

43

moved that number of places to the rightto give the meaning. In the example 3 x10' the decimal place has been moved 3places to the right 3000. giving 3000.The number 2.15 X 10' would represent2.15 x 100,000,000. Moving the decimalpoint 8 places to the right, we have2.15000000.0 giving 215,000,000.0 Belowate mot* examples;

102 = 10X 10 or 100;10' 10 x 10 x 10 or 1000

2 x 10" 2 x 10 x 10 x 10 x 10 x10 x 10 or 2 x 1,100,000 or 2.000,000.

Probk ins:(7) What does 8 x 10' mean?

Write the numeral indicated by:(8) 6 X 10' =(9) 5 X 10'(10) L5 x 10" =(It) 2.5 X 10s =

Write the following numbers in scien-tific notation:(12) 5,000 =(13) 61/2 million =(14) 30,000 =(15) 5,500 =

If the number is less than one the ex-ponent will be negative. (.1) is written

10-1; (.01) 10-2;10 x 10 10 x 10 x

10 x 10(.0001) as 10-' and so on. When

the exponent is negative it indicates thatthe decimal point must be moved to theleft that number of places. For example

1.10 10

2.1100

5 X (2.15 x ) would bexwritten its 0.0215 (0.02.15) In the samemanner 2.54 X 10-" would indicate0.000002.54 (.00000254) In a like manner0.000000008.02 is written 8.02 X 10'.(Remember to count the number of placesto the right or left of the decimal point,not just the zeros.)

For practice with small numbers, com-plete the following expressions:(16) 0.00001 = i x 10 ?

(17) 0.00065 = ? x 10 ? (31) 9,000,000,000.000,000,000 =(18) 6.15 x 10 s = (incidentaly, this is(19) 5.06 x 10-s = approximately the number(20) 3.45 X 10-6 = of miles to the galaxy(21) 0.000001 = ?. x 10 ? Andromeda, 9 quintillion miles)

For an overall review, complete the fol- (32) 7 x 107 =lowing: (33) 8 x 10-s =(22) 30,000 = (34) 3.546 X 10 I§ =(23) 700 = (35) 1 = ? x 10?(24) 900,000 = (36) 93 million =(25) 40 = (37) 1 /10 million = one ten millionth(26) 10-s = ? x 10 ?(27) 10" =(28) 10s =(29) 10-s = Now you should have enough basics to(30) 2.541 x 10-5 = understand and enjoy this booklet. As you

Table 1.Conversion FactorsTo change the units in column I to the units in column 2, multiply by the conversionfactor in column 3. These are approxmate values.

MetricFrom

to EnglishTo Factor

EnglishFrom

to MetricTo Factor

1 2 3 1 2 3Millimeters Inches .03937 Inches Millimeters 25.4

(mm.) (in.) (in.) (mm.)Millimeters Centimeters 1/10 Centimeters Millimeters 10

(mm.) (cm.) (cm.) (mm.)Centimeters Inches (in.) .39 Inches Centimeters 2.54

(cm.) (in.) (cm.)Meters (m.) Kilometers 1/1000 Kilometers Meters ( m.) 1000

(km.) (km.)Meters (m.) Inches (in.) 39.37 Inches (in.) Meters (m.) 1/39.37Meters (m.) Feet (ft.) 3.28 Feet (ft.) Meters (m.) 1/3,28Kile'neters English statute 0.62 English statute Kilometer 1.61

(km.) miles (mi.) miles (mi.) (km.)Nautical miles Kilometers 1.853 Kilometers Nautical miles 1/1.853

(km.) (km.)Nautical miles Statute miles 1.15 Statute miles Nautical miles 1/1.15Cubic inches Cubic feet 1/1728 Cubic feet Cubic inches 1728Ounces (oz.) Grams (gm.) 28.35 Grams (gm.) Ounces (oz.) 1/28.35Kilograms Grams (gm.) 1000 Grams (gm.) Kilograms 1/1000

(kg.) (kg.)Kilograms Pounds (lbs.) 2,205 Pounds (lb.) Kilograms 1/2.205

(kg.) (kg.)Kilograms Liters of 1 Liters of Kilograms

(kg.) 1120 H2O (kg.)Liters (1.) Cubic

centimeters1000 Cubic

centimetersLiters (1.) 1/1000

(cc) Cubic inches Liters (1.) 1/61Liters (1.) Cubic inches 61 (cu. (in.)

(cu. in.) Quarts (qt.) Liters (1.) .95Liters (1.) Quarts (qt.) 1.05

(In computing we usually omit the periods on the abbreviations)

44

read it, you will find many conversions. in-cluding these. Work each one out to fullyunderstand and to feel the full impact ofthe sizes of the numbers given here.

CONVERSION FACTORSWhen you read scientific papers, you

find that the language of scientists differ-ent from that used by most of us in oureveryday work. For instance, scientistsuse metric measures such as kilometers(km), millimeters (mm), centimeters(cm), nautical miles, and kilograms (kg)instead of the English units; miles, Lches(in), statute miles, and pounds (lb.). Youwill also find that temperatures. pres-sures, and other properties are expressedin units not familiar to most of us. Asyou continue in school and, in life, you willfind that these terms keep appearing. Ifyou learn to convert from one system toanother, you will find that lectures andpapers will mean more to you. When tak-ing science courses, such as physics andchemistry, you will find that you need, notonly new science and mathematics, I_Autalso a new language.

For these reason: a table of conversionfactors has been included for your use.In reading this chapter, you, as a student,

tit

LatINDINGROCKET

SAS. ALTITUDELESS THANEARTH RADIUS

should use this table to convert oil un-familiar units to units with which you arefamiliar so that you will have the properperspective of the concepts and be able tounderstand them. You probably will haveoccasional questions. You should answerthese questions as you come to them.Check your answers with those given inthe back to make sure you understandwhat is being explained in the chapter.

GENERAL METHODS OFSTUDYING THE UPPER

ATMOSPHEREThere are three related ways to obtain

data for use in studying the upper atmos-phere and space as shown in Figure 1 onthis page: sounding rockets, satellites, andprobes. For our application of mathematicswe will consider the first two only.

SOUNDING ROCKETSMeteorologists have known that atmos-

pheric gases greatly influence the weatheron Earth, but for many years they haveknown very little about the atmospheresurrounding the Earth. Only after thedevelopment of rockets and satellites has

EARTHSATELLITE

NEVER ESCAPESEARTH'S GRAVITYFIELD

SPACEPROBE

ESCAPES EARTH'SGRAVITY FIELD AND ORBITSSUN OR OTHER BODY

Figure 1. Some ways 'to obtairi data

45

more defivite information about the at-mosphere become available.- An importanttool for obtaining weather data until thelaunching of weather satellites was thesounding rocket which is designed to ex-plore the atmosphere within 1,000 milesof the Earth's surface. Most of the rocketprobes have been in the 20 to 200 mileregion. Multiple staging has enabledrockets to go up to 1,000 miles. Withsounding rockets, experiments can beplaced in space for a few minutes in anearly vertical flight profile. The main ad-vantage of sounding rockets is their econ-omy, simplicity, and reliability; but theirmeasurements are limited to specificregions and times.

After World War II several capturedGerman V-2 rockets were used to reachaltitudes up to about 120 to *410 kilometers.This is about how many miles? (38) (Thisis problem 38.)

Around 19.19 after the captured V-2rockets were expended. a large number ofAerohee rockets came into use. Theserockets produced, valuable data on atmos-pheric pressure, temperature, and densityup to altitudes of 100 kilometers (km.).How many miles in altitude is this?(39)

A larger rocket named the Viking,similar in size and other respects to theV-2 rockets, but capable of carrying heavypayloads to higher altitudes, was also de-veloped especially for sounding purposes.The Viking could reach an alitude ofnearly 300 kilometers (km.). What is thisaltitude in miles?(40) With data fromthese launchings, several "model atmos-pheres" were set up by various scientists,Much of (he infognation in figure 2 camefrom sounding et data. In general,before rockets wektelsed, meterologistshad to infer the physical properties of theupper atmosphere from ground observa,Lions and balloons which rose to 30 kilo-meters (km.). Rocked gave direct evi-dence of conditions in ,the upper atmosephere and the layers ohthe atmosphere.

ATMOSPHERICMEASUREMENTS BY ROCKETS

Pressure measurements are made by at-taching pressure gauges to certain areas

46'

of the rockets known as ambient zones.These are areas on which the pressure re-mains equal to the atmospheric pressurein spite of the movement of the rocket.

Density of the atmosphere may be meas-ured in two ways. One way is to measurethe pressure on the nose of the rocket whichdepends on the speed of the rocket and onthe density of the air. Since the pressureon the nose and the speed is known, thedensity of the air can be calculated. Thesecond way is by calculating the drag ofthe atmosphere on a free-falling sphere.This method uses spheres several feet indiameter. A radar beacon attachment isejected from a rocket at some point in itsflight path or trajectory. The sphere is thentracked as it descends and the amount ofdrag calculated from its rate of descent.

Temperature measurements are difficultto make at high altitudes because of thelow density. The best way to make thesemeasurements is by using the local speedof sound. The epeed of sound is propor-tional to the square root of the absolutetemperature. Thus, if the speed of soundis known, the temperature can be cal-culated.

The local sound speed can be foundfrom the pressure distribution on the nosecone of a rocket or it ean be determinedby ejecting luminescent explosives from arocket at different intervals of altitude.By noting the time of the flash and thetime it takes for the sound to reach thelocation, the speed of sound is determined.

High altitude winds can be measuredby tracking a cloud of glowing sodiumvapor released by a rocket at a prescribedaltitude. Most of the atmospheric meas-urements that are used for our more -up-to-date atmospheric structure models havecome from sounding rocket data.

ATMOSPHERIC STRUCTUREIt is difficult to show the atmospheric

structure in any single picture becausegreat variations occur depending on lati-tude, altitude, time-of-day, and solaractivity. Variations in the upper atmos-phere are greater than in the lower at-mosphere. The density (number of gasmolecules per unit of volume) of the at-

KILOMETER

250

150

100

S4

AEROBES +1

NIKE APACHE

NIKE CAJUN

tTYPICAL ROCKETS/OPTIMIZED co*

SPECIFICOBJECTIVES)

TYPICALEXPERIMENTS

allyNEU#RAL

ATMOSPHERE

10 TN

ATMOSPHERE

PRESSURE

CONTROLLED SW

GRAVITY t SW

SOLAR 'HEATING

to-*MANDL;

(NOCTILUCENT

CLOLIOS)

'GAUGESG=OES

SOINUTTCLOUIPS

YAWNS SPHERES

MINIMUM SATELLITE ALTITUDC

6°1-66. tn/ 6 1-, IONOSPHEREX MAT FLUX

WAVELENGTH 1

$ ,ANGSTROMS)

1 0 1000 ?owl1'

1

1 ,

1

I *AY tOZONE

VERTICALMOTION:

OW We

:I Mk TI

V ION COMPMAK TON IP*ODUCT

!

SPORADIC 011

VALLEY

124.trENT s.tu2s.

1

Assoltpriert 1

looeir tourcut I

L .21.tes.AL2

MAXIMUM BALLOON ALTITUDE

RADIOTE0414...ILVES

TION

PHOTOGRAPHICSPECTRA

scAIPHOTOMETERS

Ntalli=4 0 TRY

iWTEMPERATURE

acostrosmoN

T *ODD' A

ATOMIC OXYGEN

I-

TRANSITION

REGION

-

MOLECULAR

OXYGEN

NITROGEN

,01,046

NEUTRALSPECTROMETRY

GRENADES

SODIUM CLOUDS

ROHM °AWLS

FIELD ANDPARTICLE

PHENOMENA

40/40SPNERIC

Stanfill

ARCTIC

EQUATORIAL

ANOMALIES

AURORAS7

1

1

1

1

1

I COSMIC RAW

SOGIYEAS1

L--- - -

METEORS

NIGHT GLOW

I1

1

1

1

PARTICLECOUNTERS

NARROW :umTUill DETECTORS

MILES

Figure t. Bask research requiring low attitude sounding rockets

mosphere decreases as the distance fromthe Earth increases; except for ozone,which reaches its maximum at 20 to 30miles because of the ultraviolet action ofthe sun's rays. This variation is known asan inverse proportion or inverse varia-tion, meaning that as one vskte increases.the other decreases. &Toad .t00 miles,the major constituents or the atmosphereof space consist of atotri",c L'acygen, ofatomic helium (He) at about 700 miles,and of atmdic hydrogen at 2000 miles avidbeyond.

Problems:The Earth's atmosphere on the average

exerts a pressure of 760 millimeters ofmercury (760 mm of Hg) at sea level.What would this pressure be in inches ofthercury?(41)This pressure is known as a

47

150

100

standard atmosphere (atm). Pressure de-creases roughly by a factor of 10 for each10-mile increase in altitude up to 60 miles.How would this altitude be shown in Figure37(42)At 100 miles the pressure is abouthow much in atinospheres?(43)1How'wouldthis be expressed in millimeters (mm.) andinches (in.)?(44) These figures chow thatall but one-one billionth of the Earth's at-mospheres lies below 100 miles, The pres-sure for the next 100 miles agallin changesby a factor of 10. At 500 miles, ill is about10-6 millimeters of mercury (num Hg) ; at1,000 miles about 10-'6 (mm Bg). Howwould these pressures be written in inches(in.) ?(45)The pressure la solar space isestimated to be betvitteii 0.000000000001and 0.00000000000001 mm. Hg. How wouldthis be written in scientific notation? (46 & .47).

400

200

100

0

Pressure

10-12 Atm

1011 Atm

3 x 1011 Atm

2 x 10-10 Atm

104 Atm

OZONOSPHERESTRATOSPHERETROPOSPHERE

lid! 1,1

AURORAE

NOCTILUCENT CLOUDS

METEORSNACREOUS CLOUDS

SATELLITE

VIKING

AEROBEE

V.2

(t() TEMPERATURE 100 500

Figure 3.

As mentioned earlier, most of the moremodern data on the atmospheric structureconies from sounding rockets. The prop-erties of the atmosphere had been meas-ured very accurately up to altitudes of 100kilometers (km.) and less accurately from100 to 200 kilometers (km.). Above thispoint, all information was based on extrap-olations or educated guesses based on datafrom the lower altitudes, and assumingthat the trends continue into the upperatmosphere.

Problems:Referring to figure 3, answer the fol-

lowing questions:(48) How many miles would 100 kilo-

meters (km.) be?(49) How many miles would 150 kilo-

meters (km.) be?(50) How many miles would 240 kilo-

meters (km.) be?(51) How many miles would 300 kilo-

meters (km,) be?(52) How many miles would 600 kilo-

meters (km.) be?

48

1000

(53) What is the atmospheric pressure at100 km? In atmospheres? in milli-meters ?

(54) How many inches of mercury wouldbe shown on a barometer at 100 kilo-meters (km.) ?

(55) Write out the pressure. at 500 kilo-meters (km.) in atinoispheres with-out using scientific nOtation.

(56) Write out the pressure at 200 kilo-meters (km.) as IA %you'd be withoutscientific notatiotn,

As you may. Wave noticed by now, thetemperature some at the bottom of thediagram or grotph of the conditions of theatmosphere divided into °K. K standsfor Kelvin ryr absolute temperature. Youprobably have heard that as the tempera-ture is lowered, a gas decreases in volumeand pressure. Theoretically, the tempera-ture -might reach a point where the gaswould have essentially disappeared with novolume and no pressure, This temperatureis known as absolute zero or zero degreesKelvin for one of the originators of tlw

idea. So degrees Kelvin ( °K) is absolutetemperature.

Now, if you are not thoroughly confusedalready, remember that we have two othertemperature scales as well (centigrade orCelsius, cC and Fahrenheit, °F). This cre-ates a slight problem in conversion withwhich you will become familiar. There isno difference in the size of a degree on theCelsius and absolute scales. This meansthat there are the same number of degrees,for instance, between the freezing pointand the boiling point of water on bothscales. 273° on the absolute scale is equalto 00 on the Celsius scale, so to convertfrom °K to °C, simply subtract 273°. To

.convert °C to ° It, add 273°.However, there is a difference in the size

of a degree between the Celsius scale andthe Fahrenheit scale, To be more exact, 5°on the Celsius scale is equal to 9° on theFahrenheit scale, This ratio accounts forthe older formulae for conversion of tem-peratures. However, recently someone no-ticed that the Fahrenheit and Celsiusscales are the same at 40 degrees andderived two new and simpler formulae.With a little study on your part, you, too,should be able to understand how theseformulae were formulated.

These formulas are as follows:(F° + 40°)C = 40°

1,8F = [(C° + 40°) 1.8] 40°

Remember, begin work by performing theoperation indicated inside the parenthesisand finish by subtracting 90. If the prob-lem is not worked in the proper order, thecorrect answers cannot be obtained. Studythe examples below:Change 32°F to Celsius

(F° + 40°)C= 40°

1.8(32° + 40°)C 40° =-- 40°=

1.8 1.8C= 0° 40°-40°=0°Working the opposite way, change 0°C toFahrenheit temperature.

F = [(C° + 400) 1.8] 40°F = [ (0° + 40°) L8] 40°

F = [ (40°) 1.8] 40°F = 72°,0 40°F = 32°

49

Problems:Now, using these formulae and proce-

dures, answer the following questions fromfigure 3.(57) What is the temperature at 25 km. in

Celsius degrees?(58) What is this temperature in Fahrenk

belt degrees?(59) What is the temperature at 50 km.

on the Celsius scale?(60) What is the reading on the Fahren-

heit scale?(61) What is the temperature at 100 km.

on the Celsius scale?(62) What is the reading on the Fahren-

heit scale?(63) What is the temperature in °C at 200

km?What is the tempeiteure in °F?What is the temperature in cc at 500km?

(66) What is the temperature in °F?

(64)(65)

Because much order space information isbased on extrapoilation, one of the firstjobs assigned to the satellites was to meas-ure the properties of the upper atmos-phere. It was assumed that the satellite in-formation would follow the extrapolatedinformation fairly closely. However, theactual data ,Melded many unexpected dis-coveries, such as great variation in thedensity of tehe upper atmosphere, some ofwhich thane from day to day and are con-nected with the activity of the sun.

Because of the findings of the early sat-ellites, other satellites have been planned tofurther increase our knowledge of the at-mospheric structures. One of these, theAtmospheric Structures Satellites, weredeveloped to measure density, composition,neutral particle temperature, and electrontemperatures of the atmosphere out to 400nautical frniles. How many statute mileswould this be?(67)

It is thought that these variations andconditions farther out influence our weath-er conditions on earth.

Another type of satellite used in abr.'s-Pheric ;studies is the TIROS- (Television

EARTH ASPECT SENSORGAUGE

c?jSUN-MOONASPECT SENSOR

MASSSPECTROM [TER

RI ANTENNA

oct ELECTRON TEMPERATURE PROBEFigure 4. Atmospheric structures satellite

Infra-Red Observation Satellite) series.Infra-red equipment is used to provide in-formation oo,- how the sun's energy is ab-sorbed and reflected by the Earth's atmos-phere. TIROS also has another importantmission, which is of immediate trethatof observing the cloud cover and the move-ment of storms, Information from TIROSis used immediately by the United StatesWeather Bureau for weather analyses. In-formation now being obtained by TIROSaids greatly in weather forecastingthroughout the world.

Although TIROS is usually shown asbeing shaped like a bass drum, it is actu-ally a regular polygon with 18 sides. Inregular polygon all the sides are equal inlength, and all the angles are equal. If youwould like to see this strangley shaped sat-ellite, try drawing it yourself. The proce-dure is very simple. The only equipmentneeded are a pencil, a compass, a ruler, anda protractor. The diameter of TIROS is42 inches from the center of one fiat side tothe center of the opposite flat side. A goodscale for this project would be 1:8. Thisratio indicates that one unit on the. paperrepresents 8 actual units. How manyinches in your drawing represent the 42inch diameter of the satellite?(68) What isthe length of the radius of the satellite onthis scale?(69)

50

CONSTRUCTION OF THEBASE OF TIROS

1. Using this length, set the points of thecompass on the radius.Draw a circle lightly as shown in figure5 slightly larger than the diameter ofthe TIROS satellite using the scale of1 :8.

3. Divide the circle into 18 equal angles.How large would each angle be?(70)(see figure 5).

4. Using the center of the circle as thecenter, draw an arc (CD) in each ofthe angles.

5. With C as a center and any radius,draw an arc as the arc at E.

6. Then \ rith D as a center and with thesame radius, draw another arc inter-secting the first one at E.

7. Draw the bisector of the angle fromthe center of the circle through E, thescale length of the radius of TIROS.

8. Draw a line perpendicular to the bi-sector forming the base of the triangleand one of the eighteen sides of thebase of TIROS.

9. Use this procedure on each of the tri-angles and you will have a scale draw-ing of the base plate of TIROS.

Figure 5.

Problems:As you can see from the scale drawing of

TIROS, it is nearly circular in cross-section. Because it is so nearly circular,the volume of TIROS can be approxi-mated by using the formula for the volumeof a cylinder. Volume = 77-1.11 where r =radius, h = height and approximate 7r =3.14. The diameter of TIROS is 42 inchesand the height of TIROS V 3s 19 inches.What is the approximate volume of theTIROS weather satellite in cubic inches(cu. in.) ?(71)I f you computed the volume,you found that it is a little more than26,300 cubic inches (Cu. in.). If you checkinto a set of reference tables, you will findthat there are 1,728 cubic inches (cu. in.)in one cubic foot (cu. ft.) . Divide yourprevious answer in cubic inches (cu. in.)by 1,728, to get the volume in cubic foot(cu. ft.).

How many cubic feet (cu. ft.) of spaceare there in TIROS V?(72)TIROS VIII isagain 42 inches in diameter, but is 221/2inches high, instead of 19 inches high.What is the volume of TIROS VIII incubic feet (cu. ft.) ?(73)

For a more exact measurement you can,if you wish, use trigonometry and comecloser to the volume measurements usedby NASA. Remember that inside this 18sided polygon, there can be constructed 18congruent isosceles triangles using each

flat side as a base. Each isosceles triangleis bisected by a perpendicular (the radius)from the center of the polygon to the cen-ter of the base forming two right tri-angles. Remember that the angle at theapex of each isosceles triangle will beequal to 1, ,,t:11 of 360'. By using the tan-gent of 1/2 this angle (opp./adj.) and theprevious given information, the length tf1/2 the base of the isosceles triangle can bedetermined. Once you have the base, usethe formula f,:)r the area of the triangle

= bit) and figure the area of each

isosceles triangle. Multiply this area by18 to get the area of the base plate ofTIROS satellites. Now multiply this areaby the height of the satellite to get thevolume of a TIROS satellite.(74)

THE TIROS PACKAGEThe electronics package of a TIROS sat-

ellite is composed chiefly of the followingequipment: FM television transmitters,power supply and regulator, beacon trans-mitters, horizon sensor and associated cir-cuitry, command receivers, clock andcontrol circuitry, telemetry sensors, northindicator and associated circuitry, infra-.red sensors and package (amplifiers, FMsub-carrier oscillators, tape recorders, andFM transmitters) , two TV cameras, taperecorders, and magnetic attitude controlcircuitry. TIROS VIII had all of theseitems, as well as additional equipment forautomatic picture transmission (APT)which made it possible for ground stationsthroughout the world to receive weatherdata as the satellite orbited overhead.

51

C

Figure 6. Photograph of TIROS base plate

Many of the components are mountedon the base plate of the satellite. Becauseso much has to be included in a relatively'small space, all of the equipment must beminiaturized or made smaller to take upless space. To give an idea as what ismeant here, a section of a computer ap-proximately six to eight inches long, threeto four inches wide, and at least one andone-half inches thick has been reduced tothe size os a shirt button and does thesame job. A television camera for TIROSmay be a tube one inch in diameter andfour to six inches long.

LAUNCHING OF SATELLITESSo far, we have discussed the size and

shape of the TIROS satellites and verybriefly two of their uses. Before anythingmore can be said about the orbits and theobservations of the TIROS series, we haveto get TIROS off the ground and into orbitaround the Earth.

TIROS has been launched by the Deltabooster or launch vehicle which is approxi-mately 90 feet (ft.) high (actually 88 feetwithout the spacecraft) and 8.1 feet (ft.)in diameter with a weight of 57 tons. Itwas originally intended to be used tolaunch medium payload satellites andspace probes until newer vehicles couldbecome operational. However, the Deltahas been so successful that it has provento be one of the most reliable launch ve-hicle; possessed by the United States. Thevehicle uses a modified Thor booster as itsfirst stage which is a 57 foot, liquid-fueledrocket which generates approximately170,000 pounds r,f thrust in a burningtime of two minutes and 25 seconds.Thrust is hard to visualize, so let us try toexpress this thrust in horsepower (HP),

Now anyone who knows physics wouldsay that we cannot equate thrust andhorsepower (HP) unless the velocity isspecified. This is because the definition ofone horsepower (HP) is that one horse-power (HP) is equal to the force requiredto raise 33,000 pounds (lb.) at the rate ofone foot per minute (1 HP = 33,000 ft..lb./minute). Roughly. though, it has becnestimated that it takes about 22 horse-power (hp.) to develop one pound (lb.)of thrust at average launch conditions.

52

PAYLOAD

3RD STAGE

TRANSITION SKIRT

2ND STAGELIQUID PROPELLANT

1ST STAGETHOR MISSILE--ROCKETDYNE MB 3 BLOCK-1LIQUID PROPELLANT

ENGINEACCESSORIESSECTION

Figure 7. Delta launch vehicle

If you use this figure, how many horse-power could be developed by a first stageof the Delta Launch vehicle?(75)

The second stage of the Delta launchvehicle is an improved second stage fromthe Vanguard and Thor-Able programs,as was the first stage. It develops about7,500 pounds (lb.) of thrust for 160 sec-onds. How many horsepower (HP) aredeveloped by the second stage?(76)

The third stage is the Altair, which isa solid propellant booster. also from theThor-Able and Vanguard vehicles. As youcan see, the Delta has taken proven en-gines and modified them for better relia-

bility and newer missions. This stage pro-duces 3,000 pounds (lb.) of thrust for 10seconds to complete the launch.

Problems:How many horsepower are produced by

the Altair booster?(77) Now counting sixminutes of coasting after the burnout ofthe second stage, how many minutes andseconds does the launching of TIROS re-quire?(78) Does the successful launchingrequire more than an hour or less thanan hour?(79)

It might be interesting to make a scalemodel of the Delta launch vehicle using thedata given here as to height and diameter.Materials required for this activity wouldbe a pair of scissors, a ruler, and somewrapping paper. Use a scale of 1/4. inch =1 foot for a large representation, andshape the paper to resemble the actualvehicle.

ORBITS OF SATELLITESThe path of the satellite around the

Earth is known as its orbit. It is placedin orbit with a speed and direction (veloc-ity) which causes it to "fall" continuallyaround the Earth, Everything sent intothe outer reaches of our atmosphere atspeeds under 18,000 miles per hour or fivemiles per second falls back to the Earth.

As you probably know, a falling bodyfalls 16 feet the first second. Our satellitealso falls 16 feet in the first second; but asit falls 16 feet, it has traveled five mileshorizontally, which happens to be equal tothe curvature of the earth-16 feet in fivemiles. Thus, the satellite is still just aboutas far from the surface of the Earth as itwas in the beginning, so we say it is fall-ing around the Earth and will continue inthis manner until air drag slows or pullsit down.

This can be explained in another wayby using Newton's First Law that says "Abody in motion tends to remain in motionin the same straight tine unless acted uponby some unbalanced force." This resist-ance to a change of velocity is called"inertia". The satellite "tries" to continuein a straight line except for the unbal-

53

anced force, in this case, gravity, whichmoves it into a curved path around theEarth. The directed speed or velocityneeded to place an object into an orbit isknown as orbit velocity.

If the satellite is moving at the rightvelocity, its centrifugal force (a form ofinertia) and the force of the Earth's grav-ity will be in equilibrium, or just aboutbalanced, causing it to follow a circularorbit about the Earth. This is the hardestorbit to obtain because the exact speed isextremely hard to produce.

Most natural objects follow ellipticalorbits or forms of an ellipse. The ellipselooks like an elongated circle and is mucheasier to attain than a circular orbit. Itis a closed curve in which the sum of thedistances from any point on the curve totwo internal points, called the foci, is al-ways constant (the same). The point ofthe ellipse or elliptical orbit, as shown infigure 1, nearest the surface of the Earthis called perigee (peri meaning near andgee from geo meaning Earth). The pointfarthest front the Earth in figure 1 iscalled apogee.

The orbits of our Earth satellites arenamed according to their relationships tothe surface of the Earth; for instance, apolar orbit passes over both poles. Anequatorial orbit is over only the equator.An orbit between polar and equatorialorbit is called an inclined orbit and is de-scribed by using the angle it makes withthe equator.

The TIROS satellites are in nearly cir-cular, inclivtd orbits. The earlier satel-lites were inclined 48° to the equator;however, the inclination was increased to58° in order to view areas nearer to thepolar region where much of our weatheroriginates. Also, the higher inclinationbenefited the study of sea ice. One dis-advantage of this orbit is that the areascovered extend only from 60° N to 60° Sso that nothing in close proximity to thepolar regions could be observed. Scientistsare now planning near polar orbits forfuture TIROS missions. The orbital alti-tude of TIROS is about 380 nautical miles;how many statute miles is this? (Use yourconversion factors 9(80) A main disadvan-tage of TIROS is that it is space oriented.

(TIROS AS EXAMPLE). ,1,

DATAREADOUTSTATIONS WEATHER BUREAU

COMMANDSTELEMETERED SIGNALSTELEMETERED WX DATA

TIROS NETCONTROL(LOCATED AT GSFC)

POSITIONAL DATA FROM TRACKING INSTRUMENTS

Figure 8a.

Figure 8b. Orientation of Nimbus and TIROS satellites

54

This means that the axis of TIROS is con-stantly pointed in a fixed direction inspace. In Figure 8b, TIROS faces the Earthonly through lAi of its orbit. Even thoughpictures can be taken only in daylight, 10to 25 percent of the Earth is covered byTIROS.

While the TIROS ,weather satelliteswere being developed they provided muchvaluable data which aided meteorologistsin forecasting hurricanes, typhoons, icemelts and other veather phenomena. Al-ready these satellites helped save an un-told number of lives and property damage.After 5 years of experimental flightsTIROS will become the world's first oper-ational meteorological satellite.

WHAT NEXT?The next "generation" weather satel-

lite, is Nimbus first launched in the sum-mer of 1964. It is much larger thanTIROS. Nimbus stands 10 feet high and,with the solar paddles extended, is 5.3

feet (ft.) wide. It weighs 650 pounds(lb.), which is Ire than twice as heavy

z

41.4NEll

11,

as TIROS. The first Nimbus satellite wasplaced in an orbit about 600 nautical milesabove the earth. What would this altitudebe in statute miles.(81)

Nimbus takes advantage of many ad-vances made possible by TIROS. First itkeeps its cameras facing the earth at alltimes, thanks to a unique horizon sensingsystem. It is placed in a polar orbit, thusgiving coverage of clouds over every por-tion of the earth each 24 hours. Finally,it transmits photographs continuously toinexpensive ground stations anywhere inthe world.

The base section of the spacecraft con-tains all camera and radiation-sensingequipment and other experiments. Theupper section contains power and stabili-zation systems. Its two solar cell paddlesare pointed continuously toward the sun.

Its camera system consisted of :Three Advanced Vidicon Camera Sys-

tems (AVCS) which produce an 800 scanline one-half mile resolution picture.

One Automatic Picture Transmission(APT) system which sends instant photos

Figure 9.

55

.2Nligrailr-4111"--

ROTATION _

( A4,ilfwta

SECOND ORBIT

%kit*

81.

Nimbus solar paddles "follow" the sun

NIMBUSSPACECRAFTFIRST ORBIT

***

11

HOU' Nimbus photographs the world's weather

56

..410

SUN RAYSSECOND ORBIT

Nimbus looks at the Earth

to relatively inexpensive ground stationslocated around the world. APT uses theslow scan television technique similar tothat used in radio facsimile transmissionand has a resolution of some 3 miles.

One High Resolution Infrared Radio-meter (HRIR) system which measuresheat in the Earth and clouds and producesnighttime photographs, It has a resolu-tion of approximately 4 miles.

Polar orbit and the Earth's rotation en-able these systems to transmit more than2,000 photographs per day. Nimbus coversthe entire world in fourteen orbits or oncedaily.

Two Data Acquisition Facilities one atRosman, North Carolina and the other atGilmore Creek, Alaska receive all space-craft performance telemetry data and

57771-806 0-65-5

meteorological data via their 85-foot pa-rabolic antennas. These data are micro-waved to the Goddard Space Flight Centerin Greenbelt, Maryland. Meteorologicaldata are then sent to the U. S. WeatherBureau in Suitiand, Maryland. The Nim-bus Technical Control Center at Goddardevaluates all spacecraft performance anddetermines command instructions to besent to the satellite by the Rosman andGilmore Creek Stations.

From studies of the duration and sizesof various types of storms, it has beenfound that using one or two weather sat-ellites most hurricanes and larger stormscould be observed.

For a more continuous observation sys-tem, a Synchronous Meteorological Satel-lite system is being investigated. This typeof spacecraft might be placed in an equa-torial orbit at an altitude of 22,300 miles.At this altitude the satellite would appearstationary, because it would revolvearound the Earth at the same rate that theEarth rotates. A satellite of this typecould observe about one-third of the Earthat one time with its cameras as shown infigure 9. Thus three satellites could givecontinuous observation of the entire globe.

SATELLITE

SATELLITES

The 24-hour satellite system

\ CIRCULAR

ORBIT

SATELLITES

CONCLUSIONWe could go on indefinitely because the

study of the atmosphere is continuous.New methods are constantly being devel-oped; even at this time, a new type of

TIROS 'satellite is being readied forlaunching, which, once in orbit, will turnon its side and roll through space like awheel. Much more is on the drawingboards and in men's minds. Some day thegeneration that is in the schools of todaywill be putting their ideas and imagina-tions to work. Instead of studying the

58

weather, we might be able to do somethingabout it. Instead of warning people aboutstorms, we will be destroying them.

Scientists and engineers using scienceand mathematics will help produce theanswers in man's quest for knowledgeabout himself and the environment intowhich he was born.

Chapter IV

SPACE NAVIGATIONby

George F. BanksMathematics Teacher

D.C. Public SchoolsWashington, D.C.

ABOUT THIS CHAPTERNavigation now includes outer space as well as the earth and its atmosphere. Measure-

ment is a necessary part of navigation and a good mathematical background is essential if weare to understand the complexities of our space age.

This chapter has been developed to help you to actually experience some of the ways inwhich mathematics are used to travel through space where there are no familiar landmarks orroad signs. Therefore, the more you know of mathematics, the better you will be able to"navigate" through the exercises. Should you find that you need to know some math youhave not takenlook it up!

Figure 1.

MAPS FOR NAVIGATION

A navigator must know how to locatehis position by recognizing objects on theground which he can see from his posi-tion in the air. To help him do this theUnited States Department of CommerceCoast and Geodetic Survey compiles andprints maps called Sectional AeronauticalCharts which include prominent landmarks marked in a code which is under-stood by a navigator. See Figure 2. Thesemaps have a scale of 1:500,000. Thismeans that 1 inch on the chart represents500,000 inches on the Earth's surface.

Problems:L To the nearest mile, approximately how

many miles would 500,000 inchesrepresent?If you are to travel between two citieswhich are represented by a distance of21/2 inches between them on the chart,how far is the distance actually inmiles between the cities?

9.

6i

3. According to your map, what is theair mileage between the Benedum air-port near Bridgeport, West Virginiaand the Morgantown airport at Mor-gantown, West Virginia. The smallcircles are the symbols used to denoteairports. (See figure 2.)

.1. What is the distance between the Con-nellsville, Pennsylvania, airport andthe Green County, Pennsylvania air-port? (See figure 2.)

A navigator must know how to measuredistances accurately from his charts andalso know which way to turn in the vastocean of space to reach his distination.If he examines his chart closely he willnotice that there are two sets of lines,one set of clearly marked horizontal lines(lines of latitude) and one set of verticallines (lines of longitude). The lines oflongitude all terminate at the geographicnorth pole and the geographic south pole.They give the direction of geographic, orwhat is sometimes called "True", north.

el t., yon

cm.<1.100

1590

Of *0

'ISO I

tiAr al.e Lyn^

1745 a

Je,1,,,V lie

Cassv.,4

evaRnatThoudO

44141.141.1

ARKSBURGIII I (MN

POI ION000 14

V 166,

SOhU15

,r,91A

W11.t rdi

Ad.n

-Zots3II AIN,

NOM PIT Cel

h'iprre 1'TCrti011(1( Aeronautical Chart'

62

I Huntington Sectional Aeronautical Chart(Washington: Coast and Geodetic Survey, UnitedStates Department of Commerce, Fel»-uary f,1964 ).

TRUE NORTH

Figure 3.

For navigational purposes directions arecompared to True north; courses aremeasured clockwise in degrees from 0° to3600. Thus, to travel from A to B, figure3, a true course (TC), of 105° must benavigated. From B to A the TC is 2850.

5. What is the TC from D to C in figure3?

True coursts

6. What is the TC from 'C to D? Thiscourse may be found by adding 180°to the course from D to C. The coursesfrom C to D and from D to C are calledreciprocal courses.

The navigator uses a compass to helphim find his course direction. He know.%.;,howev.r, that it does not point to the

Geographical North Pole

Figure I,. Compass

63

Figure 5. Magnetic pole

Easterly Variation Westerly Variation

10°

Figure 6. Variations

geographic north pole but rather toanother position very near called themagnetic north pole, so he must correcthis course measure. The angular differ-ence between true north and magneticnorth at a given place is called the varia-tion at that place, To correct his coursethe navigator uses one of these formulaS:

MC = TC Var. W., orMC = TC Var. E.

MC is the magnetic course, TC is the truecourse, \Tar. \V is the variation if themagnetic north pole is in a direction westof true north, and Var. E is the variationif the magnetic north pole is in a directioneast of true north. The magnetic course isthe reading he must use on his compass tofollow the desired true course. Figure 6shows how variation is distributed overthe United States. The lines on this mapare called isogonic lines. They join placeswhich have the same variation. On thecharts published by the United StatesDepartment of Commerce the isogoniclines appear as dashed lines with theamount of varies ion and the direction ofvariation marked at the upper and lowerends of the lines, as 6°E or 4°W. At alocation where the variation is 6°E, thecompass will read 0° or 360° when themagnetic course to true north is actually6' west of that reading, or 354°; at a loca-tion where the variation is 4°W, the com-pass wql read 00 or 360° when the mag-

64

netic course to true north is 4° to the (asstof 0° or 4°. (see Figure 7).

7. From Figure 8, what is the true coursefrom A to B? Use a pi itractor.

8. w hat is the correction due to varia-tion on the true course from A to B?

9. What is the magnetic course from Ato B?

10. What is the correction, due to varia-tion, necessary to travel a TC fromC to D?

11. What MC must be used (C to D) ?12. In Figure 9, what magnetic course

must be navigated and how far is itfrom Wood County airport to the NewLexington airport?

13. Shortly after take-off from the WoodCounty airport you cross a river(marked on your chart). You noticeon your chart a prominent landmarkto the left of your course, a school.Approximately how many degrees tothe left of your course is th' landmarkfrom your position at the river?

A navigator must be able to estimate themeasures of angles and directions. Eventhough this method of navigation, contactflying, or piloting, is not complicated, itdoes nevertheless, require some knowledgeof mathematics.

Now we will study about a more ad-vanced method of naviga',,ion. We can

TRUE NORTH

6° VAR. E

MAGNETICNORTH

MAGNETICCOURSE=354°

MAGNETIC NORTH

Figure 7. Compass variation

MAGNETICCOURSE = 04°.

Figure 8. Magnetic courses

,; rrcxfucrstela

:2/vtnsI 1.,f

iOnale

11

fidaga

NewMarshfield

Figure 9. Huntington Sectional Aeronautical Chart

65

re14:-.view

develop new ideas if we perform the fol-lowing experiment and study its resultscarefully.

Figure 10. Path of plane

Experiment 1.Materials:string or thread lightweight toychalk smooth surfaceProcedure:Pull the string attached to the modelslowly along a line drawn from A to Bas shown in the diagram while blowingheavily on the model from one side. Repeatseveral times; blow lighter on some trialsand heavier on others.Observations:Did the model follow directly behind yourhand as you pulled and blew ?After a few trials, did you know whatto expect before making the next trial?What conclusion could you make about thepath of the model as you blow on it andpulled?

Perhaps you could understand the re-sults you obtained better if you knew aboutvectors, a mathematical way of represent-ing the two forces which acted on themodel.

Experiment 2.Vector representationMaterials:rubber bands masking tape1 notebook snap 4 straight pins

ring rulerweight (approx. paper clips (3 or 4)

8 oz.) !Tienfibre board or card board about 24" x 36"Procedure:

Test three rubber bands for equalstrength (stretch) by the method shown in

66

III

C

A

IVFigure 11. Vectors

(I) of Figure H. Bands of approximatelythe same strength will stretch the sameunder the weight. On the board draw CAapproximately 3 inches and extend beyondfor approximately 3 inches. Likewise drawCB 4 inches and extend for approximately3 inches (unstretched length of the rubberband).

Lay two rubber bands on the lines asshown in (II) and pin them in positionso that they will stretch when pulledtoward the pin at C. Stretch eac. of thebands and attach each to the notebookring placed over the pin at C.

The stretch in each band represents aforce acting in the direction of the raysCA and CB. These rays which representforces and the direction of these forces arecalled "vectors".

Loop the third band in the notebookring at C and stretch in the general direc-

tion of D. (111), until the pin at point C iscentered in the ring.

Measure the "stretch" along the direc-tion of D (be sure to deduct the lengthof the unstretched band). This is the force(vector) that is necessary to equalize thecombined forces represented by vectorsCA and CB. Extend DC in the directionof the dashed line and mark the amount ofstretch at E so that CD CE. You havediscovered a very important relationshipcalled the -resultant". It represents theone stretch (force) that -Would result fromthe action of the two stretches forces)that were applied at the beginning of theexperiment.

Repeat the experiment using differentforces. Do the results seem to be similar?

Through the use of vectors to representforces it is possible to find the resultantdirectly through mathematics. This is howit is done.

Problem:Find the resultant of a force of 4 poundsto the east and 2 pounds to the south.Solution:

1. Select a di, ection for north.2. Select a length to represent a unit of

force. 1 inch = 2 lb. will be usedin titis problem.

3. Draw vector AB, and vector BC asshown in the following diagram.A 41b.0

210.6

Figure 12. Resultant in vector triangle4. Draw vector AC. This is the result-

ant.

Problem:14. How long is the measure of vector.

AC? How many pounds of force doesthis represent? (1 in. = 2 lb.)

15. What is the general direction of vec-tor AC?

67

This process of finding the resultant iscalled "vector addition." The Figure 12 is avector triangle. Vector AC is called thesum of vector AB and vector BC.

When an aircraft in flight encountersthe force of wind blowing across its courseas in Figure 13 (first top frame) it willdrift from its course. The second frameshows that the blot must turn (head) hisaircraft slightly into the wind (calledcrabbing), in order to prevent drifting offcourse.

In order to determine how much hemust turn his aircraft into the wind (orcrab) the pilot must be able to solve prob-lems similar to the one which follows.

Problem:A pilot whose aircraft's average speed is150 mph wishes to travel a true course(TC), or resultant course, of 90°. He en-counters a wind blowing from 240°(toward 60°) at 40 mph.(a) In what direction must he head

(turn) his aircraft to fly his intendedcourse directly?

Crabbing

Figure 18. Affected course

0laws

DIRECTION OF TH

.33A

Figure 14. Corrected course Scale: 1° = 40 m.p.h.

(b) What will his resultant speed alongthe course be?

Solution: (See Figure 14)1. Draw a line to represent north and

mark a point on this line (A).2. Draw a long line through point A to

represent the direction of the intendedcourse, AR at 90°. This is the direc-tion of the reenitant.

3. Select a convenient unit and draw thewind vector AB. (1" = 40 mph)

4. F xnm B measure a vector P4" longto represent 150 mph so that the endtouches line AR at point C.

5. What is the direction of line BC?Measure for this direction (true head-ing, TH) at point D in the figure.

6. How long is segment AC? How manymph does this length represent? Thiswill tell the speed !-e is traveling alonghis desired course.

The solution of this problem tells thethat he must head his aircraft in a

direction of 98°, (crab to the right) andthat his resultant speed will be approxi-mately 180 mph due to the wind encoun-tered (a tail wind).

16. A pilot wishes to travel a true course(IC) of 60°. The average speed ofthe aircraft he is flying is 120 MPH.He encounters of wind of 40 MPHblowing from a direction of 280°. Inwhat direction must he head his air-craft (TH) in order to fly the de-sired course? How fast will his speedbe along this course?

17. The desired course (TC) is 40°. Ifth average speed of the aircraft be-ing flown is 160 MPH and a windfrom the east, 90°, at 25 MPH isblowing, what is the heading (TH)necessary to maintain the TC. Whatwill the speed along the TC be?

68

STARS AS SIGNPOSTSOne of the earliest references used by

man in his travels to direct him from oneplace to another was the celestial domeover his head and the many heavenlybodies. Today, after many centuries ofprogress these bodies remain one of themost accurate and reliable natural meansof ascertaining direction; scouts,sailors, aviators, and the man on the streetstill "look to the stars" for direction.Rarely is it possible to find a person whocannot locate the "Big Dipper" and the"North Star".

The use of celestial bodies as a meansof navigation, requires some knowledge ofthe Earth and its relation to the hugeimaginary dome over us which we aregoing to call the celestial sphere. A studyof figure 16, a picture of the Ear, i andthe celestial sphen!, will help you developsome new ideas.

bath Pole

Equator

Figure 15. Celestial sphere

lestialEquator

Hour Circles

Meridians

The Earth is divided by two imaginarysets of lines, lines of latitude and linesof longitude, the use of which makes itpossible to identify any paint on the sur-

w

Polaris

E

Figure 16. Celestial Nithere and the EarthGrurtir H'. ixter, Primer of Nrwip,ti,,ri (New Murk: D. anNostrand (.ornpnliy, Int., 1960),

face of the Earth. The celestial spherelikewise is divided into two sets of lines\\lila correspond to those On the Earth.Celestial parallels correspond to the paral-lels of latitude On the Earth : hour circleson the celestial sphere correspond to theterrestrial meridians or lines of longitudeOn Earth.

The terms geographic position (GP)and declination will be used frequently.See Figure 16. Geographic position can bestbe understood by imagining yourself tobe at the center of a large transparent ball,the Earth; you then imagine a light bull)shining far out from the transparent hall.I f you touch the point on the surfacewhere the light comes through to you,then the point you touch is the GI' of thatlight on the ball, The declination of apoint on the celestial sphere is tile centralangle between the celestial parallelthrough the point and the celestial equator.It is measured the same way as terrestriallatitude. Since the diameter of the Earthis small compared to the distance fromthe Earth to :be sun and stars in thecelestial sphere, the angle observed fromthe surface of the Earth is assumed tobe the same as the angle formed at thecenter of the Earth by the projectionfrom the heavenly body and the plane ofthe horizon, the plane of the equator, orthe projection of the zenith to the centerof the Earth.

The old saying, "X marks the spot",' isthe basic principle used in celestial naviga-tion. The bars which are used to make

75°W MERIDIAN

FIXEDPOSITION40°N,75°W )L.O.P.

L.O.P.

Figure 1 7. Lines of position

69

40°NPARALLEL

the X" are what the navigator designatesas lines of position. abbreviated, LUP's.These lines of position may be located byfinding ones position in terms of lines oflatitude and lines of longitude.

Finding latitude by the method called,"The nOon sight of the altitude of thesun". is perhaps one of the easiest meth-ods used. This means that the sun must besighted as it crosses the meridian of theobserver; the latitude of the observer thencan be found 1w using the formula,Latitude Zenith distance -' Declination,

orL z d.

If you stand and look to the point in thesky directly over your head. the point yousee is the zenith for your position. SeeFigure 18. To solve the formula, L = z-1 (1, first find a value for z. the zenithdistance, which is measured in degrees ofarc. The number of degrees of arc is thesame as the number of degrees in thecentral angle. From the figure yousee that the zenith forms an angle of 90with the horizon, and z is a part of thatangle, the other part of which is the alti-tude of the sun, that is,

z altitude of the sunThe altitude is measured with an instru-ment called a sextant. (See Figiae 19.)

Problents:18. An observer uses his sextant to meas-

.re the altitude of the sun. The alti-tude measure is found to he 68' 30'.Find z, the Zenith distance, in de-grees.

(Find the desired answers for the fol-lowing altitudes.)

ig "re IS. Zr)/ distan

Altitude measure

19.20.

6370' 52'.18' 26'800 05'

Zenith

compleh. the solution of the forinul::.z d, ;1 vnlue 1.01. II, the declitultion

of the nmst found..111ee valuelisted 11/0 t! /WC: .11 .14 ,1)

which hus beet) re111.0(.111Ced 1'0r you to useon pages ,A7 in :\lay-Aug, 190-1.

Probbr,/:If the meridian altitude measure of I he

sun on .1uly 10, 1961, is (hi and if thedeclination at 110011 on the date is foundin the Air Almanac to he 21 18', what isthe latitude of the position .:

L Iz 9(1 altitude, or 01 :V, therefore,L 21 30' + 21 18', or 12 18'.The latitude of the observer 12 18' N.

Prob/t.ms:Find the observer's latitude in each of thefollowing:

Altitude

Horizon

Figure 19. Measurement of altitude

70

Noon Meridian Altitude of Sun Declination Latitude

23.24.25.

65° 11'40° 32'82° 10'

15° 07'20° 12'23c.' 23'

The meridian of the observer will beused as the first LOP. Since this is a "noonmeridian altitude of the sun observation,"the only other necessary measure needed isan accurate measure of time.

Time, the rotation of the Earth, andlongitude are closely related, The naviga-tor bases his work on a time measurecalled Greenwich Mean Time . (GMT) .

GMT is the same at any certain momentfor any place on Earth. That is, when itis .4 :00 GMT in England, the time is 4:00GMT in California, and the time is 4 :00GMT in New York. The Earth makesone rotation on its axis in 24 hours. Thecount begins when the sun crosses theInternational Date Line, an imaginaryline which corresponds to the 180° meri-dian. The Earth rotates at a rate of 15°an hour. In 12 hours. the Earth will rotatethrough an arc of,

12-x 15° or 180°.

Figure 20. Rotation of the Earth

26'. Through how many degrees of arcwill the Earth rotate in (a) 5 hours;

71

(b) 9 hours; (c) 15 hours; (d) 3hours and 20 minutes; (e) 202/3hours; (f) 24 hours?

27. By using the. symbols, A,. for arc, hfor hours, and r for the rate of rota-tion, write a formula for this rela-tionship.

The following table gives a more de-tailed account of this relationship :

Table 1.Arc-time relationships

Time Arc24 h 360°

1h 15°1m 15'45 1'14 .25'

John C. Hill, II, Thomas F. Utegaard, and Gerard Riordan.Dutton's Navigation and Piloting (Annapolis, Maryland: UnitedSlates Naval Fastitute, 1958), p. 367. The table is reproduced bypermission from Dutton's Navigation and Piloting, Copyright19.58 by U.S. Naval Institute, Annapolis, Maryland.

The Air Almanac has made use of thisconversion table in making its record- ofthe sun's position in periods of 10 minuteintervals (GMT) as it trans.its_the merid-ians of the Earth. By taking a "noonsight" of the sun, the longitude of yourposition can be determined directly fromThe Air Almanac under the column head-ing of "Sun GHA" which is adjacent tothe column marked "GMT''.Example:If the sun transits the meridian of yourposition at 17h1Oln GMT on January 1,1964, your position of longitude its takenfrom The Air Almanac is 76° 40' W. Seetable 3. Tables 2 and 3 are pages fromThe Air Almanac.

The line of longitude is then the seconddesired "line of position," necessary in find-ing a "fix'! on a position.

The Air Amanac. is published severaltimes anntal'.y, to provide in a convenientform the astronomical data required forair -navigatic n.

Table 2.A.M. LongitudesGREENWICH A. M. 196-1 JANUARY 1 (WEDNESDAY)

VENUS-3.4 JUPITER--2.1 SATURN 1.0 MOON Moon's 1GHA Dec. GHA Dec. GHA Dec. GHA Dec. P. in A.

GMTSUN ARIES

GHA Dec. GHA

h m

00 00

10

20

30

40

50

01 00

10

20

30

40

50

02 00

10

20

30

40

50

03 00

10

20

30

40

50

179 15 S23 06 99 41181 45 102 12

184 15 104 42

186 45 107 12

189 15 109 43

191 45 112 13

194 15 S23 06

196 45

199 15

201 45

204 15

206 44

209 14 S23 05211 44

214 14

216 44

219 44

221 44

224 14 S23 05

226 44

229 14

231 44

234 14

236 44

04 00 239 14 S23 05

10 241 44

20 244 14

30 246 44

40 249 14

50 251 44

05 00 254 14 S23 0510 256 43

20 259 13

30 261 43

40 264 13

50 266 43

06 00

10

20

30

40

50

07 00

10

20

30

40

50

08 30

10

20

30

40

50

09 00

10

20

30

40

50

10 00

10

20

30

40

50

11 00

)020

30

40

50

269 13 S23 05271 43

274 13

276 43

2;9 13

281 43

284 13 S23 04

286 43

289 13

291 43

294 13

296 43

299 13 S23 04

301 43

304 13

306 42

309 12

311 42

314 12 S23 04

316 42

319 12

321 42

324 12

326 42

329 12 S23 04

331 42

334 12

336 42

339 12

341 42

344 12 S23 04

346 42

349 12

351 42354 12

356 42

114 44

117 14

119 44

122 15

124 45

127 16

129 46

132 17

134 47

137 17

139 48

142 18

144 49

147 19

149 49

152 20

154 50

157 21

159 51

162 21

164 52

167 22

169 53

172 23

174 54

177 24

179 54

182 25

184 55

187 26

189 56

192 26

194 57

197 27

199 58

202 28

204 58

207 29

209 59

212 30

215 00

217 30

220 01

222 31

225 02

227 32

230 03

232 33

235 03

34

240 04

242 35

245 05

247 35

250 06

252 36

255 07

257 37

260 07

262 38

265 08

267 39

270 09

272 40

275 10

277 40

146 34 519 25

149 04

151 34

154 04

156 34

159 04

161 33 S19 24

164 03

166 33

169 03

171 33

174 03

176 .33 S19 23

179 03

181 33

184 02

186 32

189 02

191 32 S19 22

194 02

196 32

199 02

291 32

264 02

206 31 S19 21

209 01

211 31

214 01

216 31

219 01

221 31 S19 20

224 01

226 30

229 00

231 30

234 00

236 3" S19 19

239 00

241 30

244 00

246 30

248 59

251 29 S19 19

253 59

256 29

258 59

261 29

263 59

266 29 S19 18

268 59

271 28

273 58

276 28

278 5?

281 28 S19 17

283 58

286 28

288 58

291 28

293 57

296 27 S19 16

298 57

301 27

303 57

306 27

3C8 57

311 27 S19 15

313 56

316 26

318 56

321 26

323 56

89 18 N 3 03 136

91 49 138

94 19 141

96 49 144

99 20 146

101 50 149

104

106

109

111

114

116

21 N 3 03

51

21

52

22

52

119 23 N 3 03

121 53

124 24

126 54

129 24

131 55

134 25 N 3 03

136 55

139 26

141 56

144 27

146 57

149 27 N 3 03

151 58

154 28

156 58

159 29

161 59

164 30 N 3 03

167 00

169 30

172 01

174 31

177 01

179 32 N 3 03

182 02

184 33

187 03

189 33

192 04

194 34 N 3 04

197 04

199 35

202 05

204 36

207 06

209 36 N 3 04

212 07

214 37

217 08

219 38

222 08

224 39 N 3 04

227 09

2:9 39

232 10

234 40

237 11

239 41 N 3 04

242 11

244 42

247 12

249 42

252 13

254 43 N 3 04

257 14

259 44

262 14

264 45

267 15

151

154

156

159

161

164

29

59

29

00

30

00

S15 49

31 51'i 49

01

32

02

32

03

166 33 515 48

169 03

171 34

174 04

176 34

179 05

181 35 815 48

184 06

186 36

189 06

191 37

194 07

196 38 515 48

199 08

201 38

204 09

206 39

209 09

211 40 515 48

214 10

216 40

219 11

221 41

224 12

226 42 515 48

229 12

231 43

234 13

236 43

239 14

241 44 S15 48

244 14

246 45

249 15

251 46

254 16

256 46 515 48

259 17

261 47

264 17

266 48

269 18

271 49 S15 48

274 19

276 49

279 20

281 50

2J4 20

286 51 515 48

289 21

291 51

294 22

296 52

299 73

301 53 S15 48

304 23

305 54

309 24

311 54

314 25

336 34 N21 45

338 58 44

341 22 44

343 46 43

346 10 42

1'5 34 41

350 58 N21 40

353 22 40

355 46 39

358 10 38

0 34 37

2 58 36

5 22 N21 35

7 46 35

10 10 34

12 34 33

14 58 32

17 22 31

19 46 N21 30

22 10 29

24 34 29

26 58

29 22 27

31 46 26

34 10 N21 25

36 34 24

38 59 23

41 23 22

43 47 21

46 11 21

48 35 N21 20

50 59 19

53 23 18

55 47 17

58 11 16

60 35 15

62 59 N21 14

65 23 13

67 48 12

70 12 11

72 36 10

75 00 09

77 24 N21 09

79 48 08

8? )2 07

84 36 06

87 00 05

89 24 04

91 49 N21 03

94 13 02

96 37 01

99 01 21 00

101 25 20 59

103 49 58

106 13 N20 57108 38 56

111 02 55

113 26 54

115 50 53

118 14 52

120 38 N20 51

123 02 50

125 27 49

127 51 48

130 15 4?

132 39 46

135 03 N20 45

137 27 44

139 52 42

142 16 41

144 40 40

147 04 39

0

9

14

17

20

23

25

27

29

31

35

36

38

39

41

42

44

45

46

48

49

50

51

53

54

55

56

57

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

59

58

57

56

55

54

53

52

51

50

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

®Sun

SD 16'

Moon

SD 16'

Age 16

0

0

0

,4

Ai

24,

Aldebaran

JUPITER

181'

SATURN

VENUS

MARS

MERCURY121,

Antares

Spica

6,,

Regulus

Sirius0,

Table 3.--P.AL Longitudes

AS

GMT

m

GREENWICH

SUN

GNA Dec

ARIES

GHA

1.

P. Al.

VENUS 3.4

GNA Dec

196-1 JANUARY

JUPITER 2.1

GHA De:

I

SATURN. 1.0

GHA Dec

(WEDNESDAY)

MOON

GHA DecLat.

Sun-

rise

7wi-

lfghtMoon-

riseCuff

12 00 359 12 S'3 03 280 11 326 26 519 14 269 45 N 3 04 316 55 SI5 48 149 28 N20 38 h rn m m

10 1 41 282 41 328 56 272 16 319 26 151 53 3773 79

20 4 11 285 12 331 26 274 46 321 56 154 17 36 70 13430 6 41 287 42 333 56 277 17 324 26 156 41 35 68 .165 15 5240 9 11 290 12 336 26 279 47 326 57 159 05

66 10 30 96 16 33 5550 I I 41 292 43 338 55 282 17 329 27 161 29 33

64 09 51 76 17 02 49

13 00 14 11 S23 03 295 13 341 25 S19 14 284 48 N 3 04 331 57 S15 48 163 54 N20 32 62 09 24 64 17 73 45

10 16 41 297 44 343 55 287 18 334 28 166 18 31 60 09 03 57 17 40 4320 19 11 300 14 346 25 289 48 336 58 168 42 30

58 08 46 51 17 55 4230 21 41 302 44 348 55 292 19 339 29 171 06 29

56 08 32 47 /8 07 4024 11 305 15 351 25 294 49 341 59 173 30 27

54 08 19 44 18 18 3950 26 41 307 45 353 55 297 20 344 29 175 55 26 08 08 41 18 27 38

14 00 29 11 S23 03 210 16 356 25 S19 13 299 50 N 3 04 347 00 615 47 178 19 N70 25 07 59 38 18 36 3810 31 41 312 46 358 54 302 20 349 30 180 43

45 07 38 34 18 54 3h20 34 11 315 17 1 24 304 51 352 00 183 07 23

40 07 22 30 19 C9 3430 36 41 317 47 3 54 307 21 354 32 185 32 22 07 08 28 19 21 3340 N 11 320 17 6 24 309 51 357 01 187 56 21

30 06 56 26 19 32 3350 41 41 322 48 8 54 312 22 ?59 31 190 20 20

20 06 35 24 19 51 31

15 00 44 11 S23 03 325 18 11 24 SI9 12 314 51 N 3 04 2 02 S15 47 192 44 N20 1910 06 17 23 20 07 30

10 46 41 327 49 13 54 317 23 4 32 195 08 170 06 00 23 20 22 28

20 49 11 330 19 16 24 319 53 7 03 197 33 16 10 05 42 23 20 37 2730 51 40 332 49 18 54 322 23 9 33 199 57 15 20 05 23 24 20 53 2640 54 10 335 20 21 23 324 54 12 03 20? 21 14

50 56 43 337 50 23 53 327 24 14 34 204 45 130 05 02 27 21 12 2'4

35 04 49 30 21 22 2316 00 59 10 S?3 03 340 21 26 23 S19 11 329 55 N 3 04 17 04 S15 47 207 10 NM 12

40 04 34 33 21 34 2210 61 40 342 51 28 53 332 25 19 34 209 34 11

.15 04 16 37 21 48 2120 64 10 345 21 31 23 334 55 22 05 211 58 09

SO 03 54 44 22 06 1930 6F 40 347 52 33 53 337 26 24 35 211 22 08

40 69 10 350 22 36 23 339 56 27 06 216 47 07 52 03 44 48 22 14 18

50 71 40 352 53 38 53 342 26 29 36 219 11 06 54 03 32 53 22 23 17

56 03 18 61 22 33 1617 00 74 10 S23 02 355 23 41 23 S19 10 344 57 N 3 05 32 06 S15 47 221 35 N20 05 58 03 01 73 22 45 14

10 76 40 357 54 43 52 347 27 34 37 224 00 04 60 02 42 97 22 59 1320 79 10 0 24 46 22 349 57 37 07 226 24 02

30 81 40 2 54 48 52 352 28 29 37 228 48 01

40 84 10 5 25 51 27 354 58 42 09 231 12 20 00Sun- Twr Moon-

50 86 40 7 55 53 52 357 79 44 3u 233 37 19 59 Lat.set light set

0

18 00 89 10 S23 02 10 26 56 22 S19 09 359 59 N 3 05 47 05 S15 47 236 01 NI9 58

10 91 40 12 56 58 52 2 29 49 39 238 25 57 N

20 94 10 15 26 61 22 5 00 52 09 240 50 55 h m m h m m30 9r, 40 17 57 63 52 7 30 54 40 243 14 54

40 99 10 20 27 66 21 10 01 57 10 245 38 5372 79

101 39 22 58 68 51 12 31 59 40 248 02 5?70 134

68 166 12 32

19 00 104 09 S23 02 25 28 71 21 SI9 08 15 01 N 3 05 62. 11 S15 47 250 27 N19 51 66 13 37 95 11 50 0510 106 39 27 58 73 51 17 32 64 41 251 51 49 64 14 16 76 11 21 11

20 109 09 30 29 76 21 20 02 67 11 255 15 48 62 14 43 64 11 00 14

30 111 39 3Z 59 78 51 22 32 69 42 257 40 47

40 114 09 35 30 81 21 25 03 72 12 260 04 4660 15 04 57 10 42 15

50 116 39 38 00 83 51 27 33 74 43 262 28 4558 15 21 51 10 27 18

56 15 35 47 10 14 19

20 00 119 09 S23 02 40 31 86 21 S19 08 30 04 N 3 05 77 13 S15 47 264 53 N19 43 54 15 47 44 10 03 2010 121 39 43 01 88 50 32 34 79 43 267 17 42 52 15 58 41 09 53 21

20

30

124

126

09

39

45

48

31

02

91

93

20

50

35

37

04

35

82

84

14

44

269

272

41

06

41

40 50 16 08 38 09 44 22

40 IN 09 50 32 96 20 40 05 87 14 274 30 3845 16 28 34 09 25 23

50 131 39 53 03 98 50 42 35 89 45 276 54 37 40 16 44 30 09 09 24

16 58 28 08 56 2521 00 134 09 S23 02 55 33 101 20 S19 07 45 06 N 3 05 92 15 S15 47 279 19 NI9 36 30 17 11 26 08 45 26

10 136 39 58 03 103 50 47 36 94 45 281 43 35

20 139 09 60 34 106 20 50 07 97 16 284 U7 3470 17 31 24 08 25 27

30 141 39 63 04 108 50 52 37 99 46 286 32 3210 17 50 23 C8 08 28

40 144 09 65 35 111 19 55 07 102 17 288 56 310 18 07 23 07 52 29

50 146 39 68 05 113 49 57 38 104 47 291 20 30 10 18 24 23 07 35 31

20 18 43 24 07 18 32

22 00 149 09 S23 01 70 35 116 19 S19 06 60 08 N 3 05 107 17 S15 47 293 45 N19 29

10 151 38 73 06 118 49 62 38 109 48 296 09 27 30 19 04 27 06 58 33

20 154 08 75 36 121 19 65 09 112 18 298 33 16 35 19 17 30 06 46 34

30 156 38 78 07 123 49 67 39 114 48 300 58 2540 19 32 33 06 32 34

40 159 08 80 37 126 19 70 10 117 19 303 22 24 45 19 50 37 06 16 35

50 161 38 83 07 128 49 72 40 119 49 305 47 22 50 20 12 44 05 56 37

23 00 164 08 S23 DI 85 38 131 19 S19 05 75 10 N 3 05 122 20 S15 47 308 11 N19 2152 20 22 48 05 47 38

10 166 38 88 08 133 48 77 41 124 50 310 35 20 54 20 34 53 05 36 38

20 169 08 90 39 136 18 80 11 127 20 313 00 18 56 20 48 61 05 24 39

30 171 38 93 09 138 48 82 41 129 51 315 24 ; 1758 21 04 73 05 10 40

40 174 08 95 40 141 18 85 12 132 21 317 48 1660 21 24 97 04 53 42

50 176 38 98 10 143 48 87 42 134 51 320 13 15

Prab/cms:28. Use Th Air Almanac pages and find

the longitude of an observer whotakes a sight of the sun as it transitshis position at 20 h O0 m GMT, onJanuary 1, 196.1. Try this one

99 A navigator takes a "noon sight" asthe sun transits his position and re-cords the following:Date January 1. 1961Time 17 h 0 in GMTAltitude of the sun in transit 73 02'.Find the latitude and longitude of theaircraft.

30. If the TC of the aircraft is approxi-mately 270'. what large Americancity is the aircraft approaching pro-vided your original position or pointof reference is given by the latitudeand longitude in problem 29. Use allyou have found out to see if you cananswer this one.

31. Shortly after take of from an air-port near a large American city an

aircraft made a moon meridian alti-tude" sight and recorded the follow-ing:Date January 1, 196.1Time 07 h OO rh GMTAltitude of the moon in transit 72 09'.If the TC of the aircraft is 32(1 .

from what city does the aircraft ap-pear to be departing?

Experimcni :"Make a Sextant" measure the altitudeof the moon and Polaris.Ma feria is:large drinking straw pinprotractor threadsmall weight masking tapeGa.Nlard Johnson and I rei rig A d ler , Diseanr the Stars (NewYork : Sentinel. 1954 Direct ions art' used /n permission ofSentinel Books Po 1,1 Aers. l fur,

Proccdarc:With masking tape, fasten the protractorto the straw as shown. The 90 mark andthe arrow which marks the center of the

Figure 21. Simple transit

74

i1i1Sk .....lik)\1111 he ill line Willi the stray fill1 he \\ eight suspended hy tluOad from 11E,

(Till el' of the \\ 11:1..:(. of theProtractor. 05 shmvii. The angle of eloya_lion of a heavenly 1111.01 (til

detHillihed I,V reading front thescale.

l'71o.V.'! DO NOT use this instrumentto sight the sun. as if is never idyiaideto look directly ttl the sun. lIy doing so.you may eaUSC severe damage to your y(s.daimige \vhich may lie immediate in s111,,vases and delayed in others. /X.I/EMBER.'bO .V07' SI1007' THE

.19

.1POt).

I't:e your sextant to shoot the moon(lay or night, at approximately onehour intervals and record your find-ings. At what point, direction. did itappear to have its maximum (deva-t ion ?Vinci Polaris, the North Star, and findits elevation. The elevation of Polarisis approximately the latitude ()I' yourposition. Why is this true? Study thefigure.

Polaris

Zenith

Equatorial

ig ore Etc Nit jot? of Polar ig

Horizon

The celestial navigation presented herehas been greatly simplified. Procedureswhich have greater utility are used byprofessional navigators; they demand agreater understanding of scientific princi-ples and of mat1iematics.

75

n;ivigallim has a future inspace navigalimn. ThDtigh tel ,,1l-1,oad and the use of Speri:d sextants. i1 ishoned that on-hoard navigation and mid-ouse guidance call be accomplished oilspace craft. These instruments ore ON-peeled to lie :Ode to determine the anglebet\veen guide stars and the moon orEarth or other planets to a few secondsof arc.

Even though navigation by celestialmeans lifo: been successfully used for cen-turies. disadvant:tges are evident. Oneis the weather. Yon van1101 navigate by astar vou cannot see. To combat this weak-ness the i'nited States is launching artifi-cial star satellites. the Transit series. forexperimentation on satellite navigation.Navigational information, unaffected byweather conditions, is ftvailable from thesatellite at all times through the use ofa special instrument called a radio sextantor by using time signals and ft radar locat-ing phenomenon known as the DopplerShift.

The Doppler principle was first ex-plained by an Austrian physicist, Chris-tian Doppler, in 1812. Assume a light orsound source is snoring. lie showed that iflight or sound waves are aproaching anobserver, they will reach ldm with agreater rate that they would have had thesource been stationary. This change inrate amounts to increasing the frequency.Ile noted also that there was an increasein frequency when a moving observer ap-proached the stationary source emittingthe way.P but the frequency differed fromthe first case. When the source ot. ob-server recedes from the other, there is it

comparable decrease in frequency.

The principle can perhaps best be ex-plained by considering the case of a tuningfork moving toward an observer at therate of 1650 cm, per second while givingoff vibrations at the rate of .10 vibrationsper second. The velocity of sound is ap-proximately 33,000 cr :. per second. Theactual length of one wave is then,

, where A. reizesents one wave11 length,

v is the velocity of sound,

Figure :T. Doppler's principle

andn is the number of vibra-

tions per second. There-fore.

33,000X

140or 75 cm. (Wavelength)

with the fork vibrating at .1-10 vibrationsper second, (vps), the time required for

e complete vibration is 1 sec. The dis-440

,tanc the fork will travel 1sec. will be

4101650 cm.

d X 1650 cm.-- or 3.75 cm440 440

This means that each wave will be short-ened by 3.75 cm. or each wave will now be.

75 cm. 3.75 cm. 71.25 cm.

The velocity of sound is always the samein air whether given off by a source atrest or while moving

v == nX or n , where

v is the velocity of sound in air, n is thefrequency (vps) , aid A is the wave length.Therefore,

3,000n 163.1 vps. (frequency)

71.25This represents an increase of the fre-quency over that of the source when atrest (440 vps).

Now let us consider an example wherethe observer moves toward the source. Inone second 440 vibrations reach the ob:server plus the number of waves includedin the distance the observer has traveled.

(

) )

ur 1650-1-10 I -HO 22, or 462 vps.

75

This represents an increase of 22 vps overthe frequency when both the source andobserver were at rest.

The equations,n vn _.- , and

V v_

n, n -(1 , where

n is the frequency as heard by a sta-tionary observer, n is the actual frequencyof the sounding body, the velocity of thesounding body and v the velocity of soundin air. n. is the frequency as heard whenthe observer is in motion; v in the secondequation is the velocity of the observer. Inthe first equation, the ( ) sign is usedwhen the sound source is approaching. theobserver; the (+ ) sign is used when thesound source is rez!eding. In the secondequation, the ( ) sign indicates that theobserver is approaching the sound source;the ( ) sign indicates that he is movingaway from the sound source.Samuel Robinson Williams, Foundations of Collrge Physics (NewYork: Ginn and Company, 1937), ,s. 204. Permission fu a,cr thefOrInnill and sampir problems lens AV-Onled by Gina and Omzpany.

Problem:34. A fire engine answering a distress call

is traveling at a rate of 60 feet persecond and sounding its horn whichemits a frequency of 280 cycles persecond. What is the frequency of thehorn as heard by an observer in front 7.of him?

n /ASO cps

)141)11;Figure 24. Approaching pound

Solution:The sound source is approaching the ob-server, therefore,

flyv v,

v, the velocity of sound in air, is 1100feet per second.

n. = cycles per second.

In the tracking of satellites by using theDoppler principle, the ground stationsends out a signal to the satellite. Thesatellite upon receiving the signal immedi-ately rebroadcasts the signal back to theground station. When the satellite is ap-proaching the ground station, the fre-quency received from it by the groundstation is increased due to the Dopplereffect. This difference in frequency be-tween the original frequency and the fre-quency received by the ground station,known as the Doppler shift, can be meas-ured, and from this measurement thevelocity of the satellite can be computed.

Figure 25. Satellite tracking

Let us study the formula,nv

v vto aee how it may be applied to satellitetracking, First, the signals are electro-

77

magnetic waves which trace! with fluspeed of light, so, instead of v, the velocityof sound, the velocity of light, c, will beused. Second, since the signal muss travelfrom the ground source to the satellite andreturn, 2v, must be considered. With thesechanges the formula now becomes,

ncn.c 2v.,

where, n,, is the observed frequency re-turned, n is the original frequency trans-mitted, c is the velocity of light (186,000miles per second), and v. is the velocity ofthe satellite. We can find the Dopplershift, or sometimes called "beat fre-quency", (F) by finding the difference be-tween the frequency returned, n,,, and theoriginal frequency transmit ed, n, by sub-tracting n from both sides If the formulaand simplifying the result.

F = n ncn n, and

c 2v.

F = n n2nv.

c 2v.Now, the difference between the speed oflight, c, and twice the velocity of the satel-lite, 2v. and the speed of light is so small,the denominator, c 2v,, can for aZi prac-tical purposes be assumed to be the sameas the speed of light, therefore,

F = n,, n2nv.

This is one formula, eased on the Dopplerprinciple, that is used to determine thespeed of spacecraft, aircraft, or auto-mobiles. The radar units that you see onthe highways that are used to monitortraffic work on the same principle; thesignal that is received from the vehicle isa reflected signal, however, rather thana signal that has been rebroadcasted.

Here are two problems for you to try.

RADAR

Figure 26. Radar control

Problems:35. A police radar unit transmits a signal

of 100 megacycles and receives a re-flected signal from an auto. If this"beat frequency", n n, is 20 cyclesper second, what is the speed of theoncoming. auto?

Solution:

Given:n n = 20 cycles per second

n 100 megacycles per second100 X 10 " cps = 108

CPS.e := 186,000 miles per second or

1.86 X 10 mi. per sec.2nyF = n' n , or,

202 .. 10 8

. Complete the1.86 10 ' solution.

What is speed of the auto in mph?36. The same radar unit, (problem 42), is

used to check the speed of traffic ina 35 niph zone. If the Beat frequencyobserved from an oncoming ear is 10cycles per second, is the car withinthe legal What is his speed?

A similar technique is applied to findthe speed for tracking of the TransitSeries and other satellites.

Another important phase of trackinginvolves finding the position of the satel-lite in the plane of its orbit. This is im-portant, for, if the satellite is to be useful,the exact position of the zltellite must beknown at all times as welt as the positionit is expected to have at any future time.

The circular orbit has often been sug-gested as possibly the best orbit to use forthe navigation satellites. Assuming thatthe satellite has been successfully placed

78

in an orbit about the Earth, and that itsorbit has been determined through ob-servation by optical and electronic means.to he circular, then its position at a cer-tain time can be computed.

Transmitting Ssteite

Figure'. A satellite of the Earth

First, a reliable reference point must beselected, such as line OEC. By using theformula,

wt.

where 6 is the angle formed at the centerof the Earth, (0) ; w is the angular velocityexpressed in degrees per minute, and t isthe time in minutes. Here is an example.

Example:The tracking of a satellite revealed that thesatellite has a circular orbit and has anangular velocity of 4° per minute. If itsposition was at the reference point C at12 h 30'n GMT, what is its position at 13 '00 in? (by angle measure from the refer-ence point).

Solution:The measure of the Central angle at 0may be found by solving the formula,

0 = wt.= 4° per minute, and t = 30

minutes, therefore= 4° 30, or 120°.

Problems:Find the central al:-gle formed in each ofthe following orbits if:37. 2' per min.; t = 50 min.33. per min.; t 1 hr.39. 1 per min.; t 12 hr.40. 1/1.'- per min.; t 24 hr.41. Explain your answer for number 40.

By using the procedure just explained, theposition of a satellite in its orbit can becomputed and relayed by a ground stationto any aircraft needing the information:

According to the latest publications,navigation by satellite is still in the ex-perimental stage.

Several theories have been proposed re-garding the best way to us::: these naviga-tion satellites. One suggested possibilityfavors placing eight satellites in synchron-

ous orbits. each at an altitude of 22.300miles with orbital velocities <u (i890 milesper hour, and in orbital planes inclinedat an angle of 11.5'' to the equatorialplane. These sal ellites would each appearto remain over a common meridian, travel-ing a path 11.5' north and then 11.5" southof the Equator. Another proposal wouldinvolve a system of four satellites in polarorbit with orbital planes at 45'' intervals.Still another system being studied wouldinvolve what is described as a large num-ber of satellites distributed with randomphase about four different orbits at analtitude of some 6000 miles, supported bysix ground stations stategically locatedabout the globe.

Many problems remain to be solved re-garding the satellite's equipment and theequipment of the would-be users. I wouldSuggest that you look further into thisproblem of navigation since many progres-sive and useful ideas come from youngscientist such as you!

700

\-7

0;0

V= 4

C.- -***"-

Chapter V

THE RIDDLE OF MATTER AND MOTIONby

Demald R, 111a,rcy3Iont gooier!, County Public Schools

Rockville, Maryland

ABOUT THIS CHAPTERWe are born and reared within the reach (the "field") of a force we call gravity. It seems

to pull all masses towards the center of the Earth. Jack and Jill fell down the hill; HumptyDumpty fell off the wall; and Darius Green crashed his flying machine. Their painful expe-riences added to our own, make us so familiar with the "down pulling" force of gravity thatwe can hardly imagine living without it. Yet, as common as it is, gravity is one of the mostchallenging riddles of nature. Consider, for a moment, the fact that we can block or screen outother "field forces" such as magnetism and electrostatic fields, but nothing yet known canblock or even weaken the field of gravity. In aviation and the space sciences, we have beenable to counter-act gravity by using jets and rockets to push or "lift" in opposition to the"pull" of gravity; but gravity is still present, even with the orbiting satellite. You will have agreater understanding of the nature of falling objects after you have read and experiencedsr :ne of the problems encountered by Galileo in his long search for the secrets of gravitation.

81

THE TEACHER OFALEXANDER THE GREAT

Greet;e The Fourth Century B. C.

Carefully feel the difference in weightbetween two rocks (or coins) of consider-able difference in size. Gravity is "pull-ing" noticeably harder on the larger one.If released -Du might "logically" expectthe rocks fall with speeds related totheir weightsthe rock which is twice asheavy falling twice as fast. Now, dropthe rocks together several times. Doesthe larger one always hit first or do theyseem to fall togetoer? a Place both rocks(or coins) in one hand and toss them afew feet to the front several times. Doyou get the same results as before? b

Your reply should Le checked each time by re-ferring to the lettered answers in the answersection. The greatest understancling will cometo those wha, provide their own answers beforechecking.

More than two thousand years ago, theGreek philosopher Aristotle (Air'-iss-totle) was convinced that heavier ol-jectsshould fall "quicker" than light ones. Hewas such a great teacher and writer thatthis thinking was accepted without ques-tion for over fifteen hundred years.

Figure 1. Aristotle

It was sometimes argued that when ob-jects of different weights appear to falltogether, it was only because the fallingmotion was too fast for accurate observa-tion. "Certainly you can see that a stonefalls faster than a featherthen whyshouldn't a large stone fall faster than asmall stone?" Read more about Aristotleand you will find (as is often true). that

82

most of his teaching was more sound. Butit was not pUt to use for almost a thcq-sand years. It was misunderstood. Dui-ing all those years written aut7-,erity wasaccepted without careful -observation andtesting (experimentation).

The early Greek philosophers wereamazingly close to our present understand-

of the nature of matter and motion.Their knowledge was even more extraor-dinary in that it was acquired with "vir-tually no benefit of experiment or care-ful measurement." "The ancient philoso-pher6 thought a great deal about the WHYof phenomena, but they seldom experi-mented to find out the HOW or 110WMUCH." They lacked the laboratoryequipment to demonstrate and to test theirtheories.

CHALLENGE TO THE PAST

Holy -- The Sixteenth. Century A. D.

In 1581 a seventeen year old Italian boy,Galileo Galei, arrived at the University ofPisa to begin the study of medicine as en-couraged by his father. It soon becameapparent that young Galileo's interestswere more in the physical sciences thanin medicine. His intense curl.-;iiy madehim more interested in the events hap-pening aoound him which could not be ex-plained with existing knowledge.

A Lamp Lights the WayIt has been written that Galileo enjoyed

sitting in the great cathedral, during timeswhen few people were present, to "th'ilkout things." It was during one of thesevisits that he watched a "warder" lightone of the oil lamps that was hanging onthe wall from a chain. When the lamp wasreleased it began to swing back and forthas a pendulum Galileo was fascinated bythe lamp's graceful motion. During thisperiod of contemplation his acquaintancewith medicine suggested the use of theheart's steady beat as a means of tirOngthe swings of the pendulum. He reasonedthat this would permit him to "see" withgreater depth and clarity than the eyealone.

Figure Goli:co owl the swirigiug lomp

glide back and forth. 'rule time of one-round-trip- of (he pendulum "bob- iscalled thQ pendulum's PERIOD. Youmight use a lock or some 011)01' dense andheavy minter as a bob for your pendulum.Suspend the bob with a cord at least twometers long and the motion will be easierto observe. Get permission to drive asmall nail into the top edge of a doorframe. where it cannot be seen, as a sup-port for your pendulum.

The swinging lamp observed by Galileoprobably didn't swing through an arcgreater than sixteen degrees. and neithershould your pendulum. Compute or ex-periment to estimate the are distance forit two. meter pendulum.'

Use a protractor and rule to make a scale draw-ing .from which you can measure the arc with astring or tape measure.

HOW many heart beats does it take foryour pendulum to swing -to-and-fro" one

Figure 8. Tlw Pulsi logia time?

Try to capture a portion of Galileo's de-light by making a pendulum and usingyour pulse to check the time it takes to

83

If you can't take your pulse at your wrist,,youcan easily feel the pulsation of the carotid ar-teries by gently grasping the throat just belowthe jaw bone.

The period can be measured much moreaccurately by timing- it through ten con-secutive periods and taking one tenth ofthe total time.

Galileo found a very practical use forthe pendulum by blending his knowledgeof medicine and physics to invent the'pulsilogia-, which was simply a stick \Vitha string and bob attached of sufficientIt ng-th to swing with it period or half pe-riod equal. to it normal pulse .beat. Thelength could be zuljusted for comparingslower or faster pulses by simply windingthe string around the supporting hook soas to change its length. AIarks were madeon the stick as a scale of comparison. How(10 you think physicians took a patient'spulse before the puisilogia acid how dothey take it today? ,

You might wish to use it stop watch, aclock with a second hand, or a metronometo make more accurate measurements.'

-2R0 NTAINER

FAUCET

SYPHONHOSE -12-

Galileo used a water clock, for furtherstudy of matter in motion. You may wishto construct a water clock similar to theplans shown below ..-ts a means of making.your observation mole meaningful.".

PENDULUM. RHYTHM.AND RATIO .

Which or the three fact ors labeled on Fig-ure (To you think have :tit effect )11 theperio of a pendulum? Test your predic-tion by varying each of these factorswhile holding the others constant. Startby winding up the extra cord so as to havea pendulum with a 21.5-coniimeter length(from ccidi of bob to support). Reduce

Electronic Met l'01101110;: are available whichbare blinking lights and audible signals,

"The handle of a gallon bleach jug is sawedoff uf Mr top and forced to bend down as aspout by folding in the plastic just beneath.

WATER CLOCK OR PHOTO STOP CLOCK

fABOUT 1 /8 IN HOLE

F;

CamFLOW

CONTINUOUS ACCUMULATIONOF TIME

RHYTHMIC TIME INTERVALS

PIN HOLE

...411111111

WATER CLOCK (DRIPPING) OR METRONOME

Figure 4. Rythinial time intervals and continuous accumulation of lime

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411C STANCE../4

MASS OF BOBFigure 5. Pendulum

or increase your chosen variable (the arc,the mass, or the length) by using the setof "square numbers" (0, 1, 4, and 9) asfactors. Make a rough graph of your re-baits with the period (T) plotted on thehorizontal axis (X axis) and the chosenvariable on the vertical (or "Y") axis.rAlways multiply the "square number" factorby the first value chosen for the variable inorder to get new values.

You might wish to increase the length byextending the set of square numbers onthrough 16, 25, and 36 if you can find ahigh enough support. (CAUTION: Re-quest assistance from the school custodianin attaching these longer pendulums.)

What conclusion is suggested both bythe effect of varying the mass of the pen-dulum bob and by the results observed inthe rock or coin experiment performedearlier? g

What pattern of change do you see inthe results of this experiment which indi-cates a "relationship" between the pendu-lum's Length L and period T? hGravity is the "restoring force" which causesthe pendulum to accelerate after having stoppedat each end of its swing. Check answers onpage 20.

85

This relationsh.p may be stated in the"shorthand" language of algebra as L « T2which reads "the length is proportional tothe period squared" or reversed toT Vt. If either the period T or thelength L change, the other must have alsochanged, and the amount of this changecan be found by comparing the old quan-tities to the new by stating ahem as com-parative fractions or RATIOS. just as youcould compare three to four with the frac-tion (:si).

Ratios may be equated to each other ifthey represent comparisons of quantitieswhich are definitely related by a specificpattern of change, such as the obvious pat-tern between the length of the pendulumL and the period of swing T. Therefore,the ratio which compares the "old" lengthL to the "new" length L can be writtenLo/L, and is equal to the ratio comparingthe "old" period of swing TO to the "new"period T, ONLY if the pattern of relativechange, which was observed experiment-ally, is written into the equation. So, theratio L/L. equals the ratio T'/T.", or theold length is to the new length as thesquare of the old period is to the sqt!re

the new period. Such statemeW ofequality between comparative fractions(ratios) are called PROPORTIONS; theyare very useful in describing natural law,and as tools for finding an unknown quan-tity which perhaps cannot be measured di-rectly.

The proportional relationship betweenchanging the length of a pendulum and thechanged caused in its period of swing cannow be written:

OLD LENGTHNEW LENGTH

LOr

OLD PERIOD'NEW PERIOD'

To2

To2

'f any one of the four quantities is un-known while three are known, the un-known can be found by "solving the equa-tion" algebraically.

Use the above equation to find the length(L.) a pendulum should be for a "grand-father" clock in which the one way swing

from "tic" to "tot" tLkes exactly one sec-ond. Such a pendulum is called a "secondspendulum". Remember that from "tic"to "too" is only a half cycle: therefore, onesecond is oniy one half the pendulum'speriod (T).* Use the length and periodfrom one of the pendulums which youthink was accurately timed in the previousactivity as a -standard" to.represent the-old" length ( L) and period (T) fac-tors in the equation) (The new period Tis 2 seconds).

Supplemental ProblemsUse the proportional relationship be-

tween a pendulum's length and its periodto solve the following problems (let the"seconds pendulum" of the last exerciseserve as your "standard" for stating newratios) :

1. What will the period be for a pen-dulum of 3.92 meters length?

Figure 6. Angel Falls

86

Colorado's Royal. Gorge bridge couldsuspend a pendulum with a 35 sec-ond period. 1 -IGw deep must theRoyal Gw.gc, be?What would be the theoretical periodof a one mile pendulum?

1. Is there a vertical drop any ,:here onearth where pendulum could be sus-pended so as to have a period orabout one minute?

5. In 1851, the French physicist JeanFoucault (Foo-Koh') demonstratedthat the earth rotates by suspendinga large iron ball on a wire about 200feet long with a "free swiveling-hook. The pendulum continued toswing, in one direction with respectto space, as the floor beneath itturned hour by hour with the Earths'rotation. What was the period ofFoucault's pendulum?

THE LEANING TOWER OF PISAGalileo's pendulum indicated that heav-

ier objects do not fall faster, as most peo-ple had believed fo7 almost two thousandyears ; but many would not accept the "fall-ing" of the pendulum bob as being directlyrelated to the free fall of unrestrainedmatter. The story is told that in order tosettle this argument Galileo staged a pub-lic demonstration in which he dropped amusket ball and a cannon ball, of aboutone pound and one hundred pounds respec-tively, from the famed Leaning Tower ofPisa. There is no record of this demonstra-tfon ; but such records may have been de-stroyed, because the idea of "equal fall"was vi,-;ry unpopular with the ruling powersas it challenged the established and offici-ally recognized order of nature. It is re-corded that a pro-Aristotelian scholar usedthe Leaning Tower during Galileo's life-time to demonstrate .uncqual fall. Thisdemonstration was probably performedwith one ball of solid iron and the otherof wood or sheet metal. What role wouldair have in such an experiment; and whywouldn't it have influenced Galileo's twosolid metal balls to the same extent?

* In 1657 the Dutch astronomer, Huygens (Hi'-gunz) used Galileo's discovery to produce ac-curate, pendulum-regulated clocks,

(Cr

-.-

Figure 7. Leaning Tower of Pisa

Drop a coin and a dollar bill, or a stoneand a piece of paper, at the same time.Now, tightly fold the dollar bill or paperin half five or six times an drop themagain.k In falling great distaires throughair the more dense objects would eventu-ally gain greater velocities than the foldedpaper, due to their greater ability to shovethrough the air as it compresses in frontof them at the greater speed attained inlong falls. The same factor (frictionaldrag due to air resistance) would havecaused the wooden ball to fall behind theiron ball when dropped from the LeaningTower.

87

Yon may perform the previous experi-ment with a large c()in and a small piece ofpaper, preventing air drag On the paperby laying it flat (no corners sticking up)on top of the coin.* same frictionalrestraint of the air "rubs" the heat shield

.--% ...." /:/ ,,',46/Gicowdre,--------- //'---

A % -1- ',- /"'..-= f.

,..,=.

Figure H. Re-entry

of returning space vehicles and the sur-faces of meteors until they reach the in-candescent -.emperatures cause theirfiery entry into the Earth's atmosphere.Air resistance permits the parachutist toglide to earth at about 15 mi./hr. (22 ft./sec.) rather than the nearly 120 mi./hr.velocity attained by a "free falling" man.Sharpen your skill in using proportionalratios by calculating the velocity in feetper second attained by a failing "skydiver" using the three velocity values ofthe last sentence as your three knownfactors)

Figure 9. Sky-diver

* A "feather and guinea tube" will permit oneto observe the free fall of a feather and a coinin the absence of air.

LEANING TOWER ACTIVITYYou may not have a leaning tower from

which to demonstrate "equal fall", but youprobably can get permission from theprincipal to use the school flagpole if theproject is to be supervised by a teacher.*You are more likely to be give.: permis-sion if:

A. You have proven yourself to be aresponsible student in the past.

B. You explain that no one will beclimbing the pole.

C. You make it clear that only SOFTobjects which weigh less than threepounds will be hoisted up the pole.Permission is granted then proceedIf

as follows:1. Prepare a paper carton of the type

used for canned goods (about7" X 14" X18") as shown in Figure 10.Secure three or four heavy canvasbags of about one quart capacity.The change bags used by banks andretail stores are ideal and sometimesare given away when soiled or youcan purchase canvas or ticking andmake them. Put about one pint ofsand in one of the bags and dry beansin another. Close the tops securelybut allow plenty Of room inside toprevent splitting. upon impact.

3. Attach the box to the flagpole chainwith a cord tied from the broomstick to the chain at the lower end.

.1. Attach the to of the box by pullingthe chain down through the slit cutin the upper end ; and placing a longpencil or thin brittle stick throughthe loop, .lust under the top edge. toprevent the chain from pulling out.

5. Tie a steel measuring tape to thechain. just below the box; and hoistthe chain high enough to tie a hand-kerchief. as a marker, at one or bothpoints shown in the drawing, depend-ing on the pole's height.

6. Load the bags of sand and beansand hoist them steadily to the top(without jerking). The bags maybe (lumped together by a gentle tugon the chain which releases the topof the box.

88

7. Repeat the demonstration severaltimes and try to verif'; the time offall to the markers with the aid ofa "seconds pendulum". You couldhave an assistant sound out therhythm of the seconds pendulumwith a snare drum."'

Calculate the arcrogc speed of the fall-ing lings up ti the time of impact.* A stopwatch, or our water clock, may he usedto measure the time tor, 1l-ow can youdetermine the distances fallen by measur-ing the shadows of the flagpole and a verti-cal yard stick? "

By comparing the distances fallen du-ing the first and second intervals, it is ap-parent that the speed of fall is increasing(or ACCELERATING). The rate of this"speeding up," however, is not so appar-ent, except for the clues given by the loca-tion of the handkerchief, as shown in thedrawing. After one second of falling thebags have moved 16 feet; so their nurturespeed was 16 feet per second during the1st second of fall. What "instantaneous"speed did the bags have at the 8tort of the1st second? It seems logical to thinksince the speed "averaged out at 16 feetper second during the whole 1st second,from a beginning speed of zero feet persecondthat the final speed should be asmuch greater than 16, as 16 is greater thanzero; or 32 feet per second. Notice thatthe bags fell (48 minus 16\ or 32 feet fur-ther during the 2nd second than (luringthe 1stthis also suggests that the speedis increasing :12 feet per second for eachsecond of fallingas it did during the 1stsecond in going from zero feet per second

If you happen to live near Niles, Illinois, youmight arrange a trip to the "Leaning. Tower ofNiles" for your reenactment of Galileo's demon-stration. The tower Niles is a good replicaof the Pisa tower and is open to the publicfree of charge. It was built as a water towerin 1920 and is about the height Of a ten-storybuilding while the tower of Pisa stands twiceas high.

"It is often considered best to use the wordvelocity rather than speed when referring tospeed in a particular direction; however, wherebrevity is essential to understanding, the one-syllable word seems the better choice.

1- At the very beginning of the first second thebags were not moving at all; so their speedat that instant would he . . .

BROOMSTICK

771-806 0-65- 7

Sec page 95 for a related free fall activity

89

to 32 feet per second. The speed, then, ischanging 32 feet per second during thepassing of each second of time. Thus, therate of change of speed (or ACCELERA-TION ) is 32 feet per second per second.This same acceleration may be abbrevi-ated as 32 ft./secsec. or 32 ft./am-2 Asmall letter "a" is usually used as a sym-bol for Acceleration; however, when theacceleration is caused by gravity it is cus-tomary to use the letter 'g "; so, in thisexample g = 32 ft./sec.2

6. How far should the bags fall duringthe third second if the accelerationremains constant? (assume the poleto be high enough to permit this)

7. At what distance should the thirdhandkerchief be from the box tomark the limit of fall after threeseconds?

"DILUTED GRAVITY"You have surely observed, just as Gali-

leo did, that the motiort of free-faLingIxdies is too fast for detailed study. Galileoreasoned that the rapid motion of a free-falling ball could be restrained by allow-ing it to roll down an inclined plane. Thetime of fall would then be lenghtetted("diluted") by a factor.proportional to theslope of the grooved board which he usedor an inclined plane. Even though side

rs, such as friction, prevented Gali-leo from discovering the actud whount ofincrease in velocity (or acceleration)

STONEFILLED

WATERFILLED

caused by the pull of -nravity; he was suc-cessful in making a great discovery con-cerning the relationship between the timeof fall and the distance fallen.

With a little patience, you should be ableto repeat a form of Galileo's "dilutedgravity" experiment which may enable youto observe the orderly relation betweenthe time an object falls and the distanceit falls. Galileo, in his relentless quest forknowledge, required years of study andhours of patient repetition of experimentsin order to zentually see through theclouds of side effects and uneven measure-ments which usually guard nature's se-crets. In the interest of simplicity and ofsaving time, you may find it convenient touse the following "set-up" for this experi-ment:

The inclined plane should be a goodstraight board about six or eight incheswide. Position books under the hoard soas to raise one end exactly three inchesabove the door at a distance of six feetfrom the other end. Compare the heightof the inclined plane with its length bystating it as a ratio.° How do you thinkgravitational acceleration (or "g") will beaffected by this set up? P

Use a glass jar or bottle with eitherstraight or concave sides tilled with a fairlydense material such as crushed stone, sand,or water. The jar or bottle must haveexactly the same diameter at both the.shoulder and the base if it is to roll true.

SECONDS"BEAT"

TOWELBUFFER

3 IN.6 ft.

Figure 11. Inclined plane used to ,*-dy gravity

Practice releasing- the jar at the starting1111 e. hy lifting your hand staight up( without pushing) until you can releaseit right on the seconds heat of an au-dibly timing device (metronome or dri,ping water). Position four alert assist-ants along the board, with chalk in hand,ready to mark the position of the jar afterthe first, second. thiol, and fourth sec-onds respectively. Repeat the operationlour times. rotating the positions of theassistants, so as to have a set of fourmarks at each position, viiich call heroughiv averaged out with single marks.Measure aml tabulate the distances fromthe starting. line to each mark.'i Can youdetect a pattern suggesting a relationshipbetween the distance rolled during the firstsecond and the other distances?Try dividing the distance traveled in one sec-ond into the distances traveled in two, three,and four scowls. Cmnpare 11w results.

Make a graph with the time plotted on thex axis and the distance on the yCompare this graph to graph "f" of the re-lationship between the pendulum's lengthand period, They should have about thesame shapea parabolic curvewhichshows not only that the distance factorincases with the time factor, but thatthis increase is greater than the corre-sponding increase in the time factor. Itis an uccricrated increase caused by the"pull" of gravity.

Figure 12. Student preparing graph.

From an analysis of his inclined planeexperiment, Galileo was able to announcethat the distance an object falls is di-rectly proportional, to the square of theelapsed time (or s 0: t'2).

91

Refer to the tabulation of data obtainedfrom the inclined plane activity (item ""in the answer ;:ection). The distances inthe table are cumulative from the instantthe jar or bottle started to roll. What werethe dktances traveled in rfIch of the lourseconds ?' Or you-se, -the distance traveledin each second'', asked for in the last ques-tion. is the average speed or velocity dur-ing that particular second. How muchdoes the average velocity increase from onesecond to the next? " This increase ofvelocit from one time interval to the nextis called acceleration; so the answer toquestion """ is the acceleration in inchesper second pr')' sreood (or in :sec.2) for therolling jar or bottle. Notice that the ;lcceleation from one second to the next isalways the same, From this observat ion.Galileo was able to announce at second ma-jor principle concerning gravityMat th,,aecc/cratioa of a faUiall hotly is constant.lie had demonstrated with the inclinedplane that the acceleration was COliStallt,for a rolling hall; and he reasoned, cor-rectl, that free-fall was similar to the mo-tion of a hall on a very steep and smooth

ACCELERATION ISA CHANGE IN VELOCITY

The acceleration, (change in rate ofmotion) viiiCh the force of gravity exertson an object here on the Ea,,th's surface issuch a coalition experience that we oftenuse it to describe accelerations due toother forces. We speak of booster rocketsaccelerating at so many "g's" causing theastronauts and equipment to experience acrushing "pull", many times that of grav-ity alone, as the booster presses Upwardagainst them. You may experience asimilar sensation, to a small degree, whenriding in an elevator.

There is no record of Galileo having de-termined the actual of g, the down-ward acceleration due to the Earth's grav-ity. However, he certainly set the stagefor its later discovery, with the develop-ment of better equipment and proceduresfor exper"-,ientation. Today "g", the ac-celeration to gravity, is measured di-

Figure 13. Astronaut in seat during launch

Lk& AL

elevator ride

92

reedy by scientists in the Nationai Bureauof Standards by accurately timing the free -fall of a quartz rod.

Jf

,..=1111V..66Figure 15. Measurement of acceleration of gravityPhotograph courtesy of The National flu rca u of Standards, UnitedStates Oeparhnepl of Commerce.

Since gravity is the "restoring" forcewhich causes a pendulum to vibrate, anychange in the downward pull of gravitycauses a change in the pendulum's period;and so, pendulums have been the standardmeans of measuring g for years. If g isgreater the pendulum bob "falls" faster;therefore, its period is shorter. Portable"gravimeters" are used by oil prospectorswhich measure g by the amount a delicatespring or fibre is stretched by the weightof a metal bob. Such instruments havebeen used to make gravity surveys of dif-ferent regions which have shown that gis not exactly the same at all places onEarth. The difference in the measure ofg has presented a problem in determiningworld records for athletic events: a broadjumper in Canada falls a little faster to-ward the ground than a jumper in Mexicoat the same elevation, because g is a littlegreater as you approach the poles of theEarth.

1

Figure 16. Broad jumper

MEASURING "g"The following- activity will enable you

to make a rough measurement of g foryour locality. The activity is based di-rectly on the principle of the pendulum asdeveloped by Galileo and is, in fact, asimple (but ingenious) combination of apendulum and a free-falling metal haft'''.The fall of the metal ball is intercepted bya wood strip about 120 cm. long, swingingfrom a loosely fitting nail as shown in fig-ure 17.

The pendulum's period is first found byusing ti clock to time a series of swings (atleast 30 periods). A single thread . fas-tened to the ball and passed over two ni.ilsand down to the strip so as to hold itaside as shown. Hold the ball away fromthe board and thoroughly blacken it witha candle. The candle may then be used toburn the thread so as to release both theball and the pendulum simultaneously. Theblackened ball will mark the strip at thepoint of impact so that the distance fallenby the ball. in one quarter of the pendu-lurn's period, can be measured directly. Theacceleration due to gravity can then hecalculated with Galileo's fmmulit for con-stantly accelerated motion:

s 12 a t2 or for free fall: s 1,:) gwhere s is the distance, fallen as measuredand 't is the time of fidl (or one-fourth thestrip's period).

PROJECTIONIn 16-12, the year of Galileo's death in

Italy, Isaac Newton was born in Englandand was destim.-(1 to continue the searchwhich led eventually to his discovery of

Variations of this activity are found in severalphysics' texts and the UNESCO Sourer Bookfor Science Teaching, p. 125.

Figure 17. Apparatus for measuring "g".

93

thr unirc rsa law Of it a ion . Nexqonsurely must have had Galileo in mind \vitenhe protested to those who would idolizehim: "If I have seen farther than others.it is by standing on the slumIders ofgiants."

Each g-eat disco.,,ery concerning gravityhas revealed new riddles along withunderstanding. In this century the Ger-man-American scientist and mathemati-cian, Albert Einstein, has modified New-ton's statement of the nature of gravita-tion with his "theory of general relativity"and has questioned the very existence of a"force of gravity" as being necessary tocause the acceleration of falling objects.His "principle of equivalence" states that11(1 observation or measurement can dis-tinguish between the effects due to gravityand those which would be caused by theaccelerated movement of the observer'ssurroundings.

Visit your school or city library and findsome of the hooks that are listed in the

94

bibliography. You will find them very in-teresting and the time invested in themwill greatly increase your understandingof gravity and motion.

111 ALr -G(1-e.

E S7'E ,N1 i = ate-e

ESSENTIAL TOOLSSupplemental Activity

A FORMULA is a short hand deviceuseful in solving a problem. It is an ab-breviated statement of a natural law asobserved and carefully tested by scientistsand mathematicians.

Take a string and wind it one timea jar lid or coin to form a circle.

Cut the string at the point of overlap andstraighten this "circumference" to form astraight line. Now. stretch this "circum-ferential" string back and forth across thediameter of the lid or coin as many timesas it will reach. How many diameters arein the circumference? Repeat the processwith a coin or lid of a different size?

Figure 20. String and lid

You have been comparing diameterswith circumferences by diriding the cir-cumference c by the diameter d. Such acomparision by division may be written inany of the following ways: (DT, c d, or

A RELATED FREPotatoes or blocks are fastened to a

light rope at intervals of 16 units, 48 units,80 units, etc. and then the rope is hoistedvertically with the greatest interval beingfarthest from the ground. An old washtubis placed beneath the rope as a soundingboard. When the rope is released, the

c.:d; which are simply three ways of writ-ing in symbols "How many times does thediameter fit into the circumference." Acomparison of two quantities by divisionis called a ratio. Ratios are usually writtenas fractions such as c/d; of course, thefraction may be changed into decimal formby performing the division.

,Vith the string and coin, you have seenthat the circumference is always about 3and 1/7 times as long as the diameter, re-gardless of the circle's size. The ratio isapproximately 3 1[1, 22/7, or 3.14 and iscalled a "constant" because the ratio of thecircumference to the diameter neverchanges. This particular constant is use:1so often that it has been labeled with theGreek letter (pi). We define 77 as theratio c/d.Thus, the natural law concerning the re-lationship between a circle's diameter andits circumference can be written as aformula: c/d = v, or c = 77 X d, or d c /r.If either c or d is unknown, or not easilymeasured directly, it can be approximatedby algebraic solution of the equation madeby simply substituting numbers for thesymbols in the formula. Use the ratio "v"to approximate the following:

8. How far does the Earth travel alongits nearly circular orbit in one year?The mean distance from the sun tothe Earth is about 93 million miles.Use 3.1-1 for your approximationof 7r.

9. What is the approximate thicknessof an oak tree whose "girth" is tenfeet? Use 22/7 for an approxima-tion of v.

You are not breathing deeply of life unlessyou can enjoy such simple demonstrations oftruth.

E-FALL ACTIVITYpotatoes or blocks fall with constantly ac-celerating 21 velocities so as to arrive atthe tub in rhythmatic order. If the unitsselected are feet, of course, the potatoesimpact on the second. (adapted fromSutton's Demonstration Experiments inPhysics)

951 qb

Chapter VI

THE MEASURE OF SPACEby

Ned R. GehrisScience Teacher

Plymouth- IV hitemarsh Joint School System, Pennsylvania

ABOUT THIS CHAPTER"Astronomy compels us to look upwards and leads us from one world to another."Plato

Until a few centuries ago man knew only one world, the planet on which he lived. Fromthis small world, which is measured in numbers well within our understanding, we look to thesky in the search for more knowledge. Until the first telescope was used by Galileo in thesixteenth century, man thought that the Earth on which he lived was so important thateverything in the sky revolved around it. With the use of the telescope, Galileo soon realizedthat Copernicus was correct when he said that everything revolved about the sun. This wasunbelievable to the people of that time. With advances in astronomy, the sun and its solarsystem, of which the Earth is a part, were found to be a part of a huge galaxy. When stillother galaxies were discovered, the Earth seemed smaller.

You have already been taught to understand things in terms of measurement; bydescribing the beginning and the ending point of the object in question. But are you able toconceive something having no beginning or ending points? Can we know the boundaries ofsomething the measure of which we cannot even begin to describe? Unlike men of centuriespast, we are now able to explore and venture into the space around us. But, with everyquestion answered, more cuestions arise.

971

AN EASY CONVERSIONPROCESS

Many times, even in your daily :Activi-ties, you are required to change the units ofa measurement to units of another. It maybe as simple as finding the number of eggsin a given quantity of dozens, or changingfeet per second to miles per hour. The keythought is knowing p.nd remembering theunits you are given and the units you needto find.

In your mathematics class you havelearned that multiplying a quantity by onedoes not change its value. There are quan-tities which can be substituted for one.The following are a few of them.

1 dozen 12= 1 or ,112 1 dozen

5,280 feet7-= 1 or

5,21

8m0if l

ee

1 mile et

60 seconds 1 minute- 1 or1 minute 60 seconds= 1

2.54 centimeters = 1 inch1 inch Qr 2.54 centimeters

The above unities and others are the basesfor conversion from unit to another.

If you wanted to find the number ofhours in one week, do you know whetheryou should multiply or divide? Follow theexample below to see if you were correctin your Choice.

7 days 24 hours1 week X 1 week X 1 dayThe week

and day units can be eliminated by "can-cellation" leaving only the desired unit.Think of the expression as:

1 week X 7 days X 24 hours1 week X 1 day

Dividing by 1 week yields:

1 X 7 days X 24 hours1 X 1 day

Dividing by 1 day yields:

1 X 7 X 24 hours1 X 1

Having taken care of the units, the re-quired calculations are clearly shown. Inthis particular case the calculations wouldbe 1 X 7 X 24 hours = 168 hours.

99

The above example was quite easy, sotry the more difficult following- example.Calculate the number of centimeters in 0.5mile. (Hintremove the denominators bydividing first by 1 mile then by 1 kilo-

1.61 kilometersmeter.) 0.r, mile X X1 mile100,000 centimeters

1 kilometer Again the mile andkilometer units are conveniently elimi-nated leaving oniy the desired centimeterunit. The calculations are as follows:0.5 1.61 x 100,000 centimeters80,500 centimeters.

A still more difficult conversion mightbe that of changing the units for a rate ofmotion. Suppose an European journalpublishes an article stating that a sizablemeteor falling through our atmospherehad a speed ( :1 50 kilometers per second.For you to best understand this speed youwould probably have to ch?,nge it to milesper hour. This is done in the followingway:

50 kilometers 3,600 seconds1 second 1 hour

.1 mile1.61

. Which units remain when

you "cancel'? By following through withthe calculations you should get a speed of111,801.2 miles per hour.

You and your friends can think up sev-eral more of these conversions beforegoing farther with this booklet. .eft :r alittle practice you will find it easier towork the problems by setting them up inthe above mentioned way when possible.Try different methods. Find one that youunderstand then use it for convertingfrom one system to another.

DISTANCESIf the distance from the Earth to our

moon at this moment is 238,857 miles, areyou able to calculate the distance in kilo-meters? How long would it take a satel-lite to travel from the Earth to the planetVenus if the velocity of this satellite is 10kilometers per second and it must travela distance of 64,800,000 kilometers? Whatwould be the velocity of a satellite in milesper minute if its circular orbit was 28,260

Figure 1. Satellite distance

miles long and it revolved around theEarth every 118 minutes?

All three questions mentioned above areconcerned with measuring one of severalquantities. The scientist, as well as your-self, is concerned with measurement. Bothyou and the scientist then use the meas-urements to describe what is present orwhat is happening at a particular timeand place. (List several quantities thatyou and a space scientist might wish tomeasure.)

Before we can speak of velocity andacceleration, we should first be concernedwith the distance between two givenpoints. Even though there are many unitswhich can be used to describe a certaindistance, we will be mainly concerned withthe metric system of measurement. Know-ing the prefixes to the most commonmetric units can be a great help to you.The meanings are as follows: kilo = onethousand (1,000); centi = one-hundredth(0.01); and milli = one-thousandth(0.001). Table 1 shows metric equivalentswith the abreviations. The meter is thebasic unit. Table 2 shows metric and Eng-lish equivalents. Complete tables 1 and 2.Think: Why do you not need to completethe darkened spaces?

Many countries on the Earth are usingthe metric system. So until the UnitedStates adopts this system of measurement,you will need to be able to convert dis-tances from one system of measurement tothe other.

100

Problems: Refer back to your completedtables. Remember the meaning of kilo,centi, and milli)

1. The zodiacal light is believed to becaused by sunlight reflected by a ringof small dust particles around the sun.If these dust particles range in sizefrom 0.001 to 1 millimeter in diameter,what is this range of size in (a) ,eenti-meters, and (b) inches?

2. The passive Echo II satellite bas asatelloon skin 0.0007 of an inch thick,which is only a fraction as thick as ahuman hair. What is this thickness in(a) centimeters, and (b) nillimeters?

3. If the diameter of the nueleus of acomet is 1,4 kilometers, what is thisdiameter in (a) meters, (b) feet, and(c) miles?

4. TIROS I (Television Infra,Red Obser-vation Satellite) transmitted Nviltlierinformation to receivers on the Earthfrom an orbital range of 428.7 to 465.9miles above the Earth's surface, Whatwas this distance range in (a) kilo-meters, and (b) meters?

5. Echo II is a passive satellite that re-flects radio-waves sent to it instead ofreceiving and transmitting as an ac-tive-repeater satellite relays informa-tion. Echo H has a diameter of 135feet. What is this diameter in meters?

6. (a) If the diameter of dwarf stars 'sgenerally between 1/2 and 4 times the

TABLE 1.Metric equivalents

Centimeter Millimeter1 Kilometer

km

1 Centimetercm

TABLE 2.English-metric equivalents

English to metric

1 Inch

25.40 Millimetersmm

Centimeterscm

0.0254 Meterm

1 Foot

300 Millimetersmm

Centimeterscm

0.30 Meterm

1 MileMeters

m

1.61 Kilometerskm

Figure Tiros

101

Metric to English1 Millimeter

mm0.039 Inches

in

1 Centimetercm

Inchin

0.033 Footft

1 Meterm

Inchesin

3.28 Feetft

Milemi

1 Kilometerkm

3280 Feetft

0.62 Milemi

Earth's diameter (7,913 miles), whatis their range of sizes in kilometers?(b) The visible diameter of the sun is864,000 mites. What is the visible di-ameter of the sun in kilometers?(c) Betelgeuse (beRle-juice), a super-giant star, has a diameter about 450times the diameter of the sun. What isthe diameter of Betelgeuse in kilo-meters?

7. The Earth's magnetic field blends withthe interplanetary magnetic field atabout 100,000 kilometers above theEarth's surface. What is this distancein miles?

and (x) is the x-coordinate, the focal point(f) can easily be found. Figure 6 showswhat is meant by the above terms, andhow a parabola differs from a sphere.In figure 6, assume the focal length ofthe parabolic mirror to be three. You canthen assign a value to (y) , square it. andsolve for (x) . These numbers are thenplotted on the x- and y-coordinates.

Problen11. The 200-inch mirror of the Hale tele-

scope is coated with a very thin mo-lecular layer of aluminum whichserves as the reflecting surface. Findthe focal length in feet and in metersof this telescope if x = 0.9 feet wheny = 10.0 feet.

IS. Find the focal length of a parabolicmirror in a do-it-yourself telescope ifx 0,5 inch when y = 6 inches. Whatis the focal length in centimeters?

Figure 7. Orbiting Astronomical ObserratoriJ

16. The planned orbiting astronomicalobservatory (OA()) will have a pa-rabolic mirror 0.9 meter in diameter.Find the focal length of this mirror ifx = 1.38 meters when y = 4 meters.Graph the parabolic, cross-section aswas done in figure 6.

Occasionally astronomers find an objectwith a parabolic orbit passing through oursolar system. Most of these objects arecomets which expel gas particles due tothe sun's heat. These gas particles reflectsunlight as they pass near the sun, muchas dust floating in a beam of light. Forthis reason we are able to observe them.

102

If an object has a parabolic orbit with thesun at the focal point of the orbit. itmeans that it is traveling with a speed inexcess of 616 kilometers per second. Thevelocity of an object with a parabolicorbit passing close to the sun but notdrawn into the sun will carry it so farbeyond our solar system it will iik.Ne- re-turn.

Prob/cms:17. What is the above velocity (escape

velocity) of the object in (a) milesper second, (b) kilometers per hour,and (c) miles per hour?

18. A comet with a parabolic orbit passedwithin 7 million kilometers of the sun(focal length of the parabola). Con-struct a small table of values for thex- and v- coordinates and draw agraph showing the curve of the com-et's orbit.

Figure 8. A near collision

19. One of the many theories of the originof the solar system is a near collisionbetween the sun and another star.This star would no doubt have had avelocity great enough to give it a pa-rabolic orbit, as it approached thesun, and it might have passed withina range of 1 million to 100 millionmiles of the sun. Draw the graphs ofthe two parabolas for a comparisonof the two using a convenient scale.

Objects traveling with a velocity greatenough to give them a parabolic orbit arethe exception rather than the rule. If thevelocity of an object were to slow down to

the point where it would repeat the sameorbit around the sun. it would have a longperiod of revolution (many hundreds ofyears) and its orbit would be termed asnear-parabolic. If the slowing down proc-ess were to continue, the object wouldrevolve around its primary, such as oursun, in D. much shorter period of time andits orbit would be termed an ellipse.

The planets all have elliptical orbits asdo their satellites, and their average dis-tances from the sun are measured in as-tronomical units. An astronomical < it isequal to about 93 million-miles (usuallygiven as 92,870,000 miles), which is theEarth's average distance from the sun.

20. How many kilometers are equal toone astronomical unit?

numbers, find the sum of each column andthen divide each column by 10. The num-bers shown in row 4 of table 3 each repre-sent a planet successively farther from thesun. The first is. of course, Mercury, thesecond Venus, the third Earth, and thefourth Mars. The only other planetsknown to exist at that time were Jupiterand Saturn. At first Bode's "rule" Etetwith little excitement. Then in the year1781 Uranus was discovered. Bode merelyextended his calculations which at thattime had Saturn in the position farthestfrom the sun. Bode's calculation and theactual distance of Uranus from the sunclosely agreed. Because of this a group ofEuropean astronomers began a vigoroussearch for the yet undiscovered planet be-tween the orbits of Mars and Jupiter,

TABLE 3.---Bode's rule

Objectfrom sun 1st 2nd 3rd 4th 7th 8th 9th 10th

Double eachsucceeding no. 1) 3 6 12

Add 4 toeach column 4 4

Total eachcolumn 4 16

Divide eachNumber by 10 .4 1.6

Actualmean distancefrom sun (A.U.) 0.3g 0.72 1.00 1.52 2.77 5.20 9.54 19.18 30.60 39.52

Planet name Mercury Venus Earth Mars Jupiter Saturn 9 ? ?

Bode's "Rule"

Near the end of the eighteenth centurya German astronomer. Bode, noted thatthere seemed to be some degree of regu-larity in the distances of the planets fromthe sun. Bode was able to construct a tableshowing the distances of the planets fromthe sun in astronomical units. To do this,Bode started with the number 0 followedby the number 3. After this step thenumber 3 is doubled (6) which in turn isdoubled (12) and so on. You may usetable 3 to perform the same calculationswhich Bode performed.The next step in Bode's calculations, andnow yours, is to add four to each of the

103

which was predicted by Bode's "rule." Inthe year 1801 an object was discovered inthis area.21. Do you know what this object was?

The last two currently known planets inour solar system are Neptune and Pluto.Bode's "rule" can be applied to these twoPlanets if you assign a distance of 30 as-tronomical units to Neptune and use anextention of Bode's calculations fromUranus to find the distance of Pluto fromthe sun. This lack of orderly progressionof Bode's calculations for Neptune andPluto can be explained by the fact that.Pluto's orbit carries it between Neptuneand Uranus at its closest approach to the

sun. You can check some reference booksto find reasons for Pluto's irregularities.It should be pointed out here that NeptuneWa :4 discovered mathematically by itsgravitational influence on the orbit of

ra 11 US, and Pluto was discovered mathe-matically by its gravitat'Jnal influence onthe orbits of both Uranus and Neptune.This is just mile of the many contributionsnrIthematics has made in the space sci-ences.

e

Problems:(Example) If an object is 0.4 astro-nomical units ( AU) from the sun, what isits distance in miles?

93 000 000 mi0.4AUX = 37,200,000 miles.

1AL'

99. Using Bode's "rule" (table 3), calcu-late the distance of the planets fromthe sun in (a) miles, and (b) kilo-meters. You may want to construct achart to show the distances of theplanets from the sun in astronomicalunits, miles, and kilometers.

It might interest you to know howprecise Bode's estimate of the plane-tary distances was. This can be calcu-lated by using the following relation-

shi p;correct value Bode's value

Xcorrect value

100 = percent of error.(Example using the distance of Mars fromthe sun)

1..52 1.6 X 100 = 5.3 percent of1.52

error2 3. Calculate the percent of error of

Bode's planetary estimates for eachplanet usir.7 the figures in table 3.What do you think of the accuracy ofBode's planetary estimates? Keep inmind that his work was done in the1700's.

24. The closest 'visible star to the Earth,other than the sun, is Alpha Centauri.If Alpha Centauri is 25,240,000,000, -000 miles away, how many astronomi-cal units does this distance equal?

104

. Using scientific notation what is thedistance to Alpha Centauri in miles?

Figure 9.

As was previously mentioned, the plan-ets and their satellites do not have circu-lar orbits, but elliptical orbits. You candraw an ellipse. All you do is to take twopins and stick them into ti piece of paper.Then taking a piece of string and a pencil,draw the ellipse as is shown below in fig-ure 9, As you move the pins fartherapart and still use the same length ofstring, you will see that the new ellipse iselongated. If, on the other hand, you movethe pins closer together, you will see thatthe ellipse becomes more nearly circular.

Anything with an elliptical orbit willhave its primirry at one of the two pinholes. These pin holes are called the focii(fO-si, plural for focus) of the ellipse. Asyou can see from figure 9,. and from yourown drawings, toe distance of the pencilpoint from any one of the pins changesconstantly as the pencil is moved to tracethe ellipse. A planet or satellite with anelliptical orbit will also be at different dis-tances from its primary as it mo 'es alongits elliptical path, Figure 10 sln,ws thenames for the rvo special points of ellip-tical orbits which bring the object closestto and take it fai thest awa:i from itsprimary.

What do the prefixes and suffixes mean infigure 10?

perihelion

Figure 10.

perigee

Problems:26. Calculate the average distance that

the satellites in table were from theEarth when they were launched intotheir orbits in (a) miles, and (h)kilometers.

27. If the moon's perigee distance is221,463 miles and its apogee distanceis 252,710 miles, what is the moon'saverage distance from the Earth in(a) kilometers, and (b) astronomicalunits?

SatelliteExplorer VIIEcho IOrbiting solarobservatory (050Explorer XIVRelay ISvncom lITIROS VIII

28. If a particular comet has a periheliondistance of 0.05 of an astronomicalunit and an aphelion distance of 87.4'.astronomical units, what will be theaverage distance of this comet fromour sun?

29. If a moon probe were to place a satel-lite in an orbit around the moon witha "perilanar- distance of 9,000 kilo-meters and an "apolunar" distance of11,000 kilometers, what would be theaverage distance of this satellite fromthe moon ?

TABLE 4.--Distances of satellites

perigee distance311 miles

miles

343.4

171.2

1316.5

35,790.5702

milesmileskilometerskilometerskilometers

apogee distance673 miles

1049 miles

369 miles61,190 miles7423.5 kilometers

35,805.9 kilometers753 kilometers

EccentricityAs was izcxiously mentioned in the ex-

periment on drawing an ellipse, thefarther apart the two pins are moved themore elliptical or elongated the ellipse willbecome. Eccentricity describes the shapeof the ellipse, which is indicated by a num-ber from zero (a circle) to nearly one. Ifthe eccentricity becomes one, the curve isno longer an ellipse but a. parabola. Eccen-tricity is quite important to scientistswhen launching a satellite. A weather

771-806 0-65-8 105

satellite, such as TIROS, must remain ata constant distance from the Earth to giveus the best results. Hence, low ecceiThicityis desirable in such an orbit. On the otherhand, a space probe such as Explorer XIVrequires a satellite to take measurementsover a wide range of distances from theEarth. In this case an orbit of high eccen-tricity would be desirable. The eccentricity(e) of an orbiting object can easily becalculated by using the relationship e = c-.

a

Focal LengthIn astronomy there are many areas

where astronomers art, concerned withdistance calculation. One of these areas isthe calculation of the focal length of mir--ors in reflecting telescopes, which areused to study objects in space. The focallength is the distance from the mirror toa point upon which light rays are focusedafter being reflected by the mirrors. Mir-rors are used in the largest optical tele-scopes, such as the 200-inch reflecting tele-scope at the Mount Palomar Observatoryin California.

Figure 3.

C = center of Curvature

CD = CB = radius of Curvature (R)

CB = the normal to theincident light ray AB andthe reflected light ray BE

ABC = angle of ;ncidence

CBE = angle of reflection

i = r

f = focal point of mirror

Any line which is perpendicular toanother line is called a 'ku».n/a/. Ln figure3, line EF is a normal to the surface ofthe mirror. If the incident light ray (lineAD) is 50° from the normal, then the re-flected light ray (line DB) will also be 50'from the other side of the normal. This.simply, is the law of reflection: The angleof the incident light ray is equal to theangle of the reflected light ray.

Problems:8. If the incident light ray is 75° from

the noL^lni, will be the angle ofthe reflected light n,y?

9. If the reflected light ray is Li"' fromthe normal, wh-t was the angle of theincident light ray?

10. (a) If the incident light is paral-lel to the normal. where will that 4htray he reflected':(b) What will be the angle I tweenthe reflected ray and the normal'?

Flat mirrors are not used as the prin-cipal mirrors in reflecting telescopes, be-cause a flat mirror will not focus incidentlight rays to a point. A simple kiwi of

Figure 4.

106

curved mirror is a spherical mirror wherethe reflecting surface is part. of a sphericalobject (a ball). Spherical mirrors ;seefollowing discussion of parabolic mirrors)used in astronomy are concave sphericalmirrors; that is, the reflecting surfacewould he the inside of a hall-shaped ob-ject. To find the focal point of a concavespherical mirror you need know only theradius of curvature of the mirror, whichis the same as the radius of the imaginarysphere of which the mirror is a part. Fig-ure 1 shows a cross-;eetion of a concavespherical mirror. The focal point or focallength (f) ( oncave spherical mirror

is 1 the of curvature (R), This can

be expressed symbolically as f = R

Pi ob/ems:11. Find the focal length of the following

,oncave spherical mirrors using thegiveninches,inches,inches,meter, (h) 17 meters, (i) 41 meters,(j) 38.4 meters.

19. (a) Which of the mirrors in problem11 is the most curved (having thesmallet radius of curvature) ? (b)Which of the mirrors in problem 11is the least curved (having the longestradius of curvature) ?

13. The Schmidt telescope of the PalomarObservatory has a concave sphericalmirror with a radius of curvatureequal to 26 feet. Find the focal lengthof this mirror in (a) feet, and (b)meters.

radius of curvatures; (a) 18(b) 3 fea, (c) 31 feet, 3(d) 71 feet, (e) 99 -ieet, 4(f) 75 centimeters, (g)

Using spherical mirrors in reflectingtelescopes, however, presents a problem.Spherical mirrors focus with sufficient a,!-curacy only those light rays which are re-flected from the near-center of the mi.:my.If a light ray is reflected from the near-edge of the mirror, it is focused behind thepoint where reflected rays closer to thecenter of the mirror are focused. Thiseffect, called spherical aberration, is rem-

107

edied in the Schini:i telex .ope by using acorrective lens. Srli ,il aberration.shown in figure 5. -s the sharpnes.-of the image at al point of tInmirror.

Figure 5.

To solve the problem of cr :L1 aber-ration, scientists designed a ic -phericalmirror which wou'd focus all ins .dent lightrays at a sharply deli. point. Such amirror is called a para] ,lie or paraboloidalmiffor, Finding the focal point of a pa-rabola is a bit mere difficult than for aspherical mirro but using the formulay2 = 2fx. where (y) is the y-coordinate

Figure 6.

1 =3y x

0 0± 2 ?t,

±3 11/2

+44-1/6

6 6

See figure 11 for the meanim:: of (a) and(c) . AF, = perigee distance. BF, = apo-g,'e distance.

a-7! AD or

c = AD perigee distance = line DF,e AD AF, = DI',

perigee apogee distance

Figure 11.

Problems:30. One of the first successful launches by

the Goddard Space Flight Center wasExplorer VI in August, 1959. One ofthe tasks of Explorer VI was to meas--are various levels Of radiation in theVan Allen belts around the Earth.(Do you think that this satellite waslaunched into an orbit of high eccen-tricity?)

31. Calculate to three decimal places theeccentricity of the orbit of ExplorerVI if its perigee distance, wore 157miles ar.'! itJ apogee distance were

m

32. Pioneer V was designed and launchedinto an orbit around our sun In in-vestigate interplanetary space.perihelion distance of Pioneer V were74.9 million miles ;Ind it.; aphelion dis-tance were 92.3 million miles, calcu-late the eccentricity of its orbit tothree decimal places.

TIROS II was latincl-e.sd in No;ember.1960. One of its tasks was to televiseand transmit information on clowicover over the Earth. Do you thinkthe orbit of TIROS 11 was planned tohave high or low (-Teel-It-licit-Y.!

3.1. Calculate to three decimal places theeccentricity of the orbit of' TIROS 11if' its perigee and apogee distanceswere .107 and 431 miles respectively.The Orbiting Solar Observatory. OSOI, was launched in March, 1962, intoan orbit with perigee and apogee dis-tances of 343.5 and 369.8 miles re-spectively. Calculate the eccentricityof its orbit to three decimal places.

36. On July 26, 1963, Syncom I 1 waslaunched, This satellite \vas to have a24-hour orbit which, if successful,would ;time: r to remain stationaryover a certain point on the Earth. Tohave such an orbit, would Syncomhave high or low eccenti icity?

37. If the orbit of Syncom II has perigeeand apogee distances of 22,230.1 and22,239.7 miles respectively, calculate

.10), ).

-C;

(,( ?'t , -_1A

1-\

Figure 12. Syncom II

108

Pi

V

Cean

Ju

Sa

Ut

PI

to seven decimal places the eccentric-ity of its orbit and round off to sixde 'mal places.

38. For those of you for whom mathe-matics is a challenge, complete table5. Refer to figure 11 when needed.

TABLE' 5.---Distances in astronomical units

anetPeriheliondistance

0.3076

Apheliondistance

Averagedistance*

(c)Figure 12 Eccentricity*

?.rcury 0.4666

0.7284nus 0.7182

irth 1.0000 0.0170

0.1417irs 1.5237

res (Asteroidsd Planetoids)

piter

2.7673 0.077

5.2028 0.5342 0.048

turn 0.9016 0.056

'anus

:ptune

0.047

29.7812 30.0577

Lito 49.3576 39.5177

From: Robert H. Baker, Astronomy (New York: D. Van Nostrand Company, Inc., 1959).

VELOCITYSo far during the entire discussion, we

were concerned with distance measure-ments which were unrelated to time. Nowwe are going to introduce time measure-ments with distance to get a new quantity.This new quantity describes how muchdistance is traversed in a certain amountof time. For example, if you can walkfour miles in one hour in a given direction,you are walking with a velocity of fourmiles per hour. Velocity also implies direc-tion indicated usually with a vector. Veloc-ity (v) is related to the distance (d) andthe time (t) in the following way; v = d

.

Problems:

39. If a particular satellite traveled30,000 miles in 6 seconds, what wouldthe velocity of that satellite be inmiles per second ?

-10. If Vanguard III were traveling with avelocity of 18,522 miles per hour atperigee after launching, what is thevelocity in (a) miles per minute, (b)

109

miles per second, and (c) kilometersper second?

41. Vanguard III had a perigee velocityof 29,820 kilometers per hour and anapogee velocity of 20,349 kilometersper hour. (a) What was the averageorbital velocity of Vanguard III? (b)What was the same average orbitalvelocity in kilometers per second?

42. If the light arriving here this momentleft the sun 81/2 minutes ago, how fastdoes iight travel in (a) miles per sec-ond, and (b) kilometers per second?(Assume the Earth is 93,000,000miles from the sun.)

Probably without realizing it, you havejust calculated the approximate velocity oflight; the correct value being 186,272miles per second. Knowing the velocity oflight enables you to calculate the distancelight travels in a given amount of time.By changing the original velocity equation

v = d to d = vt you can easily solve for

the distance.

43. Calculate the distance light travels inone year (365.25 days) in (a) miles,

Figure 13. Radio telescope

(b) kilometers, and (c) astronomicalunits.

The distance you have just calculated inproblem 43 is the distance light tra:Tels inone ligizt: year. The light year, as a unitof measurement, is used to describe thedistances to the nearby stars, not to men-tion the more distant stars and galaxies.44. What is the diameter of the Milky

Way (the galaxy in which we live) inlight years if an object traveling witha velocity of 0.484 the velocity of lightmust travel 206,612 years to cross ourgalaxy?

45. In the near future, man may venturea trip to the closest visible star,Alpha Centauri. If the space vehiclecould travel ..a,t 0.43 the velocity oflight, and the trip took 10 years, howfar away is Alpha Centauri?

46. If a satellite were launched anear circular orbit 35,400 kilometersfrom the Earth and had a velocity of10,950 kilometers per hour, what dis-

110

tance in kilometers would be coveredin one orbit if the h^riod of revolutionwas 23.3 hours?

The time required for a signal to travelfrom a satellite to the Earth can be usedto calculate how far away that satellite isfrom the Earth.47. If it takes 4.00 seconds for the infor-

mation sent by a space probe satelliteto reach the Earth, how far fron theEarth is that satellite?

48. Radio astronomy is a relatively newmethod of studying celestial objects.if a radio signal were sent toward adistant object in the sky and were re-flected back to Earth by that object,how far from Earth would that objectbe if the time between the sendingand receiving of the radio signal were31 years? (Radio waves travel at thesame velocity as does light.)

The time required for something totravel a given distance at a certain veloc-ity can be calculated by using another

Gamma Rays X-Raysviolet

Visible/Ultra/ ii1

EARTH

Figure 14From: Robert H. Baker, Astronomy (New York: D. Van Nostrandcompany, Inc., 1917.4).

111

variation of the velocity formula v = t .

By solving for (t) you would get t

49. If light travels 93 million miles fromthe sun to the Earth (1 astronomicalunit) and has a velocity of about186,000 miles per second, how longvould it take for the light to get fromthe sun to the Earth?

50. How long does it take light to travelfrom the sun to the planet Saturn?(Check table 3 for Saturn's actual

distance from the sun in astronomicalunits.)

51. If you were on the moon, how longwould it take a radio signal sent byyou to reach the Earth ? (Check theanswer sheet, problem 27 for themoon's average distance from theEarth.)

Wa(' LengthVisible light is termed as electromag-

netic radiation. The visible spectrum canbe broken down by a prism or other re-fractive devices into its various colors be-cause each color has a different wavelength (table 6). An easy Vi!." to remem-ber the order of the colors from the longto the short wave length is to take the firstletter of each color and make the name"ROY G. BIV."

TABLE 6.Colors in a spectrum

Red Orange Yellow Green Blue Indigo Violet

Visible light, however, is just a verysmall part of the total electromagneticradiation spectrum, which is shown belowin figure 15.

Short wave radiation

All the various forms of electromagneticradiation travel at the same velocity butdiffer in wave length as is shown below infigure 15.

PrOtiten28:

52. If a solar disturbance occurred thismoment on our sun, how long wouldit take gamma radiation to reach theEarth if the Earth is exactly 1 astro-nomiyl unit away from the sun'?

53. The Crab Nebula, a famous radiosource, was a star which becalm anova when it exploded some 4,410years ago. The Chinese, in the yearA.D. 1051, recorded seeing this stargreatly increase in brightness. (a)During what possible Earth year didthe star that produced the CrabNebula explode? (b) How far awayin light years is the Crab Nebula?

54. Suppose a star within our galaxy (theMilky 'Way) exploded and became anova on December 31, A.D. 1964.How far away wou!ii this nova be ifthe radio noise (radiowave radiation)from the explosion did not reach theEarth until December 31, A.D.66,964'?

Ware Length and FrequencyAnother aspect of velocity is the motion

of stars and galaxies, including our ownMilky Way. To understand these velocitiesyou must first know something about wavelength and frequency. The wave length ofany particular radiation is determined bystarting at a particular point on a waveand moving along it until encounteringanother point on the wave which is iden-tical to the point from which you started.

Figure 15.

112

Long wave radiation

This is shown below on figure 16. Anywave length is the distance between thepoints A and A', or between the pointf- Band B', C and C', or D and D'. This wavelength (Alambda) is different for all thetypes of radiation shown on Table 6 aswell as on Figure 14. These wave lengthsvary in length from 0.000000000001 centi-meter in gamma radiation to 1 millioncentimeters in radiowave radiation.

B'

Figure 16.

The frequency of a wave is determinedby the number of wave lengths passing agiven point in a certain amount of time.For example, if 1,350 wave lengths pass a1.:Ant in 1 second, the frequency i,f thisradiation would be 1,350'wave lengths persecond (commonly termed as cycles persecond) . Using wave length and frequencywe can again find velocity. v = fA where(A) is the wave length and (f) is the fre-quency. This formula can also be solved

for , = 1 orf =A

Prob/cins:55. Since all types of radiation have thr

same velocity, what can you say aboutthe frequency of gamma radiation ascompared with the frequency of ra-diowave radiation?

56. The human ye can see electromag-netic radiation wave lengths fromabout 0.00004 to 0.00007 centimetersin length. Knowing the velocity oflight in centimeters per second (299,-460,000,000 cm/sec) calculate therange in frequencies that the huml-meye can detect.

57. When the velocity of sound in air is331.4 meters per second (velocity ofsound varies at different altitudes andtemperatures) , what will the wavelength of a sound wave be from a

113

sound source emitting a frequency of256 cycles per second?

58. A typical human ear can hear fre-quencies between 20 and 20,000 cyclesper second.. Again assuming the ve-locity of sound to be 331.4 meters persecond, what is the range in wavelength that a typical human ear candetect in (a) centimeters, (b) meters,and (c) feet?

59. if a satellite was transmitting at awave length of 0.00270 meters, towhat frequency would the receivingsets on the Earth have to be tuned toreceive the signals? (Check problem42 (b) on the answer sheet for themetric value for the speed of light.)

Doppler EffectWave length and frequency can also be

used to determine the velocity of a soundor light source which is in motion eithertoward or away from the observer. Whena sound or light source is in motion rela-tive to the observer, there is a shift in thewave length of the sound or light. This isknown as the Doppler effect. As far assound is concerned, you may try the fol-lowing experiment. If you were to standalong a highway while a friend blows theautomobile horn while driving past you, achange in the pitch of the sound would bequite easily noticed. The automobile hornsends out the same number of wave lengthsper second (frequency) while it is at rest orwhile it is moving. The velocity of thesound coming from the horn is also con-stant for each particular instance.

If the sound source is moving towardyou, as is shown in figure 17, the wavelengths are crowded together and therebyshortened. This would cause a higher pitchin the sound heard by the observer. Onthe other hand, if the sound source ismoving away from the c',server the wavelengths are stretched out and therebylengthened. This would cause a loweringof the pitch heard by the observer (alsoshown in figure 17). The above situationis identical with that of a passing train.

This same lengthening and shorteningof wave lengths is present when an elec-

ti

Figure 17. The Doppler effectFrom: George Gamow, Matter, Earth and Sky (Englewood Cliffs:Prentice-Hall. Inc., 1964).

Figure 18. SpectrogramFrom: Robert H. Raker, Astronomy (New York: D. Van Nostrand.7ompany, Inc.. 1959). Permission to use this photograph wasobtained from Mount Wilson and Palomar Observatories, CarnegieInstitute of Washington, Pasadena. California.

114

tromagnetic radiation source (a star) andthe Earth are moving toward or awayfrom each other. Since We speak of elec-tromagnetic radiation as an entire spec-trum (figure 14) the instrument whichrecords these wave lengths is called aspectrometer. Spectrometers record infor-mation on a photograph called a spectro-gram. Each WM e length which is presentis represented b; a well defined bright ordark line, depending on what i beingphotographed. Such a spectrogram isshown on figure 18. These spectral linescan be measured to indicate what elementsare present in the electromagnetic radia-tion source.

Figure 19 shows a drawing of a spec-trogram of moving electromagnetic ra-diation sources compared with the spec-trogram of a stationary source of electro-magnetic radiation as can be obtained in alaboratory.

The Doppler effect can be expressedchange in wave length

mathematically asvelocity of source

. This expression mayvelocity of light

be solved for any one of the four quanti-ties contained in it.

normal wave length

Prob/ents:

60. The sun (and the solar system) isspeeding toward the constellationCygnus with a velocity of 216 kilo-meters per second. If a radio astron-omer were to transmit a radio signaltoward the constellation Cygnus witha wave length of 0.003500000 meter,what change in wave length would beobserved by a possible intelligent racereceiving the signal on a planet re-volving around a star in this constel-lation?

To find the wave length of the radio signalreceived on such a planet as mentioned inproblem 60, subtract the change in wavelength from the signal transmitted fromEarth.

61. Calculate the wave length radio signalthat would be received by someoneon the possible planet mentioned inproblem 60.

Long Wavelengths Short WavelengthsFigure

62. If a satellite were launched into anorbit of high eccentricity around oursun, what would be its velocity atperihelion if the signal it transmittedhad a wave length of 7.200 milli-meters and the wave length signal re-ceived on Earth was 7.197 millime-ters? (Note: change in N\'':.'e length

wave length transmitted wavelength received.)

The larger reflecting telescopes studythe motions of galaxies so distant that thelight we observe now left those galaxiesbefore the Earth was formed (Earth isabout five billion years old) . Generally,the more distant a galaxy, the faster it ismoving away from us.63. If the spectral lines of a galaxy were

lengthened by I of its normal wave4

length, how fast would that galaxybe speeding away from us?

An angstrom unit is a very small unit oflinear measurement which is 0.00000001centimeter long.

-

Figure 20. Meleortrails

115

Electromagnetic radiation source and Earthmoving away from each other (red shift)

Electromagnetic radiation source not movingrelative to the Earth (no shift)

Electromagnetic radiation source andEarth moving toward each other(violet shift)

64. How many angstrom units are therein (a) 1 centimeter, and (b) 1 meter'?

65. If an astronomer were recordingmeteor trails on a spectrogram andnoticed that a spectral line for cal-cium which is normally 6,182 ang-strom units long were shortened 1.429angstrom units, how fast would thatmeteor be moving- through our atmos-phere in (a) miles per second, and(b) kilometer per second?

66. Suppose a scientist were to point aspectrometer toward the burninggases roaring from a Saturn, Thor,or Atlas booster engine. If the result-ing spectrogram were to show the6.640.900 angstrom units spectralline for oxygen to be displaced 0.054angstrom unit, what would be thevelocity of the gases being expelledfrom the above booster engines in (a)kilometers per second, (b) miles persecond, (c) kilometers per hour, and(d) miles per hour'?

:?.. .00..

ACCELERATIONYou should now have a fair idea of

what is meant by the concept velocity. Inshort it is a constant rate of motion in agiven direction. By this is meant that anautomobile traveling with a velocity of50 miles per hour will experience no otherquantity of linear motion as long as itcontinues moving at 50 miles per hour in

Figure 21. Acceleration effect

the same direction. The moment the au-tomobile or any other moving objectincreases or decreases its velocity, it ex-periences acceleration or deceleration re-spectively. For example, an airplane ac-celerates during take-off, cruises at acertain velocity in a given direction, andthen decelerates during landing. Deceler-ation is sometimes termed as negative ac-celeration. A simple kind of accelerationis that of a freely falling object. Figure22 shows a ball being dropped fi. n abuilding 256 feet high. It takes 4.0 secondsfor the ball to reach the ground. If youwanted to find the acceleration due togravity of a freely falling object, theformula d = 1 at' could be used. The

9

.Ater d again is the distance, a the ac-celeration, and t the time.

Example Using Figure 22:(1) solving for a, the above formula

becomes a 2d.t

2 x 256 512(2) a = = 32 feet per(4) 2 16

second' or 32 feet per second per second.The units for acceleration mean that theobject is accelerating 32 feet. per secondevery second that it falls.

116

Problems:67. Knowing the acceleration due to grav-

ity (above example), calculate thedistance the object in figure 22 fallsby the end of each second.

68. How long would it take an object tofall 1,024 feet?

69. If you were to launch a model rocketto a height of 2,000 feet in three sec-onds, calculate the approximate ac-celeration of the rocket.

70. How long would it take for a rocketwith zero velocity at 2,000 feet to fallback to the Earth?

71. If the first booster on a launch vehicleburns for 8 seconds, is separatedfrom the launch vehicle, and thenstarts descending from an altitude of1 kilometer, how long would it takefor this spent booster to splash intothe ocean? (Note: you will need tochange acceleration due to gravityinto the metric system.)

To further develop the situation, sup-pose a ball were to be thrown vertically toa height of 100 feet. On its way up theball would decelerate until it reached itsmaximum height, where it would momen-tarily stop before beginning its fall to the

ground (velocity at this point is equal tozero). Deceleration due to gravity is suchthat when an object coasts upward afterbeing propelled is 32 feet per second'.During its fall to the ground it would ex-perience the same acceleration as did theball dropped from the building in figure99.

It might interest you to know the veloc-ity of an object which has been propelledupward. To find this you can use the fol-

lowingVjlowing relationship: a = , where

(a) is the acceleration due to gravity,(vf) is the final velocity, (vi) is the initialvelocity, and (t) is the time. This formulais unique in that it clearly shows when theacceleration is ( +) or (). On its jour-ney upward its final velocity is zero at themaximum height where the ( v;) showsthe acceleration to be (). On its falldownward the initial velocity is zero at themaximum height so the (yr) shows theacceleration to be ( +).

Example Using F igltre 23:If you shot an arrow vertically to a heightof 196 feet, (a) what is the time requiredfor the upward flight, (b) what is thetime interval between the time of shootingthe arrow and the arrow striking theground, (c) what is the velocity of thearrow when it leaves the bow, and (d)what is the velocity of the arrow when itstrikes the ground?

(a) d = 1 =at', t2 2d 2 X 196

2 a 3239232

12.25

t = 3:5 seconds.(b) time up = time down. t = 3.5 X 2 =

7 seconds.V( V f(c) a = , vf v, = at

0 vi = 32 feet per sec." X 3.5 =112.0 feet per sec.(d) v, v, = at, v1 0 = 32 feet per

sec." X 3.5 sec. of = 112.0 feet persecond.

1111`I11111 -11 11 111111111

11I

11.1

t = time

Figure 22.

117

Figure 23. flight of an arrow

Problems:72. Find the impact velocity of the rocket

mentioned in problem 69 in feet persecond.

73. Find the impact velocity of thebooster mentioned in problem 71 inmeters per second.

118

74. Suppose you were on the moon wherethe acceleration due to gravity is 1.67meters per second' and you shot anarrow with r n initial vertical velocityof 33.6 meters per second. (a) what-would be thy? time of the entire flightof the arrow, and (b) how highwould the arrow soar in meters?

75. If an object is thrown vertically to aheight of 78.1 meters in 1 seconds,calculate the acceleration due to grav-ity for the Earth in (a) centimetersper second's, and (b) meters per sec-ond2.

76. If an object were propelled verticallyfrom the surface of our sun to aheight of 2,195 meters and it landed8 seconds later, calculate and comparethe acceleration due to gravity on the

with that of the moon and theEarth.

PROJECTIONThe material presented in this chapter

may have captured your interest, but whatis vet to be learned stretches far beyondthe imagination. Discovery and under-standing depend on you, who can be andhopefully who will be the mathematiciansand scientists of the future.

Some of you may think that the mathe-matical processes and problems in thisbooklet are simple, but be assured that themore proficient you become with numbersand number relationships, the mere excit-ing will be the problems you will be able tosolve.

ANSWERSChapters I through VI

andSELECTED BIBLIOGRAPHY

((tat er

Chapter I - FROM HERE, WHERE?

Table 2.-Our solar system

Name Sy tn-

Mean Distf rem

r1,t rtin .1.:.,.

a tuuSun

MillionMiles

PeriodRevolution

Side-real

days

of

Syn-die

days

MeanErre 11- Diam-I ricity. eterof inOrhit Mires

Mass Den-sity

14,0-1

Period

Rot a-tier.

111anni-

tattleat

Great-est

Bril-lhinee

EscapeVelar it ies

Memiry 0.3871 35.96 87.969

clays

115.08 0.206 2.900 0.05 6.1 08 day. 2.6 miles/sec

Venus 0.7233 67.20 224.701

days

583.92 0.007 7.600 0.01 7.06 6.4 miles/see

Ea rt h 1.0000 92.90 365.256

days

0.017 7,913 1.00 5.72 23,76.0 7 miles/sec

Ma rs

Jupiter 2.

1.72:17

7.2020

141.6

483.3

686.980

years11.862

779.91

390.88

0.093

0.048

4,200

06.800

0.11

318.4

4.12

1.35

24537.0

9,70,0

-2.0 miles/sec

:17 miles/sec

YearsSaturn 9.5388 806.2 29.450 378.09 0.076 71.500 97.3 0.71 (I. 4 22 miles/sec

Yell II'1';i nils 19.1820 1783.0 84.013 369.66 0.047 29.400 14.5 1.76 IS + 7.7 1:1 miles/see

YearsNeptune 30.0777 2791.0 164.791 367.49 0.009 28.1100 17.2 2.29 17,10.0 +7.6 14 miles/sec

Yea I'SPluto 39.7177 :1670.0 210,430 366.71 0.249

Sun 0 864,000 33E950 1.41 241,67 387 miles/see

Moon 2160 0.012 3.33 27.1.32 -12.6 1.5 miles/see

771-806 0-65- 9

Chapter II - GETTING INTO SPACE

EXERCISES: A-1 23,791.9 lb.A-2 24,466.9 lb.A-3 3.7 lb.B-1 10,000 H.P.B-2 3,000 H.P.B-3 187,336 H.P.C-1 200 secondsC-2 100 lb. per secondC-3 250 secondsD-1 3

D-9 3600 lb.D-3 250 lb.

121

Chapter III - SPACE AND WEATHER

1.

2.3.4.

5.6.

10 to the second power10 x 1010 to the eighth power10 x >: 10 x 10 x 10 x 10 x10 10100100,0(10,000

7. 8 X 10 x 10 x 10 x 10 x 10 or8 X 100,000 or 800,000

8. 6000

9. 50,00010. 1,500,00011. 250,000,00012. 5 x 10"13. 6.5 x 10614. 3 x 10115. 5.5 X 10"16. 1 x 10 517. 6.5 X 10 418. 0.000000061519. 0.000000050620. 0.0000034521. 1 x 1022. 3 x 10123. 7 x 10224. 9 x 10525. 4 x 10126. 0.00000127. 100000028. 100,000,00029. 0.0000000130. 0.0000254131. 9 x 10'832. 70,000,00033. 0.0000000834. 0.00000000000000354635. 1 x 10636. 93 x.10637. 1 x 10-738. 74.4 to 99.2 miles39. 62 miles40. 186 miles

122

41. 29.92 inches, nearly 30 inches42. 96.6 kilometers43. 1-10 atm.44. 7.6 x 10 8 mm. 2.992 X 10 8 in.45. 3.9 X 10-" in. 3.9 x 10 12 in.46. 1 x 10 12 or 10 1247. 1 x 10-'1 or 10 -1a48. 62 miles49. 93 miles50. 124 miles51. 186 miles52. 372 miles53. 7.60 X 1C-4 mm. or 1 x 10 atm.54: 2.992 x 10 3 inches55. .000000000001 atm.56. .0000000002 atm.57. -73°C58. -99.4°F59. -23°C60. -9.4°F61. -73°C62. -99.4°F63. 1127°C64. 2060.6°F65. 1227°C66. 2240.6°F67. 460 statute miles68. 51/1 inches69. 2 inches70. 20°71. 26,310 cu. in.72. 15.2 cu. ft. p. 1573. 18.03 cu. ft. round off to 18.0 cu. ft.74. TIROS V = 26,600 cu. in. TIROS

VIII = 31,500 cu. in. (approximately)75. 3,740,000 hp. approximately76. 165,000 hp.77. 66,000 hp.78. 11 minutes 15 seconds79. less80. 437.0 statute miles81 690.0 statute miles

Chapter IV - SPACE

1. Solution: 1" = -1 ft. and 1 ft.12

1 mile, therefore,5280

500,000" -- 500,000 X 1"

500,000 X1- ft.12

41,667 ft.41,667 ft. ---- 41,667 X 1 ft.

1= 41,667 X -5

mi.280

7.8 miles.1" -- 8 miles (approximately), an-

swer.2. Since 1" represents 8 miles approxi-

mately, 21/2" = 2% x 1" or 2% x 8 mi.20 mi.

3. The measure between the two airportsin inches is 3 11/16; the distance inmiles is 29%.

4. The measure between the two airportsin inches is 31i6. The distance be-tween them is, therefore, 25% miles.

5. TC from D to C is 60°.6. TC from C to D is 240°.7. TC from A to B is 78°.8. Variation is 4°W.9. MC = TC 4- Var. W

MC = 78° + 4°MC = 82°

10. Correction or Variation is 3°E.11. MC = TC Var. E

MC = 287° - 3°MC = 284°.

P. (a) MC = TC + Var. WTC 301°Var. \V = 3°MC = 301° m 4 3°MC = 304°

(b) The measure of the TC in inchesis 6, therefore the distance is 48miles.

13. The school is approximately 22° or23° to the eft of the TC at that point.

14. Vector AC = 21/4 inches or 4% lb.15. The general direction is south of east.

123

NAVIGATION

16. 48°, 150 mplh approximately.17. 48°, 1421,4 mph approximately.18. z = 90° - alt. or 21° 30'19. 26° 30'20. 19° 08'21. 41° 34'22. 9° 55'23. L = 39° 56'24. L = 69° 40'25. L = 31° 13'26. (a) 5 hr.. = 5 X 1 hr. = 5 x 15° = 75°

(b) 135°, (c) 225°, (d) 60°, (e) 310° (f) 300°27. A,. = hr.28. Longitude -= 119° 09' W.29. Latitude = 40° N.

Longitude = 74° 10'30. Philadelphia, Pennsylvania.31. Latitude = 39° N. Longitude 77° 24' W

Washington, D.C.32. When Its location was exactly south of

the observer33. The latitude of the observer, figure 22,

is the declination of the zenith point.Angle d + angle z = 90°

- Angle a angle z = 90°by subtraction

Angle d - angle a = 0°angle d = angle a

This means that the declination of thezenith pint is the same as the altitudeof Polari

34. n 296 cycles per second.35. The speed is 67 mph, (rounded).36. The car is within the legal limit. its

speed is 33 mph37. B , the central angle is 150°.38. e = 240°.39. e = 180°.40. 0 = 360°.41. The satellite will make one trip

around the Earth in one day. Sincethe Earth rotates at the same rate, thesatellite will appear to remain on thesame meridian.

Chapter V THE RIDDLE OF MATTER AND MOTION

a. The two coins or stones should alwaysland together unless dropped fromgreat distances where air drag wouldhave a noticeable effect.

b. You should get the same results as be-fore if the two objects are thrown tosame height.

c. The arc distance for a sixteen degreeswing is about 27.9 centimeters.

d. When sitting at rest, your heart shouldbeat about three times during oneperiod of a two meter pendulum.

e. Physicians probably compared thepulse rate of healthy persons to thatof the patient before the pulsilogia.Doctors usually take a patient's pulsetoday by timing it with a watch havinga "sweep" second hand.

f. Graphs

70

60

50

40

70

60

50a

40NO RELATION NO RELATION30 30

20 20

10 10

1 2 3 1 2 3PERIOD IN SECONDS PERIOD IN SECONDS

200

150

/ PARABOLIC UR EXPONENTIALRELATION

100

50

1 2 3KRIM/ IN SECONDS

g. You can conclude that over the shortdistances involved, objects fall at thesame rate regardless of their mass.

h. As the length of a pendulum is in-creased the period also increases. ITorder to double the period the lengthmust be made 22 (or 4) times greater

124

and in order to make the period threetimes greater, the length must be made32 (or 9) times greater. It can be saidthen, that the length of a pendulumvarks (or changes ) with the square ofthe factor by which the period in-creases.

i. A "seconds pendulum" (T = 2 seconds)has a length of about .98 meters.Tightly compacted (or dense) objectssuch as solid iron or lead balls are noteffected by air resistance nearly asmuch as hollow or less dense objects.

k. The unfolded paper, of course, fluttersin the restraining air while the moredense object falls quickly to the floor,but the tightly folded paper shouldreach the floor with the coin or stonefor such short falls.

1. 176 feet per second.m. One second and two seconds.n. stick's shadow pole's shadow

polesticko. 3/72 or 1/24p. The acceleration effect due to gravity

(or g) will be reduced to 1/24th thefree-fall acceleration by the inclinedplane directly; but the energies re-quired to set the jar in rotation, and toovercome the greater frictional drag,also to "dilute" gravityresulting in amuch greater overall reduction.

q.Seconds of Elapsed Time 1 2 3 4

Approximate Distancesfor Straight Jar " 16" 36" 64"

Approximate Distancesfor Concave Bottle 5" 20" 45" -

r. The distance rolled in two secondsshould have been approximately fourtimes the distance rolled in one secondand the distance after three seconds

* The bottle with concave sides, apparently be-cause of a lower friction factor, rolls fasterthan the straight sided jar and, as you mayhave discovered, has left the board withinfour seconds.

should be nine times the first second'sdistance. The distance is increasingin direct proportion with the timesquared just as the length of the pen-dulum was in direct proportion withthe period squared. Algebraicallystated then: s cc tz.

s. Graph.

z

a

5 2O

8

t.

if(2.16)

10

(1.4)1 1 1 1

1 2 3 4

TIME IN SECONDS

Tittle Interval in seconds 1 2 3 4

Avg. Ve:Leity (in./sec.)of Jar 12 20 28

(Pro-jected)

35Avg. Velocity (in./sec.)

of Bottle 5 15 25

125

u. The average velocity of the jar in-creases about 8 in./ sec. each second.The average velocity of the bottle in-creases about 10 in,/sec. each second.

Numbered problems

1. About 4 seconds.2. At least 320 meters (over 1000 ff.).3. About 80 seconds.4. Yes, a sheer drop of over 882 meters

(more than one half mile) is found atthe site of Angel Falls in South Amer-ica.

5. About 13 seconds.6. About 80 feet.7. About 144 feet.8. About 584,040,000 miles.9. About 3 and 2/11 feet in thickness.

Chapter VI - THE MEASURE OF SPACEEartth-pitoon distunck, = 384,560 kilometers.Time or satellite to get from Earth t, /MUM = 6,480,009 sec. =1,800 hours =75 days.Velocity rht s.steilke revviving around the Earth=2.39 miles/minute (miles per minute).

TABLE 1 TABLE Itkilometer = 1,000000 millimeters 1 inch = 2.54 centimeters

1 meter = 100 cemtirneters 1 foot = 30.48 cent' neters1 centimeter == +0,00001 kilometer 1 mile = 1,610 meters1 millimeter =4000! meter I centimeter = 0.39 inch

1 meter = 39.36 inches1 meter = 0,00062 mile

1. (a) 0.0.001 to 0.1 centimeter, (b) 0.000039 to 0.039 inch2. (a) 0.00178 centimeter, (b) 0.0178 millimeter3. (a) 1,400 meters, (b) 4,583 feet, (c) 0.868 mile4. (a) 690.2 to 750.1 kilometers, (b) 690,200 to 750,100 meters5. 41.2 meters6. (a) 6,370 to 50.960 kilometers (dwarf stars), (b) 1,391,040 kilometers (sun),

(c) 625,968,000 kilometers (Betelgeuse)7. 62,000 miles8. Reflected light ray will be 75° from the normal9. Incident light ray was 19° from the normal

10. (a) along the normal, (b) 0°11. (a) 9 inches, (b) 11/2 feet, (c) 15 feet 71/2 inches, (d) 351/2 feet.- (e) 4924 feet.

(f) 0.375 meter. 37.5 centimeters, 375 millimeters, (g) 0.5 meter, 50 centimeters,(h) 8.5 meters, 850 centimeters, (1) 20.5 meters, 2,050 centimeters, (j) 19.2meters, 1,920 centimeters.

12. (a) most round, (i) flattest13. (a) 10 feet, (b) 3 meters or 3.05 tn.14. f = 55.6 feet = 17 meters or 16.95 rn.15. f = 91.4 centimeters = 36 inches16. f = 5.80 (graph-figure 24)17. v =,- (a) 383 miles/see. (b) 2,217,600 kilometers/hour (c) 1,378,800 miles /hour18. See figure 2519. See figure 2620. 1 astronomical unit = 1.49,730,000 kilometers approximately21. Ceres-one of the many asteroids or planetoids22. Mercury (a) 37,200,000 miles (b) 59,892,000 kilometers

Venus (a) 65,100,000 miles (b) 104,811,000 kilometersEarth (a) 93,000,000 miles (b) 149,730,000 kilometersMars (a) 148,800,000 miles (b) 239,568,000 kilometersCeres (a) 260,400,000 miles (b) 419,244,000 kilometersJupiter (a) 483,600,000 miles (b) 778,596,000 kilometersSaturn (a) 930,000,000 miles (b) 1,497,300,000 kilometersUranus (a) 1,822,800,000 milei (b) 2,934,708,000 kilometersNeptune (a) 2,790,000,000 miles (b) 4,491,900,000 kilometersPluto (a) 3,608,400,000 miles (b) 5,809,524,000 kilometers

126

xI 3 5

3.1x103

Figure 25.

23. Mercury 5.3 percent error (to nearestVenus 2.8 percent error tenth)Earth 0.0 percent error (because

of definition of an astro-nomical unit)

Mars 5.3 percent errorCeres 1.1 percent error

24. 271,398 astronomical units25. 2.524 x 1010 miles

127

= 100 million miles

= 1 million miles

x-

Figure 21.16.

Jupiter 0 percent errorSaturn 4.8 percent errorUis.nue 2.2 percent errorNeptune }excluded because irregulari-Pluto ties in orbits make it impos-

sible to calculate percent oferror.

26. Explorer VII (a) 508.5 miles (b) 818.7 kilometersEcho I (a) 997 -miles (b) 1,605 kilometersOrbiting Solar (b) 573.5 kilometersObservatory (OSO) (a) 356.2 milesExplorer XIV (a) 30,682.1 miles (b) 49,398.2 kilometersRelay I (a) 2,709.4 miles (b) 4,370.0 kilometersSyraeom II (a) 22,194.9 miles (b) 35,798.2 kilometersTIROS VIII (a) 451 miles (b) 728 kilometers

27. (a) 381,709 kilometers, (b) 0.00255 astronomical units28. 43.73 astronomical units29. 11,500 kilometers30. yes31. e = 0.98832. e 0.10433. low eccentricity34. e = 0.02935. e = 0.03736. low37. e = 0.0002158 round off to e = 0.00021638. All distances in astronomical units (does not [include eccentricity)

PlanetsPeriheliondistance

Apheliondistance

Averagedistance (c) Eccentricity

Mercury 0.3076 0.4666 0.3871 0.0795 0.206Venus 0.7182 0.7284 0.7233 0.0051 0.007Earth 0.9830 1.0170 1.0000 0.0170 0.017Mars 1.3820 1.7654 1.5237 0.1417 0.093Ceres 2.5542 2.9804 2.7673 0.2131 0.077Jupiter 4.9531 5.4525 5.2028 0.2497 0.048Saturn 9.0051 10.0735 9.5393 0.5242 0.056Uranus 18.2814 20.0846 19.1830 0.9016 0.047Neptune 29.78i2 30.3342 30.0577 0.2765 0.009Pluto 29.6800 49.3576 39.5177 9.8399 0.24939. v - 5,000 miles /sec.40. v = (a) 308.7 miles/minute, (b) 5.1 miles/sec., (c) 8.2 kilometers /sec.41. v = (a) 25,085 kilometers/hour, (b) 7 ki!ometem/sec. approximately42. v = (a) 186,000 miles/sec., (b) 299,460 kilometers/sec.43. d = (a) 5,869,714,600,000 miles, (b) 9,450,240,506,000 kilometers, (c) 63,115.22

astronomical units44. Diameter of Milky Way = 100,000 light years45. d = 4.3 light years46. d ---,- 255,135 kilometers47. d = 744,000 miles = 1,197,840 kilometers48. d = 15.5 light years49. t =500 sec. = 81/2 minutes50. t = 4,770 sec. = 791/2 minutes51. t = 1.27 sec.52. t = 500 sec., = 81/3 minutes (same as for visible light)

128

53. (a) 2446 B.C.., (b) 3,500 light years away (the answers to this question are basedon the year A.D. 1964)

54. 65,000 light years55. Gamma radiation has high frequency and radiowave radiation has low frequency.

Radiowave radiation has long wave lengths so it takes longer for one wave lengthto pass a given point than it does for one wave length of shorter wave lengthradiation.

56. frequency range = 7,486,500,000,000,000 (purple or violet light) to 4,278,000,000-000,000 (red light) cycles/sec.

57. A = 129 meters58. A = (a) 1,657 to 1.657 centimeters, (b) 16.57 to 0.01657 meters, (c)

0.05435 feet59. f = 110,911,000,000 cycles/see, = 110,911. megacycles

cycles/see.)60. change in wave length = 0.000002525 meter61. A = 0.003497475 meter62. v = 124.78 kilometers/sec.63. v = 74,865 kilometers/sec.64. (a) 1 centimeter = 100,000,000 angstrom

angstrom units65. v = (a) 43 miles/sec., (b) 69 kilometers/sec.66. v = (a) 2.4 kilometers/sec., (13' 1.5 miles /sec.,

5,400 miles/hour67. t = 1 when d = 16 feet

t = 2 when d = 64 feet68. t = 8 sec.69. a = 444.4 feet/sec.2 approximately.70. t = 11.2 sec. (down)71. t = 16.53 sec.72. v = 3584 feet/sec.73. v = 158.7 meters/sec.74. (a) t = 40.24 sec., (b) d = 338 meters75. (a) 980 centimeters/sec.2, (b) 9.8 meters/sec.276. a = 274.40 meters/sec.2

units (b) 1

(c)

54.35 to

(a megacycle is a million

meter ,,- 10,000,000,000

8,640 kilometers/hour, (d)

t = 3 when dt = 4 when d

- 144 feet= 256 feet

129//30

A SELECTED BIBLIOGRAPHY

Ahnstrom, D. N. The Complete Book of Jetsand Rockets. Yonkers, New York: World,1959.

Asimov, Isaac. Satellites In Outer Space.New York: Random, 1960.

Beauchamp, Wilbur L., et al. Science isExplaining. Chicago: Scott, Foresman andCompany, 1963.

Bondi, Hermann. The Universe at Large.New York: Doubleday and Co., Inc., 1960.

Boyd, R. L. F. Space Research by Rocket andSatellite. New York: Harper, 1960.

Brinley, Bertrand R. Rocket Manual forAmateurs. New York: Ballantine, 1960.

Burgess, Eric. Satellites and Spacecraft. NewYork: Macmillan, 1958.

Butler, S. T. and H. Messel. The Universe ofTime and Space. New York: MacmillanCo., 1963.

Cox, Donald, and Michael Stoiko. RocketryThrough the Ages. New York: Winston,1959.

Davis, Clive E. Messages from Space. NewYork: Dodd Mead, 1961.

Dietz, David. All About Satellites and SpaceShips. New York: Random, 1958.

Dull, Charles E., et al. Modern Physics. NewYork: Holt, Rinehart, and Winston, Inc.,1961.

Elliott, L. Paul and William F. Wilcox.Physics-A Modern Approach. New York:Macmillan Company, 1959.

Fermi, Laura and Gilberts Bernardini.Galileo and the Scientific Revolution. NewYork: 1961.

Gamow, George. Gravity. New York: Double-day and Co., Inc., 1962.

Gardner, Martin. Science Puzzlers. NewYork: Viking, 1960.

Gottlieb, William. Jets and Rockets and HowThey Work. New York: Garden City, 1959.

Haley, Andrew G. Rocketry and Space Ex-ploration. Princeton, New Jersey: VanNostrand, 1958.

Hogben, Lancelot. The Wonderful World ofMathematics. New York: Doubleday, 1955.

James G. S. Rocket Building for Students.New York: Rocket Research Institute,1958.

Joseph, Alexander, Paul F. Brandwein, et al.A Source-book for the Physical Sciences(Demonstrations on pages 366 371). NewYork: Harcourt, Brace, and World Inc.,1961.

131

Knight, Clayton. The How and Why WonderBook of Rockets and Missiles. New York:Grosset, 1960.

Knight, Clayton. Rockets, M issiles, and Satel-lites. New York: Grosset, 1958.

Landau. D. L. What is Relativity (Transla-tion from Russian. Moscow: 1959). NewYork: Basic Books Inc., 1959.

Ley, Willy. Rockets, Missiles, and SpaceTravel. New York: Viking, 1961.

Mark, David. All About Missiles and Satel-lites. Cowan, 1959.

Mehrens, H. E. The Dawning Space Age.Civil Air Patrol, 1959.

Munch, Theodore W. What Is a Rocket.Chicago: Benefit. 1959.

Munroe, Kenneth. A Guide to UnderstandingJets, Rockets, and Satellites. New York:Watch, 1961.

Murchie, Guy. Music of the Spheres (Firsthalf of Chapter 10). Cambridge, Mass.:Riverside Press, 1961.

NASA and U.S. Office of Education. What'sUp There (144 page paperback on spacescience oriented mathematics). Washing-ton: Government Printing Office, 1964.

Neurath, Marie. Man-Made Moons. NewYork: Lothrop, 1960.

Neurath, Marie. Rockets and Jets. New York:Lothrop, 1960.

Newell, Homer E. Express to the Stars. NewYork: McGraw-Hill, 1961.

Newell, Homer E. Guide to Rockets, Missilesand Satellites. New York: WhittleseyHouse, 1958.

Ovenden, NIichae W. Artificial Satellites.Baltimore: Penguin, 1961.

Parker, Bertha Morris. Rockets and Missiles.Evanston, Illinois: Row Peterson, 1961.

Parkin, Charles M., Jr. The Rocket Hand-book for Amateurs. New York: Day, 1959.

Physical Science Study Committee (P.S.-S.C. Text). Physics, (Chapter 5). Boston:D. C. Heath and Co., 1960.

Pratt, Fletcher. All About Rockets and Jets.New York: Random, 1958.

Rogers, Eric M. Physics for the InquiringMind (Chapter 1 on Gravity, Interlude-Appendix on Arithmetic, page 193, andchapter 19 on Galileo). Princeton, N.J.:Princeton University Press, 1960.

Rosen, Sidney. Galileo and the Magic Num-bers. Boston: Little, Brown and Company,1958.

Ruchlis, Hy. Orbit. New York: Harper andBrothers, 1958.

Sargeant, Charles. How to Draw Rockets andSpaceships. New York: Viking, 1958.

Sharp, Elizabeth N. The Science Book-Lab ofJet Engines. New York: Basic, 1961.

Stine, G. Harry. Rocket Power and SpaceFlight. New York: Holt, Rinehart andWinston, 1957.

Taylor, John W. R. Rockets and SatellitesWork Like This. New York: Roy, 1959.

132

Trinklein, Frederick E. and Charles M.Huffer. Modern Space Science. New York:Holt, Rinehart, and Winston, Inc., 1961.

United Nations Educational, Scientific andCultural Org. UNESCO Source Book forScience Teaching (Chp. XI, sec ion B,Experiments with Gravity). Paris:UNESCO, 1962.

Wiech, Raymond E., Jr., and Robert F.Strauss. Fundamentals of Rocket Propul-sion. New York: Reinhold, 1960.

THESPACE

ENVIRONMENT

133//P/

INTRODUCTION

Ear'h unit deals with one aspect of space environment and contains a list of referencesin case the reader wishes to study the subject further.

The Earth's Atmosphere

The NASA-sponsored U. S. Standard Atmosphere, 1962 has furnished the majorportion of the material for this unit. Marginal graphs show average values of atmosphericpressure, density, and kinetic temperature for all altitudes to 700 km. The paragraphson atmospheric composition present the concentrations of both the neutral and ionizedmolecules. This unit concludes with probability contours for the extreme wind conditionsover the United States, abstracted from design data recommendations in the U. S. AirForce Handbook of Geophysics.

The Structure of the IonospherePhotoionization results in the formation of distinct regions of electron concentrations

in the upper atmosphere which are known as the ionosphere. This unit describes thecharacteristics of these regions, including the numerous variations in electron densitiesas to time and what is known of causal and accompanying phenomena.

Solid ParticlesThis unit describes the types of solid particles and their distribution in atmosphere

and space. Recent satellite experiments and ground observations form the basis forcurrent thought on this subject.

Energetic ParticlesThis unit deals witn the atomic and subatomic matter found in space. Although

negligible in size, these particles have dangerously high energies. The introductoryfigure plots the flux of the various particies as a function of their energy. The majorclassifications -- cosmic rays, particles of solar origin, and particles trapped near earth-are easily seen on this plot, as is the fact that particles of cosmic origin have thehighest energies, while the trapped particles exhibit the greatest intensities.

Electromagnetic Radiation

This phenomenon arises from two major sources: the sun and the earth. The unitincorporates recent data obtained by the Tiros satellites in a review of current knowledge.

hfagnetic Fields

This unit discusses the intensities and variations of the magnetic fields which existat the surface of the earth, in the atmosphere, ionosphere, magnetosphere, and inter-planetary space. Evidence from experiments carried by deep space probes forms thebasis for estimates of the magnetic field strength in interplanetary space.

For the contribution of their judgment and time in review of the various unitswe are most grateful to R. E. Bourdeau, Dr. W Nordberg, W. M. Alexander, Dr. C. E. Fichtel,H. H. Malitson, and Dr. J. P. Heppner, all of Goddard Space Flight Center.

EARTH'S ATMOSPHERE TABLE I

'the earth's atmosphere is a gaseous envelope surrounding theearth and extending, outward to where the kinetic velocity of the;Itrnplicric particles overcomes gravitational forces it distancestrain one-halt to one earth radius from the earth's surface. At alti-tudes up to 90 km the atmosphere is a stable, homogeneous mixture,consisting, mainly of nitrogen and oxygen molecules in the ratio ofabout 1 to I. Above 90 km the diffusion process becomes moreimportant than the mixing process, and the various atmospheric con-stituents tend to concentrate at various levels In atomic form withoxygen (having the highest atomic weight) concentrating at lowerlevels and the other elements tending to concentrate at success-ively higher levels in order of decreasing atomic weight. An addedcomplexity in the atmospheric composition above 90 km results fromthe dissociation and ion production induced by solar radiation;belov.. this altitude the atmosphere consists mainly of neutral mole-cules while at higher altitudes the concentration of ionized par-ticles is significant.

Atmospheric parameters of major interest are the pressure, tempera-ture, density, composition, and wind structure as a function ofaltitude. Up to 700 kilometers altitude, the best existent summa-yof pressure, temperature, and density, and variations therein (someestimated) is the 1962 version of the U. S. Standard Atmosphe're.Temperature, pressure, and density data from the new standard aresummarized for some altitudes in Table I and on certain of the mar-ginal figures; the document itself should be consulted for details.This unit goes beyond the standard atmosphere in that the regionabove 700 kilometers is discussed and the parameters of composi-tion and wind structure at all altitudes are included.

The atmosphere affects every space vehicle passing through it bythe drag force exerted, which is directly proportional to the densityof the atmosphere and the square of the space vehicle's velocity.In the low pressure of the upper atmosphere as well as in inter-planetary space, the evaporation of metals and bearing lubricantsr5 a consideration in spore vehicle design Physical-chemicalreactions on surfaces of instrumentation hardware, enhanced bysolar ultraviolet and energetic particle radiation, must also be con-sidered in spacecraft design An atmospheric effect of importanceon space vehicles at lower altitudes is aerodynamic heating andpressure In the radio tracking of space vehicles and spacecraft,ionization effects on radio transmission must bf. overcome. Thedegree of artificial ionization which occurs during reentry of space-craft into the earth's atmosphere is determined by the density andcomposition of the atmosphere as well as by spacecraft velocity

111-1(.111

(hit)11 il/'

(

R

OM)DEVSITY

kg Trl

0.000 288.15 10. 1 i25 4 2 1.2:50 0

11.019 216.6; ,.263, 4 2 3.6192 - 1

20.063 216. 65 5.4747 4 1 8.8035 2

12. 162 228.65 H.6798 (.) 1.3225 - 2

47.150 270.65 I. 1090 0 1.4275 . .3

2.429 270.6.5 5.8997- 1 7.5943 - 451..591 252. 5.5 1.8209 - 1 2.5109. 479.994 180.65 1,0376 - 2 2.001 . 5

90.000 1130.65 1.6437- i 3.170 - 6100.000 210.02 1.0070 - 4 4.974 -

110.000 2.57.00, 7.3527 - 9.829 . 8120.000 349. 49 2.5209 - 5 2.436 . 8

150.00 892.79 5,0599 6 1.8.36 - 9160.000 1,022.20 3,6929 - 6 1.159 - 9170.000 1,103.40 2 7915 - 6 8.036 - 10190.000 1,205.40 1.6945- 6 4.347 - 10230.000 1,322.30 6,9572 - 7 1.564 - 10300.000 1,432.10 L8828 - 7 3.585 . I I400.000 1,487.40 4.0278 - 13 6.498 . 12500.000 1,499.20 1.0949 - 8 1.577 - 12600.000 1.506.10 .3.4475 - 9 4.640 - 13700.000 1,507.60 1.1908- 9 1.5.37 . 13

Terminal number indicates power of 10 by whichpreceding number must be multiplied.

n

1/14i,e)

-

vAx.vs,

771 80h () hi 10 137

4,04,°Sp,.

Pressure, Temperature, and Density

'Table I has been extracted from the U. S. Standard Atmosphere,1963; the entries describe the idealized middle latitude, year-roundmean of three atmospheric parameters over the range of solar acti-vity. These means are more valid for the lower levels of the atmos-phere where ectual observations are more sonverons. A distinctionis, in fact, made in the referenced docament. Tabulated values forthe region below 32 kilometers are considered "standard;' valuesfor the 32-90 kilometer range are 'proposed standard,' while valuesabove 90 kilometers are described as 'speculative.'

The parameters for the region below 90 kilometers have beensufficiently observed that latitudinal and seasonal variations maybe distinguished. A detailed presentation of these vetiattotts forfour latitudes and two seasons will soon be available as suppi.meats to the 1962 standard atmosphere. Variations occompaifyingchange in latitude or season in the region below 90 kilometers may,however, be briefly described as follows. It is estimated that den-site variations range from a low of about 1 percent of the Table Ivalue at 8 kilometers to a high of about 50 pent near 70 kilo-meters. Temperature variations range from 4 'to 30 percent aroundthe tabulated values. Density variations at 90 km are probably lessthan at 70 km but increase rapidly ak-ove 90 km.

Data are insufficient It define mean values of temperature, pres-sure, and density parameters for various seasons or latitudes in the90 to 200 km altitude range; the standard atmosphere values aremans of the existing measurements.

One of the recent results of the space program is the findingthat there are considerable variations in temperature, pressure,and density above 200 km. These variation,: have been directlyrelated to solar radiation. A diurnal variation in temperature in theorder of 500 degrees K may occur in the region from 200 to 700 km.This temperature fluctuation causes diurnal density variations up toone order of magnitude above the temperature variation at thesealtitudes, Consistent with the strong correlation between density/temperature fluctuations and solar radiation in the diurnal cycle,fluctuations in density and temperature cote in a seasonal patternand also in response to solar activity.

It should be noted that the atmosphere at a given time is nearlyisothermal above 300 km. Temperature in these regions is usuallydeduced from density ruersurernents determined from satellite dragobservations.

41-17711'14:(KW)

700

100

_

10.$ 10 10s

PRESSURE (MN)

500

400

300

10-to

DENSITY KG/a M

500 1000TEMPERATURE °IC

1500

Up to 90 kilometers altitude, the atmosphere is a homogeneousmixture, largely of molecular nitrogen (78.08 percent) and oxygen(20.95 percent). Argon and carbon dioxide contribute 0.93 and .03percent respectively. The trace elements include, in order of de-creasing content, the following: neon, helium, krypton, xenon, hydro-gen, methane, nitrous oxide, ozone, sulfur dioxide, nitrogen dioxide,ammonia, carbon monoxide, and iodine. Water vapor is present inincreasing concentration toward., the ground and ozone becomes animportant trace element from 20 to 70 kilometers.

Above 90 km the atmospheric constituents tend to concentrateat differing altitudes in atomic form with elements of higher atomicweight predominating at tower altitudes and those of lower atomicweight concentrating at higher altitudes. Thus oxygen is the pre-dominant component from 200 to 1000 kilometers, helium from 1000to 3000 kilometers, and hydrogen at altitudes above 3000 kilo-meters. An increasing proportion of the atoms and molecules above90 km are ionized with approximately one-half of all constituentsbeing ionized near 1500 km.

Winds

The wind structure of the atmosphere, particularly below 90 km,is a function of locale and time; a detailed prediction can gener-ally be extrapolated only for a brief time period following themeasurement of existing conditions. Statistical summaries areavailable for both world wide and local areas, and data are oftenavailable for inclusion in summaries for new areas of interest.Such data, however, exist only within the range of balloon measure-ments (up to 30 km). The material below presents what are theextreme conditions expected over the United States, consideringaltitudes up to 30 km.

In the winter and over the windiest area of the United Statesthe strongest winds in this altitude range occur between 9 and 12kilometers altitude. The marginal figure shows the speed profileexpected to be exceeded at various probabilities. A speed of 300feet per second will be exceeded only one percent of the time inthe 9-12 kilometer region; the minimum at greater altitudes and thesame probability occurs near 24 kilometers and has a value of about80 feet per second. Available data have also been accumulated andestimates may be made 'f the probability that the expected windfalls within any range of directions.

Wind data for the region above 30 km are limited. The windsblow generally from east or west directions, and a maximum occursin all seasons at altitudes from 50 to 60 km. Much higher windsthan at lower altitudes have been observed in the 50 to 60 kmregion and above. These high wind velocities are mainly important,however, in their effect upon atmospheric circulation and do notpresent a serious problem to space vehicles because the forcerepresented by high winds at these altitudes is relatively small be-cause of low atmospheric density.

139/H0

102 102104

CONCENTRATION

IPARTIC1 ,ES

ALTITUDE(KU)

50% 1%

Parameter:Probability that givenwind speed will beexceeded

10

100 200

RIND SPEED FT/SEC

300

1000

STRUCTURE OF THE IONOSPHERE

The ionosphere, an atmospheric region characterized by the presenceof ionized atmospheric constituents, forms a spherical shell aroundthe earth which begins at approximately 50 kilometers above thesurface. if the term is restricted to its older sense, then the upperboundary of the ionosphere is the altitude at which radiosoundingtechniques become ineffective (about 110 kilometers) This regionis, however, under extensive study by satellites and rockets, andresearch has already shown that the upper boundary is indefiniteand that the region extends to the interplanetary plasma.

Various ionization reactions, triggered either by solar radiationsin the ultraviolet and X-ray regions or by primary and secondarycosmic rays, take place in the ionosphere and are productive of bothelectrons and the heavier charged particles. The density of boththe electrons and the heavier particles at any altitude is a functionof the atmospheric composition at that point and of the flux ofradiant energy. Thus the ionospheric constituents vary with altitude,time of day, solar cycle, season, latitude, and in the case of theclassical F, region, with longitude.

The most important effects of the ionosphere the reflection, re-fraction, and absorption of radio wavesare dependent on the elec-tron density of the ionosphere. A basic finding is that the electrondensity is not uniform but increases at certain altitudes, giving riseto what are known as the D, E, F, and F, regions. These densitymaxima can be directly related to radio wave reflectivity. For eachlayer there is a critical frequency; this frequency is the lower limitto the normally incident electromagnetic waves that will not be re-flected by the layer.

500 -4

MAXIMUM OFSUNSPOTCYCLE

MINIMUM OFSUNSPOT CYCLE

0101 104 106

ELECTRON CONCENTRATION(ELECTRONS/CM') 141

.1000

500

0

MAXIMUM OPISUNSPOTCYCLE

102 to' 10*

ELECTRON CONCENTRATION(ELECTRONS /CM')

D Region

The region of the ionosphere nearest the earth is the D region.Normally it is situated within the altitude range of 50 to 85 kilo-meters. The D region absorbs radio waves of interest but not soextensively as to reflect or severely refract, as occurs in the E andF regions.

Ionization in the D region is generated principally by Lymanalpha radiation. ,:osmic rays, and X-rays. There is general agree-ment that cosmic radiation is the dominant feature in lower D regionionization. In the upper D region the principal ionizing radiation isthought to be, normally, Lyman alpha radiation; the resulting ionsbeing predominantly nitric oxide and molecular oxygen. Shortlyafter certain solar disturbances, hard X-ray (below 8 angstrom units)fluxes increase to high enough levels to become the principalcause of ionization.

The resulting D region electron concentrations are not easilymeasured by land-based ionospheric sounding techniques. How-ever, limited data obtained by land-based methods and rocket flightsare consistent with an approximate figure for the peak electron con-centration of 1000 electrons per cubic centimeter occurring near analtitude of 80 kilometers.

Diurnal and solar cycle effects produce the largest variations in theD region electron densities. The D region is predominantly a day-time phenomenon. During the hours of darkness it all but disap-pears, except under conditions of increased solar activity. It isthought that the disappearance of the D region at night is caused byrecombination of the free electrons with either positive ions orneutral particles. Regardless of the phenomenon, the end result isa decrease in the absorption of radio waves as compared with day-light hours.

Certain types of solar flares are responsible for three types ofabsorption anomalies and for increases in concentration by as muchas two orders of magnitude. The Type I phei ;omenon occurs at thesame time as the solar flare, but only in the sunlit portion of theionosphere. It is called a sudden ionospheric disturbance (SID) andusually lasts approximately half an hour. The resultant radio black-out is thought to be caused by increased ionization of the lower Dregion by X-rays emitted from the sun during the flare. The secondor Type II phenomenon is associated with aurorae and local mag-netic disturbances and takes place mainly at night. Though it ismore intense in nature at higher latitudes, it has been observed out-side the auroral zone. The enhanced radio wave absorption duringthese events is thought to be due to an increased ionization fromsolar particle emission. Polar cap blackouts of the Type IIIphenomenon occur principally above the auroral zones. Theseevents occur a few hours after a solar flare and can persist for anumber of days; their effects are more noticeable during the day-light hours. As might be expected, the occurrence of the abovephenomena is closely related to the 11-year sunspot cycle.

142

,IONOSPHERED REGION

LOCATION

50 85 KM

PRINCIPAL Mi1ZINGRADIATION

L MANa.k R.4 YS

COSMIC RAYS

PRINCIPAL IONS

NO+ 02+

ELECTRON

CONCENTRATION

AT PEAK-103 I.EcmoNs/

CM A7 80 hM

MAJOR VARIATIONS

ELECTRONDENSITY

SunspotMaximum

Su...spotMinimum

Iv I I I

DAWN LOCAL TIZI/./GH TNOON

ANOMALIES

INCREASED IONIZATION

FOLLOWING SOLAR

FLARE ACTIVITY

E Region

Between 85 and 140 kilometers altitude lies the second or Eregion. Ionization in the E region is generated principally bysolar radiation in the ultraviolet range (170-1027A) and by softX-rays. Recent data, showing that the ultraviolet intensities aretwo orders of magnitude greater than formerly believed, have beeninterpreted to mean that the ultraviolet is the more important radiant.The ionization of molecular oxygen by ultraviolet radiation deter-mines the electron content in region E. Other ions thought to bepresent in varying quantities are nitric oxide and monatomic oxygen.

Electron densities in the E region ci,iained from theoreticalmodels as well as by experimental methods are in quite pod agree-ment. Concentrations of approximately 150,000 per cubic centimeterare typical for local noon at sunspot minimum and at 105 kilometers,a typical height for the density maximum.

Diurnal, seasonal, latitudinal, and solar cycle variations ofelectron densities in the E region occur with a relatively high degreeof predictability. The diurnal variation of electron densities islarge with the maximum occurring at local noon. The seasonalvariation is symmetrical about a maximum occurring during the localsummer months. The higher latitudes, though having lower mezndensities throughout the year, have a much greater overall changefrom summer to winter than the lower latitudes. Variations ofconcentration due to solar activity can amount to an increase ofapproximately 50 percent from sunspot minimum to sunspot maximum.

The irregular occurrence of relatively dense concentrations ofelectrons in the E region at altitudes near 100 kilometers is ananomaly called Sporadic E. Sporadic E densities are roughly twicethose in the layer proper. There does not appear to be any correla-tion between the solar variation and Sporadic E except that theanomalous concentrations occur near the magnetic equator duringdaylight hours and at higher latitudes at night. In the temperatelatitudes Sporadic E occurs much more often in the summer monthsthan in the other seasons. It is thought that Sporadic E is causedby the appearance of localized regions of increased ionization inthe main E region and not by increased ionization of the layerproper.

F Region

The third and highest of the ionospheric regions is the Fregion. During part of each day, it is actually two regions, denotedas the F, and F, regions with the F, region mote distinct than theF,. Throughout the remaining hours, between sunset and sunrise,the F, region disappears.

Ionization in the F region is caused principally by solarradiation in the ultraviolet range (170-911 angstrom units).The predominant ions formed are molecular oxygen and nitricoxide in the lower F, region, changing to principally monatomicoxygen in the upper F, and lower F, regions. Monatomicoxygen is the predominant ion to about 1000 kilometers forhigh levels of solar activity. Recent space experiments have

143

IONOSPHERE

REGION

LOCATION 85-140 KM

PRINCIPAL IONIZING

RADIATIONTRAVIOLETSOPT X-RAYS

PRINCIPLE IONS

(O, +) (NO4 ) (04 )

ELECTRON

CONCENTRATION

AT PEAK1.5 x 105 ELEC

CM3 AT 105 KM

MAJOR VARIATIONSELECTRON CONCENTRATION

Seasonal Variation forLow Latitudes

High LatitudeSeasonalV Iriation

00 06 12 1800 00WINTER SUMMER WINTER

ANOMALIESSPORADIC E - LOCALIZEDREGIONS OF APPROXIMATELYTWICE THE NEARBY LAYERDENSITY APPEAR;IONIZATION MECHANISMNOT KNOWN

IONOtPHERE

F REGION

LOCATIONABOVE 140 KM

WITH TWO LAYERSF1 AND F2 OBSERVED

JII

PRINCIPAL IONIZING

RADIATIONULTRAVIOLET

shown that helium ions predominate in a layer of variable thicknessabove 1000 kilometers. At higher altitudes, hydrogen ions predomi-nate.

Electron concentrations in the F region rise to a maximumbetween 300 and 375 kilometers and then taper off t3 the relativelylow levels found in space beyond the ionosphere. In the F, region atypical noon sunspot minimum value for the electron concentration isapproximately 250,000 per cubic centimeter at 170 kilometers, Elec-tron concentrations in the F, region reach a maximum on the order ofone million per cubic centimeter at approximately 320 kilometers.The electron concentrations in the F region are highly variable; thevariations being a function of diurnal, seasonal, latitudinal, solarcycle, and, for the F, region, longitudinal effects.

F. Region

The F, region variations are as a rule much more predictablethan those of the F, region. The diurnal variation of the F, electrondensities is generally symmetrical about the local ra:on maximum due'ing the hours of daylight. At night the densities fall below thosemeasurable by ionosondes (approximately 10,000 per cubic centi-meter), and the F, region becomes indistinguishable from the F,region. The seasonal and latitudinal variations of the F, region arealso directly related to the zenith Pagle of the sun, the average localnoon maxima for each month being symmetrical about the summersolstice. Concentrations throughout a solar cycle will change by afactor of about 1.75 from sunspot minimum to sunspot maximum.

F, Region

The F, region variations are complex; variations with longitudeas well as solar and latitude effects ocCar.

The diurnal variation has two major characteristics:

(a) The change in electron densities at sunrise and sunset is moreabrupt than that in the other ionospheric regions.

(b) In mid latitudes during the winter months daily variations indensity tend to be symmetric, with the maximum lagging noon byabout two hours; but at other geographical positions and duringother seasons the density-time function has two maxima, one beforenoon and one after. There are other complexities of somewhatlesser importance.

Latitude and seasonal variations aro not easily summarized..In general, values of the electron density for latitudes between 50degrees north and 35 degrees south tend to be higher than averageduring November, December and January.

There is a gradual increase in electron density from quiet toactive sun condition.

All of these variations in density are accompanied by a varia-tion in F, region height. The height is greater at night in theequatorial region and increases with increasing solar activity.

144

PRINCIPAL IONS

LONER REGION I 024 NO+MIDDLE REGION 0+UPPER REGION He+ II+

ELECTRONCONCENTRATION

2.3 K 105 ELECTRONS/CVs

AT 170 /CM (F,/

ELECTRONSICAI%

AT 320 KM (F2)

MAJOR VARIATIONSF, LAYER

ELECTRON

CONCENTRATION

Seasaaat andSala. Cycle

Limit ofObservation

00 00 1200 1800 2400SINTER SUMMER !TINTERQUIE7 SUN ACME QUIET

MAJOR VARIATIONSF, LAYER

ELECTRONCONCENTRATION

1

Hid Latitudes,(Tinter)

DAWN LOCAL raluctir

NOON

The major anomaly. is the appearance, usually at night, ofregions of higher electron densikies. This gives rise to a multi-plicity of returns to sounding appiatus. hence the term Spread Fused in zeference to this phenomenon. The frequency of occurrencevaries frcn rare occurrences at 35 degrees geomagnetic to greaterfrequencies at high latitudes with a quiet sun. In temperate lati-tudes, Spread F tends to be associated with magnetic disturbances.Recent rocket sounding experiments also indicate e dependence ofSpread F on the magnetic field; the multiple returns were believedthe result of field guided ducting along magnetic field alignedirregularities. Preliminary data from And and Alouette satellitesindicate that irregularities are associated with the Van Allenradiation belts.

145 /1V6

VARIATIONS NOTPICTURED

I) ABRUPT CHANGES ATSUNRISE AND SUNSET

2) LATITUDE AND SEASONALVARIATIONS

.1) INCREASE KITH ACTIVESUN

4) HEIGHT VARIATIONS

SOLID PARTICLES

It has long been recognized that meteors age evidence that spacemust contain solid particles. Study .Ixid deduction, particularly thatbased on %issue! observations of meteors, has resulted, fa the largerparticles. in magnitude estimates of the important parameters: it

ie. density, velocity, flux and spatial distribution. Currently,study of the collisions of the smaller particles with instrumentedportions of satellites is adding significantly to existing knowledge.

The solid particles are from one of two sources, comets or asteroids.Ninety percent of the particles found in space are estimated to beof co3tetary origin.

The principal effect of the solid particles on space vehicles is notstructural failure but rather the degradation of the exposed surfaces,particularly those of sensitive instrumentation. Mass-to-flux rela-tionships obtained to date indicate that damage from puncture issecondary to the erosion hazard.

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0

147

METEORITESS

Physical Characteristics

The solid matter land;ng on the earth falls into three categories:the iron meteorites (densities 7-8 grains per cubic centimeter), themote numerous stone meteorites (densities 3-4 grams per cubiccentimeter), and the 'dust balls' (densities 0.1-2.0 grams per cubiccentimeter.) Estimates of mean velocity with respect to the earthrange from IS to 43 kilometers per second, with 30 kilometers persecond often used in computations when a single representativevalue is 'required. The preponderance of the solid particles is be-lieved to be small (1-100 microns in diameter); particles in thissize range are collectively referred to as the interplanetary dust.The bulk of the interplanetary dust is concentrated near the planeof the ecliptic and the separate particles are, as is the earth, indirect, rather than retrograde, orbit around the sun.

There is known to be considerable variation in the physicalparameters. There is a lower limit to size imposed by radiationpressure from the sun which sweeps particles smaller than aboutone micron in diameter from the solar system. There is no definiteupper limit to size; bodies many miles in diameter are known toexist. The lower limit to velocity, relative to the earth, is 11 kilo-meters per second, the velocity acquired by a falling particle ini-tially at rest with respect to the earth.' The upper limit, 72 kilo-meters per second, is obtained by adding the earth's orbital velocityto the velocity a particle would need to escape the solar systemfrom an orbit about the sun at one astronomical unit.

Recent satellite experiments have been designed to measure thesolid particle flux (the number of encounters per unit area per unittime) for particles too small to produce a meteor detectable byvisual, optical, or radar techniques. As shown in the introductoryfigure, the measured flux of the smaller particles prove to be greaterthan would be expected by extrapolation of the older data. Of par-ticular interest, therefore, will be those future studies of the fluxin the yet unknown region between the two sets of data. Finally,the introductory figure shows what is called the sporadic, or ave-rage, particle flux. Meteor showers are a well known and oftenoccurring phenomenon and flux rates at a shower peak can rise tovalues which are four or five times the sporadic rate.

The concentration of the greater bulk of the solid material, i.e.,the interplanetary dust, in the plane of the ecliptic has been noted.Deductions based on observations of the zodiacal light indicatethat the dust concentration is highest near the sun snd that theconcentration diminishes roughly in inverse proportion to the threehalves power of the distance from the sun. There is some evidencethat the concentration may be slightly elevated in the immediatevicinity of the earth.

TYPES AND DENSITIES

IRON

STONE

DUST BALLS

7-8 Gli/CAls

3-4 CM /CM'

.1-2 GIVICIls

MEAN VELOCITY

30 KM /SEC

SIZE RANGE

1 MICRON TO MAN' MILES

VELOCITY RANGE

II KM/SEC 72 KM/SEC

VARIATIONS

1) FLUX RATES 4 or 5 TIMES

HIGMER DURING METEOR

SHOWERS

2) CONCENTRATION IS HIGHER

BOTH IN THE PLANE OF THE

ECLIPTIC AND IN THE REGIONS

NEAR THE SUN

If any particles are trapped in geocentric orbits near the earth, the relative velocities may be as low as 8 km/sec.EGO sr ill attempt to detect particles in geocentric orbits.

148

ENERGETIC PARTICLES

The existence of charged atomic and subatomic material in the spaceenvironment has long been deduced from the study of cosmic rayevents at the earth's surface. Further understanding resulted fromdata taken in those atmospheric regions accessible bg. balloons. Theadvent of rockets, satellites, and deep space probes has added sig-nificantly to knowledge, but understanding is not yet complete. It isknown that these particles are both plentiful and of various types andthat they have energies extending over a broad range. Not completelyknown are the complex processes which propagate and distribute thepenetrating particles nur is their origin definitely established. Themajority, if not all, of the energetic particles in space are apparentlyby-products of the nuclear reactions occurring in the stars, but othersources have been proposed. The energetic particle flux in the nearearth region, in fact, can be looked upon as a summation of charged,energetic material contributed from the entire universe and basicallyisotropic in nature, upon which special concentrations and orienta-tions are imposed--since these particles are charged--by the magneticfields of the sun and the earth.

The most useful classification of these particles, for the purpose ofexposition, is not by source, however, but in terms of their energy.When displayed upon an energy scale, as in the introductory figure,four categories, which intlude the important phenomena, cau be dis-cerned: galactic cosmic radiation, solar cosmic radiation, the solarwind, and radiation trapped in the earth's magnetosphere. Thesecategories are used in the following discussion.

The effects of the various energetic particles on space missions canbe serious, since both men and equipment are adversely affected byhigh radiation dose rates. Intensities of the radiation trapped in theearth's field and intensity increases resulting from solar storms aresufficiently high to yield a dangerous dose even for short missionsand shielding must be provided. The potential effect of these par-ticles on exposed surfaces must also be considered; it Is known, forexample, that solar cells are rendered inoperative by radiation unlessprotected. Also, the Wide range of intensities compounds the diffi-culties of the designer of probes which are directly intended for themeasurement of, or indirectly affected by, the presence of chargedparticles.

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149

i()" SO"ENERGY (EV)

10111 Loll roll* 101

Galactic Cosmic Radiation

Particles with energies in excess of 10 mev are usually classedas galactic cosmic radiation. Energies of some of these particlesare so high that their radius of curvature in the interplanetary mag-netic field is of the same order of magnitude as the size of ourgalaxy, thus 'local' origin is unlikely. Most of those observed,however, presumably originate in our galaxy. The favored theory isthat the cosmic radiation is a byproduct of the reactions that lead toa supernova. Theories have also been proposed which postulateboth a beginning, with lower energies, in surface eruptions from thestars and then an acceleration process, depending on the magneticfields in space, to bring the particles to their observed highenergies,

Hydrogen nuclei constitute the greater percentage of the galac-tic cosmic radiation. In order of decreasing abundance occur thenuclei of helium; of the carbon, oxygen, nitrogen group; and of neon,etc to atomic numbers as high as 26 (iron) and the nuclei of theboron, lithium, beryllium group. Electrons also occur as a minorconstituent. Because of the widely distributed sources and dielong, curved pathways of these particles, the radiation as perceiveaat some point in space is essentially isotropic, i.e., equal inten-sities are measured for any direct ion of observation. The galacticparticle flux in the near earth region lies between I and 3 particlesper square centimeter per second with tia particle flux versus energyspectrum beginning near 10' ev, rising rather abruptly to a peak fluxat 1 bev, and falling off with higher energy in approximate inverseproportion to the energy raised to the 2.5 power.

Although the net result of the transit of galactic cosmic raysthrough the magnetic fields of space is to produce evenly distributedradiation, departures from the isotropic condition are to be expectedin regions dominated by strong 'local' magnetic fields. These fieldsaffect the number of particles reaching a point as well as the iso-tropic distribution. The magnetic fields associated with the sunthus tend to shield the earth from cosmic radiation. tending to bendaway particles which would otherwise proceed to the earth. Thereis a result about a 3 to 1 change in cosmic ray intensity near theearth over the solar cycle, with the intensities lower at the time ofsolar maximum. Flare activity on the sun can in some cases in-crease the magnetic field over a large region in space; when theearth is included within such a region, cosmic ray intensities fall(the phenomenon is known as the Forbush decrease) by a variablefactor which can be as high as 15 percent of the norm. Variationsin cosmic ray intensities as measured at the earth's surface itselfinclude those in the near earth region with added complications dueto the presence of the earth's atmosphere. At altitudes between 15and 35 kilometers, the incoming primary cosmic particles hit andshatter atoms in the air introducing a new phenomenon: a complexdistribution of kiss energetic secondary particles which shower downto the earth's surface. The flux of these secondary particles varieswith altitude, latitude, longitude, and solar activity.

150

1 i_. 11C L Oc VP(

b7-!./)/ a TUP

ENERGIES

FO' 1019 ev

ORIGIN

UNIVERSE

COMPOSITION

NUCLEI OF:

H 85%He 12%

C, N, 0 I%Ne and greater - .25%H. Li, Be - .25%ELECTRONS 1-3%

FLUX

1-3 PARTICLES/CBI/SEC

VARIATIONS

I) 3 TO 1 CHANGE WITHSOLAR CYCLE

2) AS HIGH AT 10% 11THFLARE ACTIVITY

3) WITH PENETRATION INTOTHE ATMOSPHERE

4) WITH LATITUDE ANDLONGITUDE ON EARTH'SSURFACE

Solar Wind and Solar Flares

Recent space experiments have shown that the solar atmosphereextends in tenuous form as an ionized gas to distances beyond theearth's orbit and that two dynamic phenomena exhibited by thisatmosphere, the solar wind and solar flares, are of importance assources of particles which reach the near earth registers. The termsolar wind refers to the steady escape of ionized particles from thesun, moving in radial paths as a result of processes not completelyunderstood but which have been conceived as a continuous expan-sion of the solar atmosphere. Flare phenomena are abrupt, explosiveruptures of tremendous energy in the visible solar surface whichresult in increased electromagnetic radiation and in increased par-ticulate radiation, largely protons, from the sun. Solar windparticles are of low energy, but flare-ejected particles can reach thehigh energies typical of the galactic cosmic rays,

The consensus is that the solar wind is a plasma, i.e., a neutralassemblage of protons and electrons. Presumably the wind is con-tinual. A wide variation exists in reported values for the particleconcentrations in the solar wind (10. to 10' per cubic centimeter),and in the velocities (10 to 3 x 10' kilometers per second).Explorer 10 measurements showed plasma densities from 6-20protons per cubic centimeter and an energy spectrum peaked at 500ev. Mariner 2 measurements gave an energy range from 750 to 2500ev. The figure of 10 protons per cubic centimeter with a velocity of500 kilometers per second (1.5 key) was recommended in a recentNASA summation as a quiet day value.

Generally speaking, the earliest solar flare proton arrivals at apoint in the near earth region show directionality since they havebeen guided along a favorably configured magnetic field. Laterarriving protons tend to come from all directi..ais, having traveledover longer, more devious pathways or having been trapped within amagnetic field configuration which favors an isotropic arrival pat-tern. As these last statements imply, the magnetic field betweenearth and sun is not a static field. Moving plasmas carry along themagnetic fields with which they were originally associated; thusthe solar wind carries along a portion of the sun's magnetism andimposes a rough radial order or the interplanetary magnetic fieldbetween sun and earth. A large portion of the complexities in solarflare proton phenomena is believed due to the fact that flares, intheir early stages, increase the sola- plasma emission sharply alongthe line of a solar radius drawn through the flare. The field betweenthe earth and sun may, as a result of such plasma bursts, be madeeven more favorable for proton propagation to the near earth region;also, as pictured in the marginal drawing, the resulting field canenhance an isotropic proton arrival pattern.

Flare phenomena are highly variable both because of the varyingmagnetic field conditions between sun and earth and because ofvariations in the processes within the sun that generate the particles.it has been said that the most typical feature of flare phenomena istheir variability. Proton velocities can rise to near light speed dur-ing a relativistic flare, Energies of 1 mev to 1 bev are typical ofthe non-relativistic flare particles and some major flares eject par-ticles with energies as high as 10 bev, i.e., in the galactic cosmicray range.

151

ILI

SOLAR WINDCONCENTRATION:

10 PROS ONS/CM1LOCI T)':

500 kifisf.1:ENERGY:

/.5 I

SOLAR FLARESVELOCITY:

TV NEAR LIGHT SPEEDENERGY:

AS HIGH .45 10 REA'

AR giNDORDEREDMAGNETIC

FIELD

Trapped Radiation

One of the earlier and more spectacular findings of the spaceprogram was the discovery that the earth is surrounded by toroidalshaped belts of energetic protons .gad electrons. These belts werenamed the Van Allen Radiation Belts after their discoverer, JamesVan Allen. Controversy still exists as to the ultimate source of theVan Allen particles; theories postulating the sun and/or the earth'sAtmosphere have been proposed as sources. The trapping mechanismis, on the other hand, well understood. Charged particles of properenergy and direction entering the earth's magnetic field are forcedinto pathways that spiral around magnetic lines of force. Not allparticles spiral down to the surface or into the atmosphere alongthese paths; for many, as the earth's surf ace is approached, thespiral flattens until the spiraling motion is actually reversed andthe particle spirals back to the other side of the earth. The spiralagain flattens, the motion is repeated, and the trapped particlesspiral back and forth from one hemisphere to the other. It shouldbe added that each loop of the spiral is 'tighter' on the side near-est the earth and the cumulative effect of this is a drift in longi-tude superimposed on the hemisphere-to hemisphere motion.

The marginal figure shows counting rate conburs for unshieldedgeiger tubes in Pioneer 3 ^nd Explorer 4 flown through the radia-tion belts. The major fer.iures of the belts are easily identified.Their contours follow the lines of the earth's magnetic field with anopen region over both poles. There are two regions of concentra-tion where the counting rate peaks--the one at earth radii iscaused by fast-moving protons; the maximum at 3-4 earth radii isdue to energetic electrons. However, protons and electrons oflower energy are known to penetrate the whole trapping region, andthe Van Allen region can be pictured as a region more or less homo-geneous in character and populated by low energy electrons andprotons (104 key) having roughly equal flux values of 10' particlesper square centimeter per second and energies of tens of thousandsof electron volts. Superimposed on this steady background are tworegions where flux values are much lower and energies consider-ably higher. The innermost of these regions is the proton belt,which has a flux value of -102 particles per square centimeter persecond in the 10-100 mev range, with the flux value droppingsharply at higher energies. The outermost of these regions consistsof high energy electrons which have a peak flux between 102 and 10"particles per square centimeter per second for energies above 1 or2 mev. Finally, a glance at the cover figure shows that while theenergy of Van Allen particles is between 10' and 10' electron voltsthe number of particles is such that peak intensities within the beltcan be significantly higher than for solar flare particles or cosmicrays.

Of the two belts, the inner or proton belt is the more stable.Flux in the outer zone can vary in less than a day by a factor often or more, while flux in the lower zone has been observed torequire a year for a change of a factor of three.

152

TRAPPED PARTICLEMOTION

s

PROTON

COUNTING RATECONTOURS

Electrons

ELECTROMAGNETIC RADIATION

Electromagnetic waves with wavelengths eitending across the mea-surable spectrum are an important factor in the interplanetary en-vironment. Radiation occurs in the X-Ray, ultraviolet, visible andinfrared regions and at radio frequencies.

The source of major importance in the near earth region is, ofcourse, the sun. The total radiated energy (producing a flux of0.140 watts per square centimeter at the earth's mean distance)is remarkably colIMWAI and largely concentrated in the visible regionof the spectrum. Variations of as much as a thousand fold inintensity have been measured for the short wavelength solar emis-sions, but the average level of the sun's spectrum is relatively lowin this region and the short wavelength variations are a negligiblefraction of the sun's total output. The earth is a secondary sourceof lesser importance. The earth reflects a portion of the suesenergy; absorption and ?eradiation also occur. The intensity of theelectromagnetic radiation varies with distance from the source. Thespectral distribution changes only as the waves traverse differentmedia, notably the earth's atmosphere.

There are several important effects. The human body is normallyshielded from ultraviolet radiations by the atmosphere and equiva-lent shielding must be provided for manned missions. Increasedluminance in the visual region is a hazard to the unaided eye.Thermal radiations must be considered in achieving suitable tem-peratures in vehicle interiors. Radio frequency energy is import-ant when it manifests itself as noise in communication circuits.

773406 0,65-11153

Electromagnetic Radiation from the Sun

Solar radiation in the ultraviolet and X-ray regions constitutes only .2 percent of the sun'stotal emission. Flux levels are low and, with one or two exceptions, lie between .001-.0001microwatts per square centimeter in a one-angstrom band. In contrast to other regions of thesolar spectrum, this region has strong emissions at particular wavelengths; the strongest(Lyman alpha) having a flux value of about .1 microwatts per square centimeter in a one-angstromband.

The ultraviolet and X-ray emission from the sun consists of both a continuous spectrum anda line spectrum typical of highly ionized atoms. Since this radiation does not penetrate the at-mosphere, the X-ray and ultraviolet region is not well known and is the concern of continuingrocket and satellite experiments.

Some inconsistencies still exist in measurements of flux values and the complete story onvariation with time is not yet available. Ten-fold variation in the region below 140 angstromshas been observed to be correlated with the solar cycle, and significant variations accompanysolar flare activity. Flare variations tend to take the form of enhancements of the very shortwavelengths, wavelengths as short as 0.2 angstrom having been briefly observed. Current Or-biting Solar Observatory experiments are concerned with long-time study of both spectral linesand the continuous spectrum; preliminary results from OSO I indicate a 15 percent enhancementfor the 304 angstrom line and a 28 percent enhancement for the 281 angstrom line during a class2 plus solar flare.

The peak in the solar emission speCtrum occurs in the visible region. Radiation in the vis-ible and infrared regions is a continuum explainable as 6000°K black body thermal radiation fromthe sun's photosphere. Numerous absorption lines and bands appear as a result of selective ab-sorption by various constituents of the solar and terrestrial atmospheres. The terrestrial atmos-pheric constituents which give rise to the so-called telluric absorption lines and bands in thespectrum are well known and various techniques exist for predicting the solar spectrum at inter-mediate altitudes.

Since the visible and infrared waves carry a large percentage (99%) of the emitted solarenergy, total flux values for these spectral regions are well approximated by the tabulated solarconstant, which gives the total, above atmosphere flux at one astronomical unit. The visible andinfrared emission of the sun is remarkably constant. The solar constant varies, predictably, withthe earth-sun distance, but short term variations are smaller than 1 percent.

Solar radio waves are observed from the upper limit of the infrared waves to waves of 20, to30 meters length. Longer waves do not penetrate to the earth's surface through the ionosphefre.The steady state flux at the mean earth-sun distance is low and falls off with increasing waive-length.

Radio waves are emitted from solar regions lying above the photosphere with the shorterwaves radiating from the level of the chromosphere and the longer waves from the corona, orouter solar atmosphere. The temperature of the equivalent black body is thus considerablyhigher than for the visible wave emission from the cooler photosphere.

The radio wave flux values are low except when certain solar flares occur. Levels can thenincrease by as much as a millionfold at the long wavelengths. Not all wavelengths are equallyaffected and the duration of the effect is variable, sometimes lasting more than a day. Thesetransient effects are strong enough to produce severe interfering noise in communication circuits.

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Electromagnetic Radiation from the Earth

Radiant energy from the sun is in part reflected from the earth;also a fraction of the solar energy absorbed is reradiated in acontinuous spectrum in the infrared. There are atmospheric absorp-tion bands and an atmospheric window in this spectral region so thatreradiation from the earth is in part from the earth's surface throughthe window (8 to 12 microns) and in part from the atmosphere. Reflec;tion of solar radiation produces the greater fraction of the reversedflux in the .2 to 6 micron region.

The fraction of the solar energy reflected into space is known asthe albedo, and direct measurements have been made of this quantityby the Tiros satellites. Reported reflectance values range from a lowof 7 percent over the tropical Atlantic to a high of 55 percent over adense overcast above the East Central United States.

The black body radiation from the earth in the 8 to 30 micronrange has a peak near 10 microns with 288 degrees Kelvin black bodyradiation used as an approximation to the radiation from the surfaceand a 218 degrees Kelvin model for those spectral regions where theatmosphere is opaque. Tiros data show that in most cases theequivalent black body temperature for the window region correspondsclosely to the temperature of the earth's surface.

The solar reflected energy input to an orbiting vehicle can beexpected to be quite variable and to depend on the nature of thesurface slid the cloud cover underneath. Variations in albedo andequivalent black body temperatures have already been noted. Pre-cise determinations of the total input energy, both reflected andradiated, require a knowledge of the vehicle's altitude and itsorientation with respect to that portion of the earth's surface whichis being illuminated by the sun.

156

2

' 1 1

FLUX(Tunes 103 watts /cm2imirron)

288°A Mack Rod)

Rad(ation from

Earth andAtmosphere

218 Mark Dad)

ti

10 20 30WAVELENGTHS (MICRON'S)

VARIATIONS

1) WITH ALBEDO (RANGE 7-55%)

2) a, 71 VEHICLE POSITION ANDORIENTATIor.

MAGNETIC FIELDS

Magnetic fields at the surface of the earth, in the atmosphere, andextending outward into space through the earth's magnetosphere aremainly a consequence of complex electrical current systems withinthe metallic_ core of the earth. Beyond the magnetosphere there isa .region containing a highly irregular field; beyond this transitionregion is the interplanetary magnetic field, the characteristics ofwhich are related in a complex way to equally complex solar phenomena.

Since the magnetic field strengths in st,-.ce are small, their effecton electronic equipment is generally minor. Thus adverse effectsof the ambient field upon instrumentation can usually be negated byproper design or adequate shielding. Other magnetic effects in spaceinclude damping of spacecraft spin rates and creation of torqueswhich might affect spacecraft orientation. M gnetic fields also re-sult in the concentration of charged parti ,ies either in belts nearthe earth or within solar-flare ejected plasma clouds; and the fluxand energy of these magnetically trapped particles is sufficient topresent a definite hazard to space missions.

Earth's Magnetic Field

The earth's magnetic field extends outward from the core of theearth into space. Above the ionosphere, it is called the magneto-sphere. Satellite measurements indicate that the magnetosphere isnot a perfect sphere but extends about 10 earth radii in' the directionof the sun (Explorers 12 and 14) and least 20 earth radii directlyaway from the sun. (Explorer 10).

Although the magnetic field. at the surface of the earth is highlyirregular, it can, in general, be conceived as resulting from a mag-netic dipole located near the center of the earth. The total strengthof the surface field varies between approximate maxima and minimaof 0.7 and 0.25 gauss. Irregularities arise from terrestrial and extra-terrestrial influences.

Terrestrial influences include crustal differences in ferromag-netic content which cause local anomalies in the magnetic field atthe earth's surface. Major irregularities in the surface field are be-lieved related to the distribution and orientation of internal currentand eddy systems within the molten core of the earth. These cur-rants are continually but slowly changing in form and intensity,giving rise to secular or long-term changes in the surface field. Thesecular. change in most areas amounts to less than two tenths of onepercent per year.

Extraterrestrial phenomena are also responsible fol changes inthe magnetic field on the earth's surface. These variations are ofshort duration and have been observed to be related to solar dis-turbances as well as to diurnal, seasonal, and solar cycles. Dura-tion of these deviations ranges from a fraction of a second to seve-ral days with changes in intensity ranging from .01 to several hun-dred gamma (1 gamma equals .00001 gauss) except in the auroralzones where considerably larger changes are not ancommon.

The two most important factors of change are the diurnal cycle,resulting in intensity changes of 50 gamma in middle latitudes andup to 200 gamma at the magnetic equator; and magnetic storms,arising from solar disturbances, which result in variations of severalhundred gamma except in the auroral regions where changes up to2,000 gamma can occur.

Values of magnetic field strengths at the surface of the earthmay be used to obtain good approximations of field strengths up toan altitude of 5 earth radii since field strength in this inner regiondiminishes with rising altitude roughly in inverse proportion to thecube of the distance to the center of the earth. Thus, levels on theorder of 0.10 gauss will be found, at a mean altitude of 4000 kilo-meters. Above 5 earth radii the magnetosphere has a greater fieldstrength than would tie indicated by the relationship with surfaceintensities prevailing for altitudes below 5 earth radii.

158

EAR THIS MAGNETIC

FIELD

EXTENT

FROM 10 EARTH RADII IN THE

DIRECTION OF THE SUN TO

OVfIR 20 RADII IN OPPOSITE

DIRECTION

STRENGTH

BETWEEN .25 AND 0,7 GAUSS ATSURFACE

ANOMALIES ANDVARIATIONS

1. CAUSED BY CRUSTAL. DEPOSITS

2. or CHANGES IN THE EARTH'S

INTERNAL CURRENT SYSTEM

3. SOLAR ACTIVITY AND CYCLES

4. DIURNAL CHANGES OF A S

MUCH AS 200 GAMMA

5. CHANCES OF 2000 GAMMA DURING

MAGNETIC STORMS

t EXTRAPOLATIONS OF SURFACE

FIELD ARE GOOD TO

AITROXIMATELY 5 EARTH

IiADH

The Interplanetary Magnetic Field

At about 10 to 15 earth radii in the direction of the sun and togreater distances in the direction away from the sun, between themagnetosphere and the interplanetary magnetic field, there appearsto be a turbulent transition field. Here, extreme variations are pre-sent in both the strength and direction of the magnetic field vectoras a result of interaction between the magnetosphere and the mag-netic field carried along by charged particles emitted from the sun.Beyond the transition region in all directions the magnetic fieldsassociated with the solar particles become predominant. In thesefields there is a continual component from the solar particle emis-sion (the solar wind) which extends the solar magnetic field intointerplanetary regions. There is also an important but irregularcomponent related to the increased particle emission that accom-panies solar flare activity. In the absence cf flare activity, theinterplanetary magnetic field immediately beyond the transition fieldhas intensities on the order of 5 to IS gamma (Explorer 10). Varia-tions in the interplanetary field due to flares caL increase intensi-ties by as much as five times.

Furthermore, under solar flare conditions, solar magneticeffects penetrate more deeply into the earth's magnetosphere,affect the degree of ionization in the ionosphere, and cause mag-netic storms at the earth's surface.

.

INTERPLANETARY

MAGNETIC. FIELD

STRENGTH

3 - 15 GAMMA

VARIATION

AS MUCH AS 5 TIMES DURING FLAREACTIVITY

GLOSSARY OF TERMS

USED IN THE

EXPLORATION OF SPACE

161/,42-

GLOSSARY OF TERMS USED INTHE EXPLORATION OF SPACE

AAberration-1. In astronomy, the apparent displace-

ment of the position of a celestial body in the direc-tion of motion of the observer, caused by the com-bination of the velocity of the observer and thevelocity of light. 2. In optics, a deviation from)perfect imagery as, for example, distortion.

Ablating MaterialA material designed to dissipate heatby vaporizing or melting.

Ablating materials are used on the surfaces ofsome reentry vehicles. Ablating materials absorbsheat by increase in temperature and change inchemical or physical state. The heat is carried awayfrom the surface by a loss of mass (liquid or vapor).The departing mass also blocks part of the convey-Vim heat transfer to the remaining material.

AblationThe removal of surface material from a bodyby vaporization, melting, or other process; specificallythe intentional removal of material from a noseconeor spacecraft during high-speed movement througha planetary atmosphere to provide thermal protec-tion to the underlying structure. See AblatingMaterial.

AbortTo cancel or cut short a flight.Absolute AltitudeAltitude above the art

a planet at natural satellite, eithsiurfasse ofr water.

Absolute Pressure In engineering ,re, a termused to indicate pressure abo, absolute zerovalue corresponding to empty sp e as distinguishedfrom "gage pressure ".

In vacuum technology, "pressure" always cor-responds to absolute pressure, and therefore the term"absolute pressure" is not required.

Absolute TemperatureTemperature value relative toabsolute zero.

Absolute ZeroThe theoretical temperature at which allmolecular motion ceases.

"Absolute zero" may he interpreted as the tem-perature at which the volume of a perfect gasvanishes, or mare generally as the temperature ofthe cold source which would render a Carnot cycle100 percent efficient. The value of 114(4{4 tens isnow estimated to be 273.16° Celsius (Centigrade),459.69° Fahrenheit, 0° Rankine.

AbsorptionThe process in which incident electromag-netic radiation is retained by a substance. A furtherprocess always results from absorption: that is, theirreversible conversion of the absorbed radiationinto some other form of energy within and accord-ing to the nature of the absorbing medium. Theabsorbing medium itself may emit radiation, butonly after an energy conversion has occurred.

AccelerationThe rate of change of velocity.Decrease in velocity is sometimes called "negative

acceleration."

AccelerometerAn instrument which measures accelera-tion or gravitational forces capable of impartingacceleration.

An accelerometer usually uses a concentrated mass(seismic mass) which resists movement because ofits inertia. The displacement of the seismic massrelative to its supporting frame or container is usedas a measure of acceleration.

Acceptance --The act of an authorized representative ofthe Government by which the Government assentsto ownership by it of existing and identified articles,or approves specific services rendered as partial orcomplete performance of the contract.

Meese TimeOf a computer, the time required underspecified conditions to transfer information to orfrom storage, including the time required to com-municate with the storage location.

AccumulatorA device or apparatus that accumulatesor stores up, as: 1. A contrivance in a hydraulic sys-tem that stores fluid under pressure. 2. A devicesometimes incorporated in the fuel system of a gas-turbine engine to store up and release fuel underpressure as an aid in starting.

Acoustic ExcitationProcess of inducing vibration in astructure by exposure to sound waves.

Acouidic Generator Transducer which converts electric,mechanical, or other forms of energy into sound.

Acoustic VelocityThe speed of propagation of soundwaves. Also called "speed of sound."

Acquisition-1. The process of locating the orbit of asatellite or trajectory of a space probe so that track-ing or telemetry data can be gathered. 2. The processof pointing an antenna or telescope so that it isproperly oriented to allow gathering of tracking ortelemetry data from a satellite or space probe.

ActinicPertaining to electromagnetic radiation capableof initiating photochemical reactions, as in pho-tography or the fading of pigments.

Because of the particularly strong action of ultra-violet radiation on photochemical processes, the termhas come to be almost synonymous with ultraviolet,as in "actinic rays".

ActiveTransmitting a signal, as "active satellite," incontrast to "passive".

AdiabaticWithout gain or loss of heat.AdsorptionThe adhesion of a thin film of liquid or gas

to the surface of a solid substance. The solid doesnot combine chemically with the adsorbed substance.

AerobiologyThe study of the distribution of livingorganisms freely suspended in the atmosphere.

AeroductA ramjet type of engine designed to stoopup ions and electrons freely available in the outerreaches of the atmosphere or in 'the atmospheres ofother spatial bodies, and by a chemical processwithin the duct of this engine, expel particles derivedfrom the ions and electrons as a propulsive jetstream.

163

Aerodynamic HeatingThe heating of a body producedby passage of air or other gases over the body,significant chiefly at high speeds. caused by frictionand by compression processes.

AerodynamicsThe science that treats of the motionof air and other gaseous fluids. and of the forcesacting on bodies when the bodies move through suchfluids, or when such fluids move against or aroundthe bodies, as "his research in aerodynamics"

Aerodynamic VehicleA device, such as an airplane,glider, etc., capable of flight only within a sensibleatmosphere and relying on aerodynamic forces tomaintain flight.

This term is used when The context calls for dis-crimination from "space vehicle."

AeroelasticityThe study of the effect of aerodynamicforces on elastic bodies.

AeroliteA meteorite composed principally of stonymaterial.

Aeronomy-1. The study of the upper regions of theatmosphere where physical and chemical reactionsdue to solar radiation take place. 2. Science dealingwith theories of planetary atmospheres.

AeropauseA region of indeterminate limits in the upperatmosphere, considered as a boundary or transitionregion between the denser portion of the atmosphereand space.

From a functional point of view, it is consideredto be that region in which the atmosphere is sotenuous as to have a negligible, or almost negligible,effect on men and aircraft, and in which the phy-siological requirements of man become increasinglyimportant in the design of i;lircraft and auxiliaryeV( ipment,

Aerospace(From aeronautics and space.) Of or per-taining to both the earth's atmosphere and space,as in "aerospace industries".

Aerothermodynamic BorderAn altitude at about 100miles, above which the atmosphere is so rarefiedthat the motion of an object through it at highspeeds generates no significant surface heat.

AerothermodynamicsThe study of the aerodynamicsand thermodynamic problems connected with aero-dynamic heating.

Afterbody - -1. A companion body that trails a satellite.2. A section or piece of a rocket or missile that re-enters the atmosphere unprotected behind the nose-cone or other body that is protected for reentry. 3.The aft part of a vehicle.

AgenaA second stage rocket which burns liquid oxygenand kerosene, often used with an ATLAS first stageby the United States for satellite and spacecraftlaunchings.

AgravicOf or pertaining to a condition of no gravita-tion. See Weightlessness.

AirglowThe quasi-steady radiant emission from theupper atmosphere as distinguished from the sporadicemission of the our rae.

Airglow is a chemiluminescence due primarily tothe emission of the molecules O. and N:, the radicalOH, and the atoms 0 and Na. It may be due toreleased latent energy from energy stored during

164

daylight. Emissions observed in airglow could arisefrom 3-body atom collisions forming molecules,from 2-body reactions between atoms and molecules,or from recombination of ions.

Historically "airglow" has referred to visualradiation. Some recent studies use "airglow" to referto radiation outside the visual range.

Air ShowerA grouping of cosmic-ray particles observedin the atmosphere.

Primary cosmic rays slowed down in the atmos-phere emit brenisstrahlung photons of high energy.Each of these photons produces secondary electronswhich generate more photons and the process con-tinues until the available energy is absorbed.

Air SoundingThe act of measuring atmosphericphenomena or determining atmospheric conditionsat altitude, especially by means of apparatus carriedby balloons or rockets.

AlbedoThe ratio of the amount of electromagneticradiation reflected by a body to the amount incidentupon it, commonly expressed as a percentage. Com-pare Bond albedo.

The albedo is to be distinguished from the re-flectivity, which refers to one specific wavelength(monochromatic radiation).

Usage varies somewhat with regard to the exactwavelength interval implied in albedo figures; some-times just the visible portion of the spectrum isconsidered, sometimes the totality of wavelengthsin the solar spectrum.

Alpha Part icle( Symbol:He'. ) A positively chargedparticle emitted from the nuclei of certain atomsduring radioactive disintegration. The alpha particlehas an atomic weight of 4 and a positive charge equalin magnitude to 2 electronic charges hence it isessentially a helium nucleus (helium atom strippedof its two planetary electrons).

Alpha particles are important in atmosphericelectricity as one of the agents responsible for atmos-pheric ionization. Minute quantities of radioactivematerials such as radium, present in almost all soilsand rocks, emit alpha particles and those which enterthe surface air layer produce large numbers of ionsalong their short air paths. Alpha particles ofaverage energy have a range of only a few centi-meters in air, so radioactive matter in the earthcannot directly ionize the air above a height of afraction of a meter. On the other hand, certainradioactive gases, such as radon and thoron, maybe carried to heights of several kilometers (afterinitial formation during a radioactive disintegra-tion of atoms of soil or rock matter) before emittingcharacteristic alpha particles which can there ionizeair in the free atmosphere. The high density of ionpairs produced along the track of an alpha particlefavors very rapid recombination (columnar recombi-nation) that greatly reduces the effective ionizationproduced by these particles.

AmbientSpecifically, pertaining to the environmentabout a flying aircraft or other body but undisturbedor unaffected by it, as in "ambient air", or "ambienttemperature."

AmplidyneA special type of de generator used as apower amplifier, in which the output voltage re-sponds to changes in field excitation; used extensivelyin servo systems.

Analog ComputerA computing machine that works onthe principle of measuring, as distinguished fromcounting, which the input data are made analogousto a measurement continuum, such as voltages, linearlengths, resistances, light intensities, etc., which canbe manipulated by the computer.

Analog computers range from the relatively simpledevices of the slide rule or airspeed indicator tocomplicated electrical machines used for solvingmathematical problems.

AngelA radar echo caused by a physical phenomenonnot discernible to the eye.

Angstrom (1)A unit of length, used chiefly in ex-pressing short wavelengths. Ten billion angstromsequal one meter.

Anomaly-1. In general, a deviation from the norm. 2.In geodesy, a deviation of an observed value froma theoretical value, due to an abnormality in theobserved quantity. 3. In celestial mechanics, the anglebetween the radius rector to an orbiting body fromits primary (the focus of the orbital ellipse) and theline of apsides of the orbit, measured to the directionof travel, from the point of closest approach to theprimary (perifocus).

The term defined above is usually called "trueanomaly", v, to distinguish it from the eccentricanomaly, E, which is measured at the center of theorbital ellipse, or from the mean anomaly, M, whichis what the true anomaly would become if theorbiting body had a uniform angular motion.

Anomalistic PeriodThe interval between two successiveperigee passes of a satellite in orbit about a primary.Also called "perigee-to-perigee period."

AnoxiaA complete lack of oxygen. available for physi-ological use within the body. Compare hypoxia.

"Anoxia" is popularly used as a synonym for"hypozia." This usage should be avoided.

AntigravityA hypothetical effect that would arise fromsome energy field's cancellation of the effect of thegravitational field of the earth or other body.

AphelionThat orbital point farthest from the sun whenthe sun is the center of attraction. That point nearestthe sun is railed "perihelion."

The aphelion of the earth is 1.520 x 10" cm fromthe sun.

ApogeeIn an orbit about the earth, the point at whichthe satellite is farthest from the earth; the highestaltitude reached by a sounding rocket.

Apogee RocketA rocket attached to a satellite orspacecraft designed to fire when the craft is atapogee, the point farthest from the earth in orbit.The effect of the apogee rocket is to establish a neworbit farther from the earth or to allow the craftto escape from earth orbit.

ApolloUnited States program with the objective ofearth-orbiting a space laboratory, launching astro-nauts to the vicinity of the moon, and landing aman on the moon, and returning him to earth.

Arago PointOne of the three commonly detectablepoints along the vertical circle through the sun atwhich the degree of polarization of skylight goesto zero; a neutral point.

The Arago point, so named for its discoverer, iscustomarily located at about 20° above the antisolar

point; but it lies at higher elevations in turbid air.The latter property makes the Arago distance auseful measure of atmospheric turbidity. Measure-ments of the location of this neutral point aretypically more easily carried out than measurementsof the Babinet paint and the Brewster point, bothof which lie so close to the sun (about 20° above andbelow the sun, respectively) that glare problemsbecome serious.

Arc -Jet EngineA type of electrical rocket engine inwhich the propellant gas is heated by passingthrough an electric arc.

Artificat AntennaA device which has the equivalentimpedance characteristics of an antenna and thenecessary power-handling capabilities, but which doesnot radiate or intercept radiofrequency energy. Alsocalled "dummy antenna."

Artificial GravityA simulated gravity established with-in a space vehicle, as by rotating a cabin aboutan axis of a spacecraft, the centrifugal force gene-rated being similar to the force of gravity.

AssemblyAn element of a component consisting ofparts and/or subassemblies which performs func-tions necessary to the operation of the componentas a whole. Examples are: pulsing networks, gyroassembly, oscillator assembly, etc.

AsteriodOne of the many small celestial bodies re-volving around the sun, most of the orbits beingbetween those of Mars and Jupiter. Also called"planetoid," "minor planet." See Planet.

The term "minor planet" is preferred by manyastronomers but "asteriod" continues to be used inastronomical literature, especially attributively, asin "asteriod belt."

Astro--A prefix meaning "star" or "stare' and, by ex-tension, sometimes used as the equivalent of "celes-tial," as in astronautics.

Astroballistics The study of the phenomena awing outof the motion of a solid through a gas at speeds highenough to cause ablation; for example, the inter-action of a meteoroid with the atmosphere.

Astroballistics uses the data and methods ofastronomy, aerodynamics, ballistics, and physicalchemistry.

AstrobiologyThe study of living organisms on celestialbodies other than the earth.

AstrodynsmicsThe practical .application of celestialmechanics, astroballistics, propulsion theory, andallied fields to the problem of planning and directingthe trajectories of space vehicles.

AstronautI. A person who occupies a space vehicle. 2.Specifically one of the test pilots selected to partici-pate in Project Mercury, the first United States pro-gram for manned space flight.

Astronautics i. The art, skill, or activity of operatingspace vehicles. 2. In a broader sense, the science ofspace flight.

Astronomical Unit (abbr AU)In the astronomical sys-tem of measures, a unit of length usually definedas the distance from the Earth to the Sun, ap-proximately 92,900,000 statute miles or 14,960,000kilometers. It is more precisely defined as the unit

165

of distance in terms of which, in Kepler's Third Law,= I0(1 ni), the semimajor axis a of an ellipti-

cal orbit must be expressed in order that the numeri-cal value of the Gaussian constant, k, may be exactly0.01720209895 when the unit of time is the ephemerisday.

In astronomical units, the mean distance of theEarth from the Sun, calculated by Kepler's lawfrom the observed mean motion n and adopted massm, is 1.00000003.

AtlasAn intercontinental ballistic missile which a totalTHRUST of about 360,000 pounds, frequently usedas a first stage for satellite and spacecraft launchingsby the United States. It is a liquid - fueled rocket,burning liquid oxygen and kerosene.

AtmosphereThe envelope of air surrounding the earth;also the body of gases surrounding or comprising anyplanet or other celestial body.

Atmospheric DragThe retarding force produced on asatellite by its passage through the gas of the highatmosphere. It drops off exponentially with height,and has a small effect on satellites whose PERIGEEis higher than a few hundred kilometers.

Atomic ClockA precision clock that depends for its op-eration on an electrical oscillator (as a quartzcrystal) regulated by the natural vibration frequen-cies of an atomic system (as a beam of cesium atomsor ammonia molecules).

AttenuationIn physics, any process in which the fluxdensity (or power, amplitude, intensity, illuminance,etc.) of a "parallel beam" of energy decreases withincreasing distance from the energy source. Atten-uation is always due to the action of the transmittingmedium itself (mainly by absorption and scattering).It should not he applied to the divergence of fluxdue to distance alone, as described by the inverso-square law. See Absorption.

The space rate of attenuation of electromagneticradiation is described by Bouguer's law.

In meteorological optics, the attenuation of. lightis customarily termed "extinction." (The latter issometimes used with regard to any electromagneticradiation.)

AttitudeThe position or orientation of an aircraft,spacecraft, etc., either in motion or at rest, asdetermined by the relationship between its axes andsome reference line or plane such as the horizon.

Auger ShowerA very large cosmic-ray shower. Alsocalled "extensive air-shower."

AugmentationThe apparently larger semi-diameter ofa celestial body, when seen against the horizon, ascompared to its apparent decrease in size with in-creased altitude.

The term is used principally in reference to themoon.

AuroraThe sporadic visible emission from the upperatmosphere over middle and high latitudes. Alsocalled "northern lights."

Aurora AustraliaThe aurora of the Southern Hemis-phere. See Aurora.

Aurora BorealisThe aurora of northern latitudes. Alsocalled "aurora polaris," "northern lights." SeeAurora.

Axis(pl. axes) 1. A straight line about which a bodyrotates, or around which a plane figure may rotateto produce a solid; a line of symmetry. 2. One of aset of reference lines for certain systems of co-ordinates.

Azimuth-1. Horizontal direction or bearing. Compareazimuth angle, bearing. 2. In navigation, the hori-zontal direction of a celestial point from a terreNtrialpoint, expressed as the angular distance from areference direction, usually measured from 000 atthe reference direction clockwise through Mr .

AzusaA short range tracking system which gives spaceposition and velocity of the object being tracked.

B

BackoutAn undoing of things already done during acountdown, usually in reverse order.

Backup-1. An item kept available to replace an itemwhich fails to perform satisfactorily. 2. An itemunder development intended to perform the samegeneral function performed by another item alsounder development.

Baker-Nunn CameraA large camera used in trackingsatellites.

Balance-1. The equilibrium attained by an aircraft,rocket, or the like when fortes and moments areacting upon it so as to produce steady flight,especially without rotation about its axes; also usedwith reference to equilibrium about any specifiedaxis, as, an airplane in balance about its longitudinalaxis. 2. A weight that counterbalances something,especially, on an aircraft control surface, a weightinstalled forward of the hinge axis to counterbalancethe surface aft of the hinge axis.

BallisticsThe science that deals with the motion, be-havior, and effects of projectiles, especially bullets,aerial bombs, rockets, or the like; the science or artof designing and hurling projectiles so as to achievea desired performance.

Ballistic TrajectoryThe trajectory followed by a bodybeing acted upon only by gravitational forces Indthe resistance of the medium through which itpasses.

A rocket without lifting serf aces is in a ballistictrajectory after its engines cease operating.

Balloon-type RocketA rocket, such as Atlas, that re-quires the pressure of its propellants (or other gases)within it to give it structural integrity.

BarUnit of pressure equal to 10' dyne per cm' (10'baryej 1000 millibars, 29.53 in. of Hg.

Barye--Something used by British to denote pressureunit of the cgs system of physical units, equal toone dyne per cm' (0.001 millibar). See Microbar.

Beam-1. A ray or collection of focused rays of radiatedenergy. See beam width, radiation pattern. 2.electron beam. 3. A beam (sense 1) of radio wavesused as a navigation aid.

Binary NotationA system of positional notation inwhich the digits are coefficients of powers of the

166

base 2 in the same way as the directs in the conven-tional decimal system are toeffrients of powers ofthe base 10.

Binary notation employs only two digits, I and0. therefore is used exterisitvly in computers wherethe "on" and "off" positions of a switch or storagedevice can represent the two digits.

In decimal notation 111 = (1 x 10') + (1 x 10')+ (1 x 10') = 100 + 10 + 1 = one hundred andcleric

In binary notation 111 - (1 x 2t) + (1 x 2')x (1 x 2') - 4 + 2 + 1 - seven.

BionicsThe study of systems which function after themanner of, or in a manner characteristic of, or re-sembling, living systems.

BipropellantA rocket propellant consisting of two un-mixed or uncombined chemicals (fuel and oxidizer)fed to the combustion chamber separately.

BirdA colloquial term for a rocket, satellite, or space-craft.

Bit- .( From binary digit.) A unit of information.

Black Body (abbr b).-1. A hypothetical "body" whichabsorbs all of the electromagnetic radiation strikingit; that is, one which neither reflects nor transmitsany of the incident radiation.

No actual substance behaves as a true black body,although platinum black and other soots ratherclosely approximate this ideal. However, one doesspeak of a black body with respect to a particularwavelength interval. This concept is fundamental toall of the radiation laws, and is to be compared withthe similarly idealized concepts of the white bodyand the gray body, In accordance with Kirehoff'slaw, a black body not only absorbs all wavelengths,but emits at all wavelengths and does so withmaximum possible intensity for any given tempera-ture.

Black BoxColloquially, any unit, usually an electronicdevice such as an amplifier, which can be mountedin a rocket, spacecraft, or the like as a single pack-age. See Component.

Blackout-1. A fadeout of radio communications dueto environmental factors such as ionospheric dis-turbances, or a plasma sheath surrounding a reentryvehicl. 2. A condition in which vision is temporarilyobscured by a blackness, accompanied by a dullnessof certain of the other senses, brought on by de-creased blood pressure in the head and a consequentlack of oxygen, as may occur in pulling out of a high-speed dive in an airplane.

Blockhause(Also written "block house"). A reinforcedconcrete structure, often built underground or partlyunderground, and sometimes dome-shaped, to provideprotection against blast, heat, or explosion duringrocket launcWlags or related activities; specifically,such a structure at a launch site that houses elec-tronic control instruments used in launching a rocket.

BoilerplateAs in "boilerplate caspule," a metal copyof the flight model, the structure or components ofwhich are heavier than the flight model.

BoiloffThe vaperization of a cold propellant such asliquid oxygen or liquid hydrogen, as the temperatureof the propellant mass rises as in the tank of a rocketbeing readied for launch.

"Bala" ConceptConcept of a manned nuclear vehiclein which a long cable separates the manned platformfrom the reactor power system, with consequent re-duction of biological hazard and the need for heavyshielding.

Boltzmann's ConstantThe ratio of the universal gasconstant to Avogadro's number: equal to 1.3804 xl0-' ergs per degree K. Sometimes called "gasconstant per molecule," "Boltzmann's universal con-version factor."

Bond AlbedoThe ratio of the amount of light reflectedfrom a sphere exposed to parallel light to the amountof light incident upon it. Sometimes shortened to"albedo."

The Bond albedo is used in planetary astronomy.

BoosterShort for "booster engine" or "booster rocket."Booster EngineAn engine, especially a booster rocket,

that adds its thrust to the sustainer engine.Booster Rocket-1. A rocket engine, either solid or liquid

fuel, that assists the normal propulsive system orsustainer engine of a rocket or aeronautical vehiclein some phase of its flight 2. A rocket used to seta missile vehicle in motion before another enginetakes over.

In sense t the term "launch vehicle" is morecommonly used.

Boostglide Vellicle--A vehicle (half aircraft, half space-craft) designed to fly to the limits of the sensibleatmosphere, then be boosted by rockets into thespace above, returning to earth by gliding underaerodynamic control.

arguer's LawA relationship describing the rate ofdecrease of a flux density of a plane-parallel beamof monochromatic radiation as it penetrates amedium which both scatters and absorbs at thatwavelength.

Braking EllipsesA series of ellipses, decreasing in sizedue to aerodynamic drag, followed by a spacecraftin entering a planetary atmosphere.

In theory, this maneuver will allow a spacecraft todissipate energy through aerodynamic heating with-out burning up.

Breakoff PhenomenonThe feeling which sometimes oc-curs during high-altitude flight of being totallyseparated and detached from the earth and humansociety. Also called the "breakaway phenomenon."

Brenisstrahlung EffectThe emission of electromagneticradiation as a consequence of the acceleration ofcharged elementary particles, such as electrons,under the influence of the attractive or repulsiveforcefields of atomic nuclei near which the ambient,charged piArticle moves.

In cosmic-ray shower production, bremsstrahlung(in German, "braking radiation") effects give riseto emission of gamma rays as electrons encounteratmospheric nuclei. The emission of radiation inthe bremsstrahlung effect is merely one instance ofthe general rule that electromagnetic radiation isemitted only when electric charges undergo accele-ration.

British Thermal Unit (Btu)The amount of heat re-quired to raise 1 pound of water at G0 °F, 1 °F. Gen-eral usage makes 1 Btu actual 252 calories.

167

BufferIn computers: 1. An isolating circuit used toavoid reaction of a driven circuit on the correspond-ing driving circuit. 2. A storage device used to com-pensate for a difference in rate of flow of informationor time on occurrence of events when transmittinginformation from one device to another.

BurnA period during which a rocket engine is firing,as in "second burn" the second period during a flightin which the engine is firing.

Burning Rate (abbe r).Velocity at which a solid pro-pellant in a rocket is consumed, measured in a direc-tion nonaal to the propellant surface and is usuallyexpressed in inches per second.

Burnowt-1. An act or instance of the end of fuel andoxidizer bunting in a rocket; the time at which thisburnout occurs. Compare cutoff. 2. An act or in-stance of something burning out or of overheating;specifically, an act or instance of a rocket combustionchamber, nozzle, or other part overheating so as toresult in damage or destruction.

Burst-1. A single pulse of radio energy; specificallysuch a pulse at radar frequencies. 2. Solar rat.:.)burst. 3. Cosmic ray burst.

C

CalorieOriginally amount of heat require4 to raisetemperature of one gram of water through onedegree centigrade (the gram-calorie), but a moreprecise expression is that a 15° gram-calorie (cal .)is the amount of heat required to raise the tempera-ture of one gram of water from 14.5`C to 15.5°Cand is noual to 4.185t joules.

CapacityIn computer operations: 1. The largestquantity which can be stored, processed, or trans-ferred. 2. The largest number of digits or characterswhich may be regularly processed. 3. The upperand lower limits of the quantities which may beprocessed.

Capsule-1. A boxlike component or unit, often sealed.2. A small, sealed, pressurized cabin with an internalenvironment which will support life in a man oranimal during extremely high altitude flight, spaceflight, or emergency escape,

The term, "spacecraft," is preferred to capsulefor any man-carrying vehicle.

Cascade Shower.A group occurrence of cosmic rays.Also called "air shower."

CavitationThe turbulent formation of bubbles in afluid, occurring whenever the static pressure at anypoint in the fluid flow becomes 'less than the fluidvapor pressure.

Celestial MechanicsThe study of the theory of themotions of celestial bodies under the influence ofgravitational fields.

Celestial SphereAn imaginary sphere of infinite radiusconcentric with the earth, on which all celestialbodies except the earth are assumed to be projected.

168

CentrifugeA mechanical device which applies centifugulforce to the test specimen by ;means of a long rotat-ing arm to simulate very closely the prolongedaccelerations encountered in high-performance air-craft, rockets. and spacecraft.

The simulated acceleration of centrifugal forceproduced is proportional to the distanci from thecentc,r of rotation and the square of the rotationalveteran,.

CharacteristicAny dimensional, visual. functional, me-chanical, electrical, chemical, physical, or materialfeature or property; and any process-control elementwhich describes and establishes the design, fabrica-tion, and operating requirements of an article.

Chase PilotA pilot who flies in an escort upirlane ad-vising a pilot who is making a check, training, orresearch flight in another craft.

Checkout-1. A sequence of actions taken to test orexamine a thing as to st@ readiness for incorporationinto a new phase of use, or for the performance ofits intended function. 2. The sequence of steps takento familiarize a person with the operation of anairplane or other piece of equipment.

In sense 1, a checkout is usually taken at a transi-tion point between one phase of action and another.To shorten the time of checkout, automation isfrequently employed.

Cheese AntennaA cylindrical parabolic reflector enclosed by two plates perpendicular to the ey.inder,so spaced as to permit the propagation of more thanone mode in the desired direction of polarization. Itis fed on the focal line.

Chemical Fuel-1. A fuel that depends upon an oxidii,erfor combustion or for development of thrust, suchas liquid or solid rocket fuel or internal-combustion-engine fuel; distinguished from nuclear fuel. 2. Afuel that uses special chemicals, such as a boron-based fuel.

Chemical RocketA rocket using chemical fuel, fuelwhich requires an oxidizer for combustion, such asliquid or solid rocket fuel.

ChemosphereThe vaguely defined region of the upperatmosphere in which photochemical reactions takeplace. It is generally considered to include the.stratosphere (or the top thereof) and the mesa -sphere, and sometimes the lower part of thethermosphere.

This entire region is the seat of a number ofimportant photochemical reactions involving atomicoxygen 0, molecular oxygen CO:. ozone (L, hydroxylOH, nitrogen NU sodium Na, and other constituentsto a lesser degree.

Chromosphere A thin layzr of relatively transparentgases above the PHOTOSPHERE of the sun. It ismost easily observed during a total solar eclipse.

ChokesPain and irritation in the chest and throat asa result of reduced ambient pressure.

ChuggingA form of combustion instability, especiallyin a liquid-propellant rocket engine, characterizedby a pulsing operation at a fairly low frequency,sometimes defined as occurring between particularfrequency limits; the noise made in this kind ofcombustion. Also called "chuffing."

Cislunar(Latin cis "on this side".) Of or pertainingto phenomena, projects, or activity in the spacebetween the earth and moon, or between the earthand the moon's orbit.

Closed Ecological SystemA system that provides forthe maintenance of life in an isolated living chambersuch as a spacecraft cabin by means of a cycle where-in exhaled carbon -dioxide, urine, and other wastematter are converted chemically or by ohotosyrithesisinto oxygen, water, and food.

CoherentOf electromagnetic radiation, being in phaseso that waves at various points in space act in unison.

Cold-flow TestA test of a liquid rocket without firingit to check or verify the efficiency of a propulsionsubsystem, providing for the conditioning and flowof propellants (including tank pressurization, pro-pellant loading, and propellant feeding.)

CometA luminous member of the solar system cornposed of head or coma at the center of which apresumably solid nucleus is sometimes situated, andoften with a spectacular gaseous tail extending agreat distance from the head.

CommandA signal which initiates or triggers an ac-tion hi the device which receives the signal.

The orbits of comets are highly elliptical.

Communications SatelliteA satellite designed to re-fleet or relay radio or other communications waves.

Companion BodyA nose cone, last-stage rocket, orother body that orbits along with an earth satellite.

Camp lexEntire area of launch site faciales. Thisincludes blockhouse, launch pad, gantry, etc. Also re-ferred to as a "launch complex."

ComponentA self-contained combination of partsand/or assemblies within a subsystem performing afunction necessary to the subsystem's operation.Examples are: receivers, -transmitters, modulators,etc.

Composite MaterialsStructural materials of metalalloys or plastics with built-ir strengthening agentswhich may be in the form of filaments, foils, or flakesof a strong material.

Composite PropellantA solid rocket propellant con-sisting of a fuel and an oxidizer.

Computer--A machine for carrying out calculations andperforming specified transformations on informa-tion.

ConfigurationA particular type of a specified aircraft,rocket, etc., which differs from others of the samemodel by virtue of the arrangement of its com-ponents or by the addition or omission cf auxiliaryequipment as "long-range configuration," "cargoconfiguration."

ConicA conic section.Conic SectionA curve formed by the intersection of a

plane and a right circular cone. Usually called"conic."

The conic sections are the ellipse, the parabola,and the hyperbola; curves that are used to describethe paths of beadiest moving in spare.

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The circle is a special case of the ellipse, an ellipsewith an eccentricity of zero.

ConsoleAn array of controls and indicators for themonitoring and control of a particular sequence ofactions, as in the cneckout of a rocket, a countdownaction, or a launch procedure.

A console is usually designed around desklikearrays. it permits the operator to monitor and con-trol different activating instruments, data recordinginstruments. or event sequencers.

Constellation--Originally a conspicuous configuration ofstars; now a region of the celestial sphere marked byarbitrary boundary lines.

ContractorThe individual(s) s ) or concern ( s) whoenters) into a prime contract with the Government.

ContravaneA vane that reverses or neutralizes a rota-tion of a flow. Also called a "countervane."

ControlSpecifically, to direct the movements of an air-craft, rocket, or spacecraft with particular referenceto changes in altitude and speed. Contrast guidance.

Control RocketA vernier engine, retrorocket, or othersuch rocket, used to guide or make small changes inthe velocity of a rocket, spacecraft, or the like,

Coriolis AccelerationAn acceleration of a particle mov-ing in a (moving) relative coordinate system. Thetotal acceleration of the particle, as measured inan internal coordinate system, may be expressed asthe sum of the acceleration within the relative sys-tem, the acceleration of the relative system itself,and the coriolis acceleration.

In the case of the earth, moving with angularvelocity ft, a particle moving relative to the earthwith velocity V has the coriolis acceleration-2U x V.If Newton's laws are to be applied in the relativesystem, the coriolis acceleration and the accelerationof the relative system must be treated as forces. SeeG ravity.

Corona-1. The faintly luminous outer envelope of thesun. Also called "solar corona."

The corona can be observed at the earth's surfaceonly at solar eclipse or with the ,coronagraph, aphotographic instrument which artificially Mocks outthe image of the body of the sun.

2. Discharge of electricity which occurs at the sur-face of a conductor under high voltage. The phe-nomenon is dependent or ambient pressure of the gassurrounding the conductor.

Since phenomenon is enhanced by reduced pres-sure, tests must be conducted to verify that no sig-nificant corona exists within the spacecraft or itscomponents under anticipated conditions.

Cosmic DustSmall meteoroids of a size similar to dust.

Cosmic RaysThe aggregate of extremely high energysubatomic particles which bombard the atmospherefrom outer space. Cosmic-ray primaries seem to bemostly protons, hydrogen nuclei, but also compriseheavier nuclei. On colliding with atmosphericparticles they produce many different kinds of lower-energy secondary cosmic radiation (see CascadeShower,? Also called "cosmic radiation."

The maximum flux of cosmic nts, both primaryand secondary, is at an altitude of 20 km, and belowthis the absorption of the atmospkere reduces theflux, though the rays are still reedily detectableat sea level. Intensity of cosmic rayishowers has, alsobeen observed to vary with latitude, !Icing moreintense at the poles.

COSPARAbbreviation for "Committee on Spat.* Re-search," International Council of Scientific Unions.

CountdownThe time period in which a sequence ofevents is carried out to launch a rocket; the sequenceof ceefets.

Cryogenic Prcepe IlantA rocket fuel, oxidizer, or pro-pulsion fluid which is liquid only at very low tempera-tures.

Cryogenic TesnperatareIn general, a temperature rangebelow about 50°C; more particularly, temperatureswithin a few degrees of absolute zero.

CutoffAn act or instance of shutting something at-specifically in rocketry, an act of instance of seuttingof the propellant flow in a rocket, or of stoppingthe combustion of the propellant.

D

Data ReductionTransformation of observed values intouseful, ordered, or simplified informatien.

Debug-1. To isolate and remove malfunctions from adevice, or mistakes from a computer routine or pro-gram. 2. Specifically, in electronic manufacturing, tooperate equipment under specified environmental andtest conditions in order to sliza.dnate early failuresand to stabilize equipment prior to actual use.

DecelerationI. The act or process of moving, or of caus-ing to move, with decreasing speed; the state oil somoving. 2. A fore* causing deceleration; also,inertial forces sometime galled "'negative accelera-tion".

Deep Space NetA combination of aline radar and com-munications stations in the United States, Australia,and South Africa so located as to llteep a spacecraftin deep space under observation at All times.

deep Space Probes Spacecraft designed' for exploringspace to the vicinity of the moon and beyond. Deepspace probes with specific missions may be referredto as "lunar probe," "Mars probe," "solarprobe," etc

DegradationGradual deterioration in perforawance.

Delayshe time (or equivalent distance) displacementof some characteristic of a wave relative to the samecharacteristies of a reference wave; that is, the dif-ference in phase between the two waves. Comparelag.

In one-way radio propagation, for instance, thephase delay of the reflected wave over the directwave is a measure of the extra distance traveled bythe reflected wave in reaching the same receiver.

Design Engineering TestsEnvironmental tests havingthe purpose of trying certain design features prior

to finalizing design for Design Qualification Tests.For instance the structural model of the spacecraftis subjected to certain environmental exposures orDesign Engineering Tests up to design qualificationlevel in order to establish confidence in its structuraldesign.

Design Qualification TestsSeries of environmental Andother tests applied to prototype spacecraft, sub-systems, components, or experiments to determineif design meets requirements for launch and flightof spacecraft. These tests are planned to subjectspacecraft to considerably greater rigors of environ-ment than expected during launch and flight in orderto achieve maximum design reliability.

DestructThe deliberate action of destroying a rocketvehicle after it has been launched, but before ithas completed its course.

Destructs ore executed when the rocket gets ofits plotted course or functions in a way so as tobecome a hazard.

Deviation-1. In NASA quality control, specific authoriza-tion, granted tefore the fact, to depart from a par-ticular requirement of specifications or relateddocuments.. 2. In statistics, the difference betweentwo numbers. Also called "departure." It is com-monly applied to the difference of a variable fromits mean, or to the difference of an observed valuefrom a theoretical value.

Digital Computer - -A computer which operates on theprinciple of counting as opposed to measuring. SeeAnalog Computer.

DiplexerA device permitting an antenna system to beused simultaneously or separately by two trans-mitters. Compare with duplexer.

DishA parabolic type of Wit) or radar antenna, rough-ly the shape of a soup bowl.

DisplayThe graphic presentation of the output data ofa device or system as, for example, a radar scope.

DockingThe process of bringing two spacecraft to-gether while in space.

Doppler ShiftThe change in frequency with whichenergy reaches a receiver when the source of radia-tion or a reflector of the radiation and the receiverare in motion relative to each other. The Dopplershift is used in many tracking and navigation sys-tems.

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DosimeterA device, worn by persions working aroundradioactive material, which indicates the amount(dose) of radiation to which they have been ex-posed.

DovapFrom Doppler, velocity and position, a trackingsystem which uses the Doppler shift caused by atarget grieving relative to a ground transmitter toobtain velocity and position information.

Drogue PinrAelintel ty of joarachute attached to abody, wied to slow it down; also called "decelerationparachute," or "drag parachute."

Duplexes A device which permits a single antenna sys-tem to be used for both transmitting and receiving.

"Duplerer" should not be confused with "diplerer."

a device permitting an antenna system to be usedsimultaneously or separately by two transmitters.

Dynamic PressureSymbol q. 1. The pressure exerted bya fluid, such as air, by virtue of its motion, equalto one hall the fluid density times the fluid velocitysquare 34e V'.

2. The vessure exerted on a body, by virtue of itsmotion through a fluid, for example, the pressureexerted on a rocket moving through the atmosphere.

Dyne (abbr d)That unbalanced force which acting for1 second on body of 1 gram mass produces a velocitychange of 1 cm /sec.

The dyne is the unit of force in the cgs system.

DysharismA general term which includes a compleigroup of a wide variety of symptoms within the bodycaused by changes in ambient pressure, exclusive ofhypoxia.

E

EbullismThe formation of bubbles, with particularreference to water vapor bubbles in biological fluids,caused by reduced ambient pressure.

EccentricNot having the same center; varying from acircle, as in "eccentric orbit."

Esh A large plastic balloon with a diameter of 30meters and weight of 50 kilograms launched onAugust 12. 1940 by the United States and inflatedin orbit. It was launched as a passive communica-tions satellite, to reflect microwaves from a trans-mitter to a receiver beyond the horizon.

EclipticThe apparent annual path of the sun amongthe stars; the intersection of the plane of the earth'sorbit with the celestial sphere.

This is a great circle of the celestial sphere inclinedat on angle of about 23°27' to the celestial equator.

&440a* SystemA habitable environment, eithercreated rolicially. such as in a manned space vehicle,or occurrihs naturally, such as the eniroment onthe surface of the earth, in which man, animals, orother organisms can live in mutual relationshipwith each other.

Ideally, the environment furnishes the sustenancefor life, and the resulting waste products revert orcycle back into the environinen. to be used againfor the continuous support of life,

Effective Atmosphere-1. That part of the atmospherewhich effectively influences a particular process ormotion, its outer limits varying according to theterms of the process or motion considered.

For example, an earth satellite orbiting at 250miles altitude remains within the ionosphere, but be-cause the air particles are so rare at this altitude asto cause no appaeciable friction or deflection, thesatellite may be considered to be outside the effectiveatmosphere. For m...,ement of air vehicles theeffective atmosphere ends at the aerospause (whichsee.)

Election Capsule-1. In an aircraft or manned spacecraft,a detachable compartment serving as a cockpit orcabin, which may be ejected as a unit and parachutedto the ground. 2. In an artificial satellite, probe,or unmanned spacecraft, a boxlike unit usually con-taining recording instruments or records of observeddata, which may be ejected and returned to earthby a parachute or other deceleration device.

ElasticizerAn elastic substance or fuel used in a solidrocket propellant to prevent cracking of the pro-pellant grain and to bind it to the combustion-chamber case.

Electric PropulsionThe generation of thrust for arocket engine involving acceleration of a propellantby some electrical device such as an arc jet, ionengine, or magnetohydrodynamic accelerator.

Electromagnetic KadiationEnergy propagated throughspace or through Material media in the form of anadvancing disturbance in electrical and magneticfields existing in space or in the media. Also calledsimply "radiation."

ElectronThe subatomic particle that possesses thesmallest possible electric charge.

The term "electron" is usually reversed for theorbital particle whereas the term. "beta particle" re-fers to a particle of the same electric charge insidethe nucleus of the atom.

Electron VoltA unit of energy equal to 1.601 x 10-'erg. It is defined as the kinetic energy gained byan electron which is accelerated through a potentialdifference of one volt.

Electronic Data ProcessingThe use of electronic devicesand systems in the proczzesing of data so as to in-terpret the data and put it into usable form.

EllipseA plane curve constituting the locus of all pointsthe sum of whose distances from two fixed pointcalled "foci" is constant; an elongated circle.

The orbits of planets, satellites, planetoids, esndcomets are ellipses; center of attraction is a .onefocus.

Emissivity-1, The ratio of the emittance of a given sur-face at a specified wavelength and emitting tempera-ture to the emittance of an ideal black body at thesame wavelength and temperature. Sometimes called"emissive power."

The greatest value that an emissivity may haveis unity, the least value zero. It is 1 corollary ofKirchhoff's lay. that the emissivity of any surface ata specified temperature and wavelength is exactlyequal to the absorptivity of that surface at thusame temperature and wavelength. The spectralemissivity is for a definite wavelength. The totalemissivity is for ¶11 wavelengths.

2. (abbr s) Specifically, the ratio of the flux emittedby a clean, perfectly polished surface of the materialto the flux that would have been emitted by a Ertackbody at the same temperature.

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EavironmentAn external condition or the sum of suckconditions, in which a piece of ejuipment or a systemoperates. as in "temperature environment," "vibra-tion environment," or "space environment."

Environments are usually specified by a range ofvalues, and may be either natural or artificial.

EpochA particular instant for which certain data arevalid.

Escape VelocityThe. radial speed which a particle orlarger body must attain in order to escape from thegravitational field of a planet or star.

The escape velocity from Earth is approximately7 miles per sec.; from Mars, 3.2 miles per sec.; andfrom the Sun, 390 miles per sec. In order for acelestial bady to retain an atmosphere for astronom-ically long periods of time, the mean. velocity ofthe atmospheric molecules must be considerably be-low the escape velocity.

Exhaust VelocityThe speed at which the exhaust gasesare expelled from the nozzle of a rocket. It dependsupon the propellant-burning characteristics, and theover-all engine efficiency. Present exhaust velocitiesusing liquid oxygen and kerosene are of the orderof 8000 feet per second, about half the theoreticalmaximum for chemical propellants.

ExobiologyThe study of living organisms existing oncelestial bodies other than the earth.

ExosphereThe outermost, or topmost portion of theatmosphere.

In the exosphere, the air density is so low thatthe mean free path of individual particles dependsupon. their direction with respect to the local vertical,being greatest for upward moving particles. It isonly from the exosphere that atmospheric gasescan, to any appreciable extent, escape into outerspace.

Exotic FuelAny fuel considered to be unusual, as aboron-based fuel.

ExperimentA combination of two or more components,including both the sensor and associated electronics,designed for acquisition of data for space research.

Explosive BoltA bolt incorporating an explosive whichcan be detonated on enimand, thus destroying thebolt. Explosive bolts are used, for example, inseparating a satellite from a rocket.

ExtraterrestrialYrom outside the earth.

Extraterrestrial RadiationIn general, solar radiationreceived outside the earth's atmosphere.

Eyeballs In, Eyeballs OutTerminology used by testpilots to describe the acceleration experienced by theperson being accelerated. Thus the acceleration ex-perienced by an astronaut at lift-eff is "eyeballs in"(positive g in terms of vehicle acceleration), and theacceleration experienced when retrorockets fire is"eyeballs out" (negative g in terms of vehicle ac-celeration.)

Fallaway SectionA section of a rocket vehicle that iscast off and separates from the vehicle during flight,_specially such a section that falls back to the earth.

FatigueA weakening or deterioration of metal or othermaterial, or of a member, occurring under load,especially under repeated, cyclic, or continued load-ing.

FieldA region of space at each point of which a givenphysical quantity has some definite value, thus a"gravitational field," an "electric field," a "magneticheld," etc.

Film CoolingThe cooling of a body or surface, suchas the inner surface of a rocket combustion chamber,by maintaining a thin fluid Lyer over the affectedarea.

Fixed SatelliteAn earth satellite that orbits from westto east at such a speed as to remain constantly overa given place on the earth's equator.

FlareA bright eruption from the sun's chromosphere.Flares may appear within minutes and fade

within an hour. They cover a wide range of in-tensity and size, and they tend to occur betweensunspots.

Flares are related to radio fadeouts and terrestrialmagnetic disturbances.

FlashbackA reversal of flame propagation in a systemscounter to the usual flow of the combustible mixture.

FlightDescribes or pertains to travel of spacecraft orstages after liftoff. Thus, in testing, designates'spacecraft or element thereof which is to be launchedas distinct from structural model and prototypespacecraft which are test specimens only.

Flight Acceptance TestsThe environmental and othertests which spacecraft, subsystems, components, orexperiments scheduled for flight must pass beforelaunch. Theie tests are planned to approximateexpected environmental conditions and have the pur-pose of detecting flaws in material and workmanship.

Flight UnitSpacecraft which is undergoing or haspassed Flight Acceptance Tests (environmental andother tests) which qualify it fox launch and spaceflight.

FluxThe rate of flow of some quantity, often used inreference to the flow of some form of energy. Alsocalled "transpoit." 2. In nuclear physics generally,the number of radioactive particles per unit volumetimes their mean velocity.

Flux DensityThe flux irate of flow) of any quantity,usually a form of energy, through a unit area ofspecified surface. (Note that this is not a volumetricdensity like radiant density.) Compare luminousdensity.

The flux density of electromagnetic radiation ingeneral often is pre.!;:rably specified as "radiant fluxdensity" or "irradiance" in order to distinguish itfrom the slightest different concept of luminous fluxdensity of illuminance. In radar, flux density com-monly is referred to as power density. 7t is essential

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to understand that the flux density of radiation is inno sense a vector quantity, because it is the sum ofthe flux corresponding to all ray directions incidentupon one "side" of the unit area.

Forbush DecreaseThe observed decrease in COSMICRAF activity about a day after a SOLAR FLARE. Itis now believed to be caused by a shielding effectproduced by magnetic fields contained in thePLASMA cloud emitted from the sun at the timeof a flare.

Flying Test BedAn aircraft, rocket, or other flyingvehicle used to carry objects or devices being flighttested.

Free Fall-1. The fall or drop of a body, such as a rocketnot guided, nor under thrust, and not retarded bya parachute or other braking device. 2. Weight-lessness.

G

g or GAn acceleration equal to the acceleration ofgravity, approximatell 32.2 feet per second persecond at. sea level; used as a unit of stress measure-ment for bodies undergoing acceleration.

GSESee Ground Support Equipment.

Gamma RayA quantum of electromagnetic radiationemitted by a nucleus, each such photon being emittedas the result of a quantum transition between twoenergy levels of the nucleus. Gamma rays haveenergies usually between 10 key and 10 Mev, withcorrespondingly short wavelengths and high fre-quencies. Also called "gamma radiation."

GantryA frame structure that spans over something,as an elevated platform that runs astride a workarea, supported by wheels on each side; specifically,short for "gantry crane" or "gas try scaffold."

Gantry ScaffoldA massive scaffolding structure mountedon a bridge or platform supported by a pair of towersor trestles that normally run back and forth onparallel tracks, used to assemble and service a largerocket on its launching pad. Often shortened to"gantry." Also called " service tower."

This structure is a latticed arrangement ofgirders, tubing, platforms, cranes, elevators, instru-ments, wiring, floodlights, cables, and laddersallused to ',Vend the rocket.

GarbageMiscellaneous objects in orbit, usually materialejected or broken away from a launch vehicle orsatelite.

Gas CapThe gas immediately in front of a meteoroidor reentry body as it travels through the atmosphere;the leading portion of a meteor. This gas is com-pressed and adiabatically heated to incandescence..

Generrl'anIn any technical or technological develop-ment, as of a missile, jet engine, or ..he like, a stageor period that is marked by features or performancesnot marked, or existent, in a previous period of de-velopment or production, as in "second generationrocket."

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GeoA prefix meaning "earth," as in "geology," "geo-physics."

Most writers used the established terms such as"geology" to refer to the same concert on otherbodies of the solar system, as "Oa. geology of Mars,"rather than "areology" or "marsology," "geology ofthe moon," rather thar, "selenology."

GeocentricRelative to the earth as a center; measuredfrom the center of Vee earth.

GeodeticPertaining to geodesy, the science which dealswith the size and shape of the earth.

Geoid--The equipotential surface which most nearlyapproximates the mean sea level of the earth.

GeomagnetismThe magnetic phenomena, collectivelyconsidered, exhibited by the earth and its atmos-phere; by extension, the magnetic phenomena ininterplanetary space.

GeophysicsThe physics of the earth and its environ-ment, i.e., earth, air, and (by extension), space.

Classically, geophysics is concerned with thenature of physical occurrences at and below thesurface of the earth including, therefore, geology,oceanography, geodesy, seismology, hydrology, etc.The trend is to extend the scope of geophysics toinclude meteorology, geomagnetism, astrophysics,and other sciences concerned with the physical natureof the universe.

GeopotentialThe potential energy of a unit mass rela-tive to sea level, numerically equal to the work O-atwould be done in lifting the unit mass from sealevel to the height at which the mass is located;commonly expressed in terms of dynamic height orgeopotential height.

Geoprobe.A rocket vehicle designed to explore spacenear the earth at a distance of more than 9,000 milesfrom the earth's surface. Rocket vehicles operatinglower than 9,000 miles are termed "soundingrockets."

GigaA prefix meaning multiplied by one billion.Gimbal-1. A device with two mutually perpendicular

and intersecting axes of rotation, thus giving freeangular movement in two directions, on which anengine or other object may be mounted. 2. In a gyro,a support which provides the spin axis with a de-gree-of-freedom.

GnotobioticsThe study of germ:free animals.

GoxGaseous oxygen.GrainAn elongated molding or extrusion of solid pro-

pellant for a rocket, regardless of size.GravitationThe acceleration produced by the mutual

attraction of two masses, directed along the linejoining their- centers of mass, and of magnitudeinversely proportional to the square of the distancebetween the two centers of mass.

GravityThe force imparted by the earth to a mass on,or close to the earth. Since the earth is rotating, theforce observed as gravity is the resultant of the forceof gravitation and the centrifugal force arising fromthis rotation.

Ground Support Equipment (GSE)Any ground-basedequipment used for launch, checkout, or in-flightsupport of a space project.

g-sui1 or G-SuitA suit that exerts pressure on theabdomen and lower parts of the body to prevent orretard the collection of blood below the chest underpositive acceleration.

G-ToleranceA tolerance in a person or other animal,or in a piece of equipment, to an acceleration of aparticular value.

Guidance--Thn process of directing the movernentc of anaeronaut,al vehicle or space vehicle, with particularreference to the selection of a flight path. See C..414-trol.

In preset guidance a predetermined path is setinto the guidance mechanism and not altered, ininertial guidance accelerations are measured andintegrated within the craft, in command guidance thecraft responds to information received from an out-side source. Beam-rider guidance utilizes a beam,terrestrial-reference guidance some influence of theearth, celestial guidance the celestial bodies and par-ticularly the stars, and homing guidance informationfrom the destination. In active horning guidance theinformation is in response to transmissions from thecraft, in semiactive homing guidance the trans-missions are from a source other than the craft,and in passive homing guidance natural radiationsfrom the destination are utilized. Midcourse guidanceextends fro-..i the end of the launching phase to anarbitrary point enroute and terminal guidance ex-tends from this point to the destination.

GyroA device which utilizes the angular momentum ofa spinning rotor to sense angular motion of its baseabout one or two axes at right angles to the spinaxis. Also called "gyroscope."

H

Hall EffectThe electrical polarization of a ,horizontalconducting sheet of limited extent, when that sheetmoves laterally through a magnetic field having acomponent vertical to the sheet.

The Hall effect is important in determining thebehavior of the electrical currents generated bywinds in the lower ionosphere, since these windsadvect the ionized layers across the earth's magneticfield and produce a complex electrical current systemin the ionosphere. This t:Irrent system in turn pro-duces small changes in the earth's magnetic fieldas measured at the surface.

HardnessOf X-rays and other radiation of high energy,a measure of penetrating power. Radiation whichwill penetrate a 10-centimeter thickness of lead isconsidered "hard radiation."

Heat ExchangerA device for transferring heat fromone fluid to another without intermixing the fluids.A regenerator is an example.

Heat ShieldAny device that protects something fromheat.

Heat Sink-1. In thermodynamic theory, a means bywhich heat is stored, or is dissipated or transferredfrom the system under considemejoa. 2. A placetoward which the heat moves in a system. 3. Amaterial capable of absorbing heat; a device utilizingsuch a material and used as a thermal protectiondevice on a spacecraft or reentry vehicle. 4. innuclear propulsion, any thermodynamic device, suchas a radiator or condenser, that is designed to absorbthe excess heat energy of the working fluid, Alsocalled "heat dump."

HeterosphereThe upper portion of a two-pet divisionof the atmosphere according to the general homo-geneity of atmospheric composition; the layer abovethe homosphere The heterosphere is characterizedby variation .n composition, and mean molecularweight of constituent gases.

This region starts at 80 to 100 km above the earth,and therefore closely coincides with the ionosphereand the thermosphere.

HoldDuring a countdown: To halt the sequence ofevents until an impediment has been removed sothat the countdown can be resumed, as in "T minus40 and holding."

HomosphereThe lower portion of a two-part divisionof the atmosphere according to general homogeneityof atmospheric composition; opposed to the hetero-sphere. The region in which there is no gross changein atmospheric composition, that is, all of the atmos-phere from the earth's surface to about 80 or 100 km.

The homospLiere is about equivalent to the neutro-sphere, and includes the troposphere, stratosphere,and mesosphere, and also the ozonosphere and atleast part of the chemosphere.

Hot TestA propulsion system test conducted by actuallyfiring the propellants.

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Human EngineeringThe art or science of designing,building, or equipping mechanical devices or artificialenvironments to the anthropometric, physiological, orpsychological requirements of the men who will usethem.

HuntingFluctuation about a midpoint due to instability,as oscillations .zf the needle of an instrument abouta median value.

HydromagneticsSee Ma gnetohydrodynamics.

Hypersonic-1. Pertaining to hypersonic flow. 2. Per -taining to speeds of Mach 5 or greater.

Hypersonic FlowIn aerodynamics, flow of a fluid overa body at speeds much greater than the speed ofsound and in which the shock waves start at a finitedistance from the surface of the body.

ypoxiaOxygen deficiency in the blood, cells, or tissuesof the body in such degree as to cause psychologicaland physiological disturbances.

Hypoxia may result from a scarcity of oxygenin the air being breathed, or from an inability of thebody tissues to absorb oxygen under conditions oflow ambient pressure. In the latter case, watervapors from body fluids increase in the sacs of thelungs, crowding out the oxygen.

IgniterAny device used to begin combustion, such as aspark plug in the combustion chamber of a jet engine,or a squib used to ignite fuel in a rocket.

Impact AreaThe area in which a rocket strikes theearth's surface.

Used specifically in. reference to the "impact tof a rocket range.

Impact BagAn inflatable bag attached to a spacecraftor reentry capsule to absorb part of the shock oflanding.

Inertial GuidanceGuidance by means of accelerationmeasured and integrated within the craft.

InfraredInfrared radiation; electiamagnetic. radiationin the wavelength interer.,1 from the red end of thevisible spectrum on t'ae lower limit to microwavesused in radar on the upper limit.

Infrared Radiation (abbr 110Electromagnetic radiationlying in the wavelength interval from about 0.8microns to an indefinite upper botlidary sometimesarbitrarily set at 1,000 microns (0.31 cm). Alsocalled "black 14ht," "long wave radiation."

At the lower limit of this interval, the infraredradiation spectrum is bounded by visible radiation,while on its upper limit it is bounded by microwaveradiatim o` the type important in radar technology.

Whereas visible radiation is generated primarilyby intra-atomic processes, infrared radiation isgenerated almost wholly by larger-scale intra-molecular processes, chiefly molecular rotations andinternal vibrations of many types. Electrically sym-metric molecules, such as the nitrogen and oxygenmolecules which comprise most of the earth's atmos-phere, are not capable of absorbing or emittinginfrared radiation, but several of the triatomic gases,such as water vapor, carbon doxide, and ozone areinfrared-active and play important roles in thepropagation of infrared radiation in the atmosphere.

Since a slack body at terrestrial temperatureradiates with maximum intensity in the spectrum(near 10 microns), there exists a co'nplex system ofinfrared radiation currents within our atmosphere.

InjectionI. The introduc;:ion of fuel, fuel and air, fueland oxidizer, water, or other substance into anengine induction system Lr combustion chamber. 2.The process of putting an artificial satellite intoorbit. 3. The time following launching when non-gravitational forces (thrust, lift, and drag) becomenegligible in their effect on the trajectory of a spacevehicle.

More than one injection is lossible in a singleflight if engines are stopped arni, restarted.

la9ertionThe process of putting an artificial satelliteinto orbit. Also the time of such action.

Intensity--1. In general, the degree or amount, usuallyexpressed by the elemental time rate or spatialdistribution, of some condition or physical quantity,such as electric field, sound, magnetism, etc.

2. With respect to electromagnetic radiation, ameasure of the radiant flux per unit solid angleemanating from some source. Frequently, it is de-sirable to specify this as radiant intensity in orderto clearly distinguish it from luminous intense-y.

InterfaceThe junction points or the points within orbetween systems or subsystems where matching oraccommodation must be properly achieved in orderto make their operation compatible with the success-ful operation of all other functional entities in thespace vehicle and its ground support.

International Geophysical Year (abbr IGY)--By inter-national agreement, a period during which greatlyincreased observation of world-wide geophysicalphenomena is undertaken through the cooperativeeffort of participating nations. July 1957-December1958 was the first such "year"; however, precedentwas set by the International Polar Years of 1882and 1921.

International Year of the Quiet Sun (abbr 1QSY)Theinternational program for maximum observation andresearch in connection with expected period of lowsolar activity between April 1964 and December 1965.

Ion An atom or molecularly bound group of atomshaving an electric charge. Sometimes also a freeelectron or other charged subatomic particle.

Ionic Propulsion (electrostatic propulsion)Rocket pro-pulsion using the THRUST furnished by electricallyaccelerated ions. Much higher SPECIFIC IM-PULSES and EXHAUST VELOCITIES may be ob-tained than with chemical propulsion, but currentlaboratory versions of the ionic rocket are capableof furnishing a total thrust of only a few ounces.

Ionosphere The atmospheric shell characterized by ahigh ion density. Its base is at about 70 or 80 kmand it extends to an indefinite height.

The ionosphere is classically subdivided into"layers." Each "layer," except the D-layer, is sup-posedly characterized by a more or less regularmaximum of electron density.

D-layer.The D-layer exists only in the daytime.It is not strictly a layer at all, since it does notexhibit a peak of electron or ion density, but is rathera region of increasing electron and ion density, start-ing at about 70 to 80 km and merging with thebottom of the E-layer.

. The lowest clearly defined layer is the E-layer,occurring between 100 and -120 km. The F, -layer andFe-layer occur in the general region between 150and 300 'km, the Frlayer being always present anhaving the higher electron density. The existenceof a G-layer has been suggested, but is questionable.The portions of the ionosphere in which these"layers" tend to form are known as ionospheric"regions," as in "D-region," "E-region," "F-region,""G-region."

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Sudden increases in ionization are referred to as"sporadic," as in "sporadic E" or "sporadic D."

The above assumption that the ionosphere is strati-fied in the vertical into discrete layers .s currentlyunder serious question. Some evidence supports abelief that ion clouds are the basic elements of the

ionosphere. Other investigations appear to revealthe ionosphere as a kenerally ionized region charac-terized by more or less random -fluctuations of elec-tron density.

IsotropicIn general, pertaining to a state which aquantity or spatial derivatives thereof are independ-ent of direction.

IQSYSee International Year of the Quiet Sun.

JJerkA vector that specifies the time rate of change

of an acceleration; the third derivative of displace-ment with respect to time.

Joule's ConstantThe ratio between heat and workunits from experiments based on the first law ofthermodynamics; 4.186 x 10' ergs/cal. Also called"mechanical equivalent of heat."

KKelvin Temperature Scale (abbr K)An absolute tem-

perature scale independent of the thermometricproperties of the working substance. On this scale,the difference between two temperatures T, and T:is proportional to the heat converted into mechanicalwork by a Carnot engine operating between theisotherms and adiabats through Ti and T,. Alsocalled "absolute temperature scale," "thermodynamictemperature scale."

For convenience the Kelvin degree is identifiedwith the Celsius degree. The ice point in the Kelvinscale is 273.16°K. See Absolute Zero.

Kepler's LawsThe three empirical laws describing themotions of planets in their orbits, discovered byJohannes Kepler (1571-1630). These are; (1) Theorbits of the planets are ellipses, with the sun ata common focus. (2) As a planet moves in its orbit,the line joining the planet and sun sweeps overequal areas in equal intervals of time. Also called"law of equal areas." (3) The squares of the periodsof revolution of any two planets are proportionalto the cubes of their mean distances from the sun.

KeyA unit of energy, one thousand electrbn volts.

Kirchhoff's LawThe radiation law which states that ata given temperature the ratio of the emissivity tothe absorptivity for a given wavelength is the samefor all bodies and is equal to the emissivity of anideal black body at that temperature and wavelength.

Loosely put, this important law asserts that goodabsorbers of a given wavelength Ere also goodemitters of that wavelength. It is essential to notethat Kirchhoff's law relates absorption and emissionat the same wavelength and at the same tempera-ture. Also called "Kirchhoff's radiation law."

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Laser(From light amplification by stimulated emissionof radiation.) A device for producing light byemission of energy stored in a molecular or atomicsystem when simulated by an input signal.

Launch Pad The load-bearing base or platform fromwhich a rocket vehicle is launched. Usually called"pad."

Launch RingThe metal ring on the launch pad onwhich a missile stands before launch.

Launch VehicleAny device which propels and guidesa spacecraft into orbit about the earth or into atrajectory to another celestial body: Often called"booster."

Launch WindowAn interval of time during which arocket can be launched to accomplish a particularpurpose as "lift-off occurred 5 minutes after thebeginning of the 82-minute launch window."

LibrationA real or apparent oscillatory motion, par-ticularly the apparent oscillation of the moon.

Because of tibration, more than half of the moon'ssurface is revealed to an observer on the earth, crenthough the same side of the moon is always towardthe earth because the moon's periods of rotation andrevolution are the same.

Lift-offThe action of a rocket vehicle as it separatesfrom its launch pad in a vertical ascent.

A lift-off is applicable ,,nly to vertical ascent; atake-off is applicable to ascent at any angle. A lift-off is action performed by a rocket; a launch isaction performed upon a rocket or upon a satelliteor spaceship carried by a rocket.

Light YearThe distance light travels in one year atrate of 186,000 miles per second (300,000 kilometersper second.) Equal to 5.9 x 10" miles. SeePARSEC.)

Line of PositionIn navigation, a line representing allpossible locations of a craft at a given instant.

In space this concept can be extended to "sphereof position," "plane of position," etc.

Liquid-Propellant Rocket EngineA rocket engine fueledwith propellant or propellants in liquid form. Alsocalled "liquid-propellant rocket."

Rocket engines of this kind vary somewhat in com-plexity, but they consist essentially of one or morecombustion chambers together with the necessarypipes, values, pumps, injectors, etc.

Local VerticalAt a particular point, the direction inwhich the force of gravity acts.

Lon3tudinal AxisThe fore-and-aft line through thetenter of gravity of a craft.

Longitudinal VibrationVibration in which the directionof motion of the particles is the same as the directionof advs,s1ce of the vibratory motion.

O

This is in contrast with transverse *vibration!, inwhich the direction of motion is pependicular to thatof advance.

Los i. Liquid oxygen. Used attributively as in "loxtank," "lox unit." Also called "/oxygen." 2. To loadthe fuel tanks of a rocket vehicle with liquid oxygen.Hence, "losing."

Lunar Atmospheric TideAn atmospheric tide due to thegravitational attraction of the moon. The only de-tectable componets are the 2-lunar+our or semi-diurnal, as in the oceanic tides, and two others ofvery nearly the same period. The amplitude of thisatmospheric tide is so small that it is detected onlyby careful statistical analysis of a long record, beingabout 0.06 int, in the tropics and 0.02 mb in themiddle latitudes.

Lyman Alpha RadiationUltraviolet radiation at awavelength of 1216 A emitted by atomic hydrogenwhen it passes from its first excited electronic stateto its ground state. Light of this short wavelengthis not transmitted by the earth's atmosphere, and astudy of this extremely important line in the sun'sspectrum was made only with the advent of rocketand satellite astronomy. The Lyman alpha transi-tion is the longest wavelength member of the Lymanseries of atomic hydrogen, and the strongest ultra-violet line emitted by the sun.

MMach Nenther(After Ernst Mach (1838-1916),

Austrian scientist.) A number expressing the ratioof the speed of a body or of a point-on a body withrespect to the surrounding air or other fluid, or thespeed of a flow, to the speed of sound in the medium;the speed represented by this number.

If the Mach number is less than one, the flow iscalled "subsonic" and local disturbances'can propa-gate ahead of the flow. If the Mach number isgreater than one, the flow is called "supersonic" anddisturbance cannot propagate ahead of the flow,with the result that shock wares form,

Magnetic StormA worldwide disturbance of the earth'smagnetic field.

Magnetic storms are frequently characterized by asudden onset, in which the magnetic field undergoesmarked changes in the course of an hour or less,followed by a very gradual return to normality,which may take several days. Magnetic storms arecaused by solar disturbances, though the exact natureof the link between the solar and terrestrial dis-turbances is not understood. Sometimes a magneticstorm can be linked to a particular solar dis-turbance.' In these cases, the time between. solarflare and onset of the magnetic storm is about oneor two days, suggesting that the disturbance iscarried to the earth by a cloud of particles thrownout by the sun.

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MagnetohydriodynamicsThe study of the interactionthat exists between a magnetic field and an elec-trically -conducting fluid. Also called "magneto-plasmadynamics," "magnetogasdynamics," "hydro-magnetics," "MILD ."

MagnetometerAn instrument used in the study ofgeomagnetism for measuring any magnetic element.

MagnetosphereThat part of the earth's atmospherewhich exists by virtue of the earth's magnetic field.The magnetosphere consists of trapped particles,mainly electrons and protons, which spiral aboutthe magnetic lines of force from pole to pole, andgradually process eastward or westward, dependingon their charge. Particles are lost by the magneto-sphere when they descend into the atmosphere athigh latitudes. It is believed that particles are fedinto the magnetosphere by effects associated withthe arrival of PLASMA clouds ejected duringSOLAR FLARES as well as from the beta decay ofneutrons produced by COSMIC RAYS striking theupper atmosphere. Particles may also be injectedinto the magnetosphere by high altitude nuclearexplosions. (See VAN ALLEN BELTS.)

MagnitudeRelative brightness of a celestial body. Thesmaller the magnitude number, the brighter thebody.

Decrease of light by a factor of 100 increases thestellar magnitude by 5.00; hence the brightest ob-jects have negative ?magnitudes. (Sun: 26.8; meanfull moon; 12.5; Venus at brightest: 4.3; Jupiterat opposition: 2.1; Sirius: 1.6; Vega: +0.2;Polaris: +2.1). The faintest ears visible to theNaked eye on a clear dark night are of about thesixth magnitude.

Main BangWithin a radar system, the transmittedpulse.

Main Stage-1. In a multistage rocket, The Stage thatdevelops the greatest amount of thrust, with or With-out booster engines. 2. In a single-stage rocketvehicle powered by one or more engines, the periodwhen full thrust (at or above 90 percent) is attained.

A sustainer engine, considered as a stage after(booster engines have fallen away, as in "the mainstage of the Atlas."

ManonteterAn instrument for measuring pressure ofgases and vapors both above and below atmosphericpressure.

MariaThe large, darker areas, of generally circularoutline on the lunar surface. It has been suggestedthat they are caused by lava flow following theimpact of large meteorites during the last stages offormation of the moon.

MarinerThe initial unmanned exploration of the planetsis being conducted in the United States under. theMariner program. Mariner 2, launched August 26,1962, passed within 21,000 miles of Venus onDecember 14, 1962, and radioed to earth informationconcerning the infrared and microwave emission ofthe Owlet, and the strength of the planet's mag-netic field. Future flyby missions to both Venusand Mars are planned.

Mars I An instrumented spacecraft launched br theSoviet Union on November 1, 1962, designed to

investigate the interplanetary medium and transmitphotographs of Mars to the earth. It is programmedto pass the planet in June. 1963, when it will be atts. distance of 150 million miles.

MaserAn amplifier utilizing the principle of microwaveamplification by stimulated emission of radiation.Emission of energy stored in a molecular or atomicsystem by a microwave power supply is stimulatedby the input signal.

MassThe measure of the amount of matter in a body,thus its inertia.

The weight of a body is the force with which it isattracted by the earth.

Mass-Energy EquivalenceThe equivalence of a quantityof mass m and a quantity of energy E, the twoquantities being related by the mass-energy relation,E =Inc', where c the speed of light.

Mass Ratio--,The ratio of the mass of the propella. ntcharge of a rocket to the total mass of the rocketcharged with the propellant.

MateTo fit together two major components of a system.Mean Free PathOf any particle, the average distance

that a particle travels between successive collisionswith the other particles of an ensemble.

MechanoreceptorA nerve ending that reacts to me-chanical stimuli, as touch, tension, and acceleration.

MegaA prefix meaning multiplied by one million as in"megacycler."

MemoryThe component of a computer, control system,guidance system, instrumented satellite, or the likedesigned to provide ready access to data or instruc-tions previously recorded so as to make them bearupon an immediate problem, such as the guidance ofa physical object, or the analysis and reduction ofdata.

MercuryThe initial man-in-space program of the UnitedStates. The first manned sub-orbital flight tookplace on April 23, 1961, and the first orbital missionon February 20, 1962. Two others followed on May24, 1962 and October 3, 1962. An 18 orbit flightis scheduled for April, 1963.

Mesosphere-4. The atmospheric shell between about 20km and about 70 or 80 kin, extending from the topof the stratosphere to the upper temperature mini-mum (the mesopause.) it is characterized by a broadtemperature maximum (the mesopeak) at about 50km, except .possibly over the winter polar regions.

2. The atmospheric. shell between the top of theionosphere (the top of this region has never beenclearly defined) and the bottom of the exosphere.(This definition has not gained general acceptance.)

MeteorIn particular, the light phenomenon which re-sults from the entry into the earth's atmosphere ofa solid particle from space: more generally, anyphysical object or phenomenon associated with suchan event.

MeteoricOf or pertaining to meteors, or meteoroids.MeteoriteA meteoroid which has reached the surface

of the earth without being. completely vaporized.

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MeteoridA solid object moving in interplanetary space.of a size considerably smaller than an asteroid andconsiderably larger than an atom or molecule.

Meteorological RocketA rocket designed primarilyfor routine upper-air observation (as opposed (Iresearch) in the lower 250,000 feet of the atmosphere,especially that portion inaccessible to balloons, i.e.,above 100,000 feet. Also called "rocketsonde."

MEVA unit of energy, one million electron volts.

Micro-1. A prefix meaning divided by one million. 2. Aprefix meaning very small as in .urnicrometeorite."

Microbar (abbr .,b) The unit of pressure in thesystem and equal to one dyne per square centimeter.

MicrometeoriteA very small meteorite or meteoriticparticle with a diameter in general less than amillimeter.

MicronOne millionth of a meter, abbreviated if.

Microwave RegionCommonly, that region of the radiospectrum between approximately 1000 Mc and300,000 Mc.

Corresponding wavelengths are 30 cm to 1 mm.The limits of the microwave region are not clearly

defined but in general it is considered to be the regionin which radar operates.

MillibarA unit of pressure equal to 1,000 dynes persquare centimeter, or 1/1,000 of a bar.

The millibar is used as a unit of measure of atmos-pheric pressure. a standard atmosphere being equalto 1,013.25 millibars or 29.92 inches of mercury.

Mini.A contraction of " miniature" used in combination,as in "rninicomponent," "miniradio," "minitransistor."

MiniaturizeTo construct a functioning miniature of apart or instrument. Said of telemetering instrumentsor parts used in an earth satellite or rocketwhere room is at a premium. Hence, "miniaturized,""miniaturization."

Minimum Ionizing .SpeedThe speed with which a freeelectron must move through a given gas to be ableto ionize gas atoms or molecules by collision. Inair at standard conditions, this speed is about 10'cm/sec.

MinitrackA satellite tracking system consisting of afield of separate antennas and associated receivingequipment interconnected so as to form inter-ferometers which track a transmitting beacon in thesatellite itself.

MissileAny object thrown, dropped, fired, launched, orotherwise projected with the purpose of striking atarget. Short for "ballistic missile," "guided missile."

Missile is loosely used as a synonym for "rocket"or "spacecraf t" by some careless writers.

Mock-UpA full-sized replica or dummy of something,such as a spacecraft, often made of. some substitutematerial, such as wood, and sometimes incorporatingfunctioning pieces of equipment, Such as engines.

Mode of PropagationIn transmission, a form of propa-gation of guided waves that is characterized by aparticular field pattern in a plane tiansversed thedirection of propagation, which field pattern it

independent of position along the axis of the wave-guide.

In the case of uniconductor waveguides the fieldpattern of a particular mode of propagation is alsoindependent of frequency.

Mode of Vibration Jive a system undergoing vibration, acharacteristic pattern assumed by the system, inwhich the motion of every particle is simple har-monic with the same frequency.

Two or more modes of vibration may exist con-currently in a multiple-degree-of-freedom system.

ModulationSpecifically, vibration of some characteristicof a radio wave, called the "carrier wave," in ac-cordshce with instantaneous values of another wave,called the "modulating wave."

Variation of amplitude is amplitude modulation,variation of frequency is frequency modulation, andvariation of please is please modulation. The forma-tiott 7of very short bursts of n :en trier Wail', separatedby relatively long periods during which no carrierwave is transmitted, is pulse modulation.

Module-1. A self-contained unit of a launch vehicle orspacecraft which serves as a building block forthe overall structure. The module is usually desig-nated by its primary function as "command module,""lunar landing module," etc. 2. A one-package as-sembly of functionally associated electronic parts;usually a plug-in unit.

ModuleAn aggregate of two or more atoms of a sub-stance that exists as a unit.

MoleculeAn aggregate of two or Thom atoms of asubstance that exists as a unit.

Moment (abbr M)A tendency to cause rotation abouta point or axis, as of a control surface about itshinge or of an airplane about its center of gravity;the measure of this tendency, equal to the productof the force and the perpendicular distance betweenthe point of axis of rotation and the line of action ofthr force.

Moment of Inertia (abbr I)Of a. body about an axis,the .14.:mr', where m is the mass of a particle of thebody and r its distance from the axis.

Momentumquantity of motion.Linear momentum is the quantity obtained by

multiplying the mass of a body by its linear speed.Angular momentum is the quantity obtained bymultiplying the moment of inertia of a body by itsangular speed.

The momentum of a system of particles is givenby the sum of the moments of the individual particleswhich make up the system, or by the product of thetotal mass of the system and the velocity of thecenter of gravity of the system.

The momentum of a continuous nied;um is givenby the integral of the velocity over the mass of themedium, or by the product of the total mass of themedium and the velocity of the center of gravity ofthe medium.

MonopropellantA yocket -propellant= consisting of a'single substance, especially a liquid, capable of pro-ducing a heated jet without the addition of a secondsubstance.

M-RegionName given to _a region of activity on thesun when the nature of that activity cannot bedetermined. -

The M-region used in accounting for recurrentmagnetic storms with a period the same as theperiod of solar rotation relative to the earth, 27.3days. See Magnetic Storms.

MultiplexerA mechanical or electrical device for shar-ing of ,a circuit by two or more coincident signals.

MultiplexingThe simultaneous transmission of two ormore signals within a single channel.

The three bask methods of multiplexing involvethe separation of signals by time division, frequencydivision, and phase division.

MultipropellantA rocket propellant consisting of two- or more substances fed separately to the combustion

chamber..

Multistage BocketA vehicle having two or more rocketunits, each unit firing after the one in back of ithaS exhausted its propellant.' Normally, each unit,or stage, is jettisoned after completing its firing.Also called a "multiple-stage rocket" or, infrequently,a "step rocket."

Musa AntennaA "multiple-unit steerable antenna" con-sisting of a number of stationary antennas, the com-posite major lobe of which is electrically steerable.

NACA (abbr)National Advisory Committee of Aero-nautics.

NanoA prefix meaning divided by one billion, as in"nanosecond," one billionth ofd second.

Nanosecond (abbr nsec)-10-' second. Also called"millimisrosecond."

NASA (abbr)National Aeronautics and Space Adminis-tration.

NASC (abbr)National Aeronautics and Space Council.Natural Frequency-1. The frequency of free oscillation

of a system. For a multiple-degree-of-freedom sys-tem, the natural frequencies are the frequencies ofthe normal modes of .vibration. 2. The undampedresonant frequency of the rotor gimbal and itselastic restraint. It is expressed in cycles per unittime. 3. Specifically, of a gyro.

Nautical MileA unit of distance used principally innavigation. For practical navigation it is usuallyconsidered the /ength, of one minute of any greatera& of the earth, the meridian being the greatcircle most commonly used. Also called "sea mile."By international agreement of 1 July 1959, U.S., GreatBritain and nearly all maritime nations establishedthe International Nautical Mile, equal to exactly1852 meters. Using the yard-meter conversion factoreffective July 1, 1959, the International Nautical Mile

- is equivalent to 6,076.11549 international feet.

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NASA's Designated RepresentativeA representative ofthe NASA installation stationed at supplier's plantor a representative of the inspection agency to whomquality assurance functions have been delegated.

NASA InstallationA major organization unit of theNASA; includes Headquarters and field installations.Field installations are assigned specific missions inthe NASA space program.

NeutronA subatomic particle with no electric charge,and with a mass slightly more than the mass of theproton.

Protons and neutrons comprise atomic nuclei; andthey are both classed as nucleons.

NeutrosphereThe atmospheric shell from the earth'ssurface upward in which the atmospheric constituentsare for the most part un-ionized, i.e., electricallyfleutral.

The region of transition between the neutrosphereand the ionosphere is somewhere between 70 and 90km, depending on latitude and season.

Newton's laws of motion - ..A set of three fundamentalpostulates forming the basis of the mechanics ofrigid bodies, formulated by Newton in 1687.

The first law is concerned with the principle ofinertia and states that if a iyody in motion is notacted upon by an external force, its momentum re-mains constant (law of conservation of momentum.)The second law asserts that the rate of change ofmomentum of a body is proportional to the forceacting upon the body and is the direction of theapplied force. A familiar statement of this is theequation

P =maWhere P is vector sum of the applied forces, m

the mass, and a the vector acceleration of the body.The third law is the principle of action and reaction,stating that for every force acting upon a body thereexists a corresponding force of the same magnitudeexerted by the body in. the opposite direction.

Noctilucent CloudsRarely observed clouds of unknowncomposition which occur at great height. Photo-metric measurements have located them between '75and 90 km. They resemble thin cirrus, but usuallywith a bluish or silverish color, although sometimesorange to red, standing out against a dark night sky.Sometimes called "luminous clouds."

Node-1. One of the two points of intersection of theorbit of a planet, planetoid, or comet with the ecliptic,or of the orbit of a satellite with the plane of theorbit of its primary. Also called "nodal point"-

That point at which the body crosses to the northside of the reference plane is called the ascendingnode; the ether, the descending node. The line con-necting the nodes is called line of nodes.

2. A point, line, or surface in a standing wavewhere some characteristic of the wave has essentiallyzero amplitude.

The appropriate modifier should be used beforethe word "node" to signify the type that is intended;e.g., displacement node, velocity node, pressure node.

- S. A terminal of any branch of a network or aterminal common to two or more branches of anetwork. Also called "junction point," "branchpoint," Jill. "vertex."

Naise-1. Any undesired sound. By extension, noise isany unwanted disturbance within a useful frequencyband, such as undesired electric waves in a trans-mission channel or device. When caused by naturalelectrical discharges in the atmosphere noise may becalled 'static."

2. An erratic, intermittent, or statistically randomoscillation.

If ambiguity exists as to the nature of the noise,a phrase such as "acoustic noise" or "electric noise"should be used.

Since the above definitions are not mutually ex-clusive, it is usually necessary to depend upon contextfor distinction.

Nonrelativistic ParticlesParticles which possess avelocity small with respect to that of light, which is186,000 miles/second or 3 x 10" centimeters persecond. (See RELATIVISTIC PARTICLES.)

Nonthermal RadiationElectromagnetic radiation emit-ted by accelerated charged particles not in thermalequilibrium. The distribution of energy with fre-quency of nonthermal radiation usually differs fromthat of blackbody or THERMAL RADIATION.CYCLOTRON and SYNCHROTRON RADIATIONof charged particles in magnetic fields are examplesof nonthermal radiation, as is the light from afluorescent lamp or the AURORA.

Normal Mode of VibrationA mode of free vibration ofan undamped system. In general, any compositemotion of a vibrating system is analyzable into asummation of its n 'nal modes, also called naturalmode, "characteristic mode," and "eigen mode."

Normal Shock WaveA shock wave perpendicular, orsubstantially so, to the direction of flow in a super-sonic ,flow field. Sometimes shortened to "normal

. shock."

NoseconeThe cone-shaped leading end of a rocketvehicle, consisting of (a) a chamber or cl-..mbersin which a satellite, instruments, animals, plants, orauxiliary equipment may be carried, and (b) anouter surface built to withstand high temperaturesgenerated by aerodynamic heating.

In a satellite vehicle, the nosecone may becomethe satellite itself after separating from the finalstage of the rocket or it may be used to shield thesatellite until orbital speed is accomplished, thenseparating from the satellite. See Shroud.

NozzleSpecifically, the part of a rocket thrust chamberassembly in which the gases produced in the chamberare accelerated to high velocities.

Nuclear FuelFissionable material of reasonably longlife, used or usable in producing energy in a nuclearreactor.

Nuclear RadiationThe emission of neutrons and otherparticles from an atomic nucleus as the result ofnuclear fission or nuclear fusion.

Nuclear Reactor,--An apparatus in which nuclear fissionmay be sustained in self-supporting chain reaction.Commonly called "reactor."

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NucleosynthesisThe production of the various elementsoccurring in nature out of hydrogen nuclei or pro-tons. Examples of nucleosynthesis are: thermo-nuclear reactions in stars and interactions involving

fast, charged particles (COSMIC RAYS) near starsor in the interstellar medium.

NucleusThe positively charged core of an atom withwhich is associated practically the whole mass of the%tom but only a minute part of its volume.

A nucleus is composed of one or more protons andan approximately equal number of neutrons.

0OAOThe Orbiting Astronomical Observatory which

will make possible telescopic observations in theinfrared, visible, ultraviolet, and x-ray regions froma stabilized platform above the obscuring effects ofthe earth's atmosphere. The first OAO will belaunched using an ATLAS-AGENA by the UnitedStates late in 19113 or early in 1964, with successiveflights at six-month intervals.

OccultationThe disappearance of a body behind anotherbody of larger apparent size.

When the moon passes between the obseri-er anda star, the star is said to be occulted.

Octane The interval between any two frequencies hav-ing the ratio of 1:2.

The interval in octaves between any two fry=quencies is the logarithm to the base 2 (or 3.322times the logarithm to the base 10) of the frequencyratio.

Oculogravic IllusionThe apparent displacement of anobject in space caused by the difference which mayexist between the direction of the vertical and thatof resultant g.

Oculogyral IllusionThe apparent movement of an ob-ject in the same direction as that in which one seemsto be turning when the semicircular canals of theinner ear are stimulated.

OGOThe Orbiting Geophysical Observatory will be astandardized satellite designed to undertake a largevariety of geophysical experiments, including investi-gations of the MAGNETOSPHERE, the earth's mag-netic field, MICROMETEORITES, and radiopropagation. The fi tst launching using an ATLAS-AGP.NA is scheduled by the United States for 1963,the following for ;964.

Orbit-1. The path of a body or particle under the in-fluence of a gravitational or other force. Forinstance, the orbit of a celestial body is its Oathrelative to another body around which it revolves. 2.To go around the earth or other body in an orbit.

Orbital ElementsA set of 7 parameters defining theorbit of a satellite.

Orbital PeriodThe interval between successive pas-sages of a satellite.

Orbital Velocity-1. The average velocity at which anearth satellite or other orbiting body travels aroundits primary. 2. The velocity of, such-a body at anygiven point in its orbit, as in "its orbital velocityat the apogee is less than at the perigee."

Order of MagnitudeA factor of 10.

fun quantities of the same kind which differ bylegs than a factor of to ore maid to be of the sameorder of magnitude. "Order of magnitude" is usedloosely by teeny writers to item,/ a pronounced dif-ference 4n quantity but with the difference murkless or tnurh snore than a factor of JO.

OrthogonalAt right angles. .

OSOThe Orbiting Solar Observatory. OSO I waslaunched 14; the United States on March 7, 1962. itis designed in particular to gather information onthe ernissfion by the sun of x and y isys, ultravioletbet: offintrons, protons, and electron.: which cannotbe obtained from the earth's surface. A secondsimilatr'OSO will be launched in 1963, with improvedversions following.

OtolithA small calcareous concretion located in theinner ear which plays a part in the mechanism oforientation.

OutgassingThe evolution of gas from a solid in a'Vacuum.

OxidizerSpecifically, a substance lnot necessarily con-taining oxygen) that supports the combustion of afuel or propellant.

OZONEThe molecule O,. It is produced in the upperSTRATOSPHERE by the PHOTODISSOCIATION of0: and subsequent union of 0 and 02. Ozone absorbsultraviolet strongly in the wavelength region from2000 to 3000 A.

Ozonosphere -=The general stratum of the upper atmos-phere in which there is an appreciable ozone con-centration and in which ozone plays an importantpart, in the radiative balance of the atmosphere. Thisregion lies roughly between 10 and 50 km, withmaximum ozone concentration at about 20 to 25 km.Also called 'ozone layer.'

PPad.- Launch Pad.ParagliderA flexible-winged, kite-like vehicle designed

for use in a recovery system for launch vehicles oras a reentry vehicle.

Parameter-1. In general, any quantity of a problemthat is not an independent variable. More specifically,the term is often used to distinguish, from dependentvariables, quantities which may be more or lessarbitrarily assigned values for purposes of the prob-lem at hand. 2. In statistical terminology, anynumerical constant derived from a population or aprobability distribution. Specifically, it is an arbi-trary constant in the mathematical expression of aprobability distribution.

ParsecA unit of distance commonly used to measureinterstellar dimensions. It is the distance at whichan ASTRONOMICAL UNIT, the mean distance ofthe earth from the sun, would subtend an angle ofone second of an arc. A parsec equals 3.26 LIGHTYEARS.

PartAn element of a component, assembly or sub-,assemtly which is not normally subject to further

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subdivision or disassembly or maintenance purposes.Examples are: resistors, transformers, electron tubes,relays, etc.

Passive Reelecting a signal without transmission, as"Echo is a passive satellite." Contrasted with"active."

Payload-1. Originally, the revenue-producing portion ofan aircraft's load, e.g.. passengers, cargo, mail, etc.2. By extension, that which an aircraft, rocket, orthe like carries over and above what is necessary forthe operation of the vehicle during its flight.

PeriA prefix meaning near, as in "per.gee."

PerigeeThat orbital point nearest the earth when theearth is the center of attraction.

That orbital point farthest from the earth iscalled "apogee." Perigee and apogee are used bymany writers in referring to orbits of satellites,especially artificial satellites, around any planet orsatellite, thus avoiding coinage of new terms foreach planet and moon.

PerihelionFor an elliptic orbit about the sun, the pointclosest to the sun.

Pencil-Beam Antenna.A unidirectional antenna, so de-signed that cross sections of the major lobe by planesperpendicurar to the direction of maximum radiationare approximately circular.

PerihelionThat orbital point nearest the sun when thesun is the center of attraction.

That orbital point farthest from the sun is called"aphelion." The term "perihelion" should not beconfused with "parhelion," a form of halo.

PeriodThe interval needed to complete a cycle. Oftenused in reference to time of complete orbit.

PerturbationSpecifically, a disturbance in the regularmotion of a celestial body, the, result of a forceadditional to those which cause the regular motion.

Photodissociation The :emoval of one or more atomsfrom a molecule by the absorption of a quantum ofelectromagnetic or photon energy. The energy ofthe photon absorbed by a system such as an atomor molecule increases in direct proportion to thefrequency of the radiation. Simple molecules such as01, Ns, CO:, 11,0 which are the primary molecularconstituents of the atmosphere can only be photo-dissociated .by ultraviolet or higher frequency(shorter wavelength) light. They are not dissociatedby visible light (See PHOTOIONIZATION.)

Photo IonizationThe removal of one or more electronsfrom an atom or molecule by the absorption of aphoton. As with PHOTODISSOCIATION, ultravioletor shorter wavelength light is required to photo-ionize simple molecules.

PhotonAccording to the quantum theory of radiation,the elementary quantity, or "quantum" of radiantenergy. It is regarded as a discrete quantity havinga mass equal to by /e, where h is Planck's constant,v the frequency of radiation, and c the speed oflight in a vacuum.

Photon EngineA protected type of reaction engine inwhich thrust would be obtained from a stream ofelectromagnetic radiation.

Although the thrust of this engine would beminutt, it may be possible to apply it for extendedperiods of time. Theoretically, in space, where noresistance is offered by. air particles, very high speedsmay be built up.

PhotosphereThe intensely bright portion of the sunvisible to the unaided eye. The photosphere is thatportion of the sun's atmosphere which emits thecontinuous radiation upon which the Fraunhoferlines are superimposed. In one sun model, the photo-sphere is thought to be below the reversing layer inwhich Fraunhofer absorption takes place. In anothermodel, all strata are considered equally effective inproducing continuous emissions and line absorption.

Physiological accelerationThe acceleration experiencedby a human or an animal test subject in an accelerat-ing vehicle.

PickoffA sensing device, used in combination with agyroscope in an automatic pilot or other automaticor robot apparatus, that responds to angular move-ment to create a signal or to effect some type ofcontrol.

Pickup-1. A device that converts a sound, scene, orother form of intelligence into corresponding electricsignals (e.g., a microphone, a television camera, ora phonograph pickup.) 2. The minimum current, volt-age, power. or other value at which a relay will com-plete its intended function. 3. Interference from anearby circuit or system.

LPico A prefix meaning divided by one n million.

PioneerA series of DEEP SPACE PROBES designedto investigate the interplanetary medium. Pioneer I,launched October 11, 1959, determined the radialextent of the earth's MAGNETOSPHERE, and madethe first determination of the density of MICRO-METEORITES in space. Pioneer 5, launched March11, 1960 made the first measurements of the effectsof a SOLAR FLARE far from the earth's magneticfield, and established a record of radio communica-tion of 22.5 million /piles, since exceeded only byMARINER 2.

PipaSignal indication on the scope of an electronicinstrument, produced by a short, sharply peakedpulse of voltage. Also called -"blip."

PitchoverThe programed turn from the vertical thata rocket under power takes as it describes an arcand points in /'direction other than vertical.

PlagesClouds of calcium or hydrogen vapor that showup as bright patches on the visible surface of the sun.

Planck's Constant (abbr h)A constant, usually desig-nated h, of dimensions mass x length' x timeequal to 6.6252 x 10-'1 erg sec. It scales the energyof electromagnetic radiation of frequency v suchthat the radiation appears only in quanta nhv, nbeing an integer.

Planck's LawAn expression for the variation of mono-chromatic emittance (emissive power) as a functionof wavelength of black-body radiation at a giventemperature; it is the most fundamental of the radia-tion Iowa.

Plane:.--.x celestial body of the solar system, revolvingaround the sun in a nearly circular orbit, or a similar

i$2

body revolving around a star.The larger of such bodies are sometimes called

"principal planets" to distinguish them from aster-oids, planetoids, or minor planets, which are com-paratively very small.

An inferior planet has an orbit smaller than thatof the earth; a superior planet has an orbit largerthan that of the earth. The four planets nearest thesun are called "inner planets"; the ethers, "outerplanets." TAS four largest planets are called "majorplanets." The world "planet" is of Greek originmeaning, literally, wanderer, applied because theplanets appear to move relative to the stars.

PlasmaAn electrically conductive gas comprised ofneutral particles, ionized particles, and free electronsbut which, taken as a whole, is electrically neutral.

A plasma is further characterized by relativelylarge intermolecular distances, large amounts ofenergy stored in the internal energy levels of theparticles and by the presence of a plasma sheathat all boundaries of the plasma.

Plasmas are sometimes referred, to as a fourthstate of matter.

Plasma EngineA reaction engine using magneticallyaccelerated plasma as propellant.

A plasma engine is a type of electrical engine.

Plasma JetA megnetohydrodynamic rocket engine inwhich the ejection of plasma generates thrust.

Plasma Sheath-1. The boundary layer of chargedparticles between a plasma and its surroundingwalls, electrodes, or other plasmas.

The sheath is generated by the interaction of Hi;plasma with the boundary material. Current flowmay be in only one direction across the sheath (singlesheath), in both directions across the sheath (doublesheath), or when the plasma is immersed in a mag-netic field, may flow along the sheath surface at rightangles to the magnetic field (magnetic currentsheath.)

2. An envelope of ionized gas that surrounds a bodymoving through an atmosphere at hypersonicvelocities.

The plasma sheath affects transmission, reception,and diffraction of radio waves; thus is important inoperational problems of spacecraft, especial4 duringreentry.

PodAn enclosure, housing, or detachable container ofsome kind, as: (a) an engine pod, (b) an ejectioncapsule.

Polarization-1. The state of electromagnetic radiationwhen- transverse vibrations take place in someregular manner, e.g., all in one plane, in a circle,in an ellipse, or in some other definite curve,

Radiation may become polarized because of thenature of its emitting source, as is the case withmany types of radar antennas, or because of someprocesses to which it is subjected after leaving itssource, as that which., results from the scattering ofsolar radiation as it passes through the earth'satmosphere.

Posigrade RocketAn auxiliary rocket which fires in thedirection in which the vehicle is pointed, used forexample in separating two stages of a vehicle.

Pound (abbr lb)-1.. A unit of weight equal in the UnitedStates to 0.45359237 kilograms. 2. Specifically, a unit

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of measurement for the thrust or force of a reactionengine representing the weight the engine can move,with 100,000 pounds of thrust.

PrecessionChange in the direction of the axis of rota-tion of a spinning body, as a gyroscope, when actedupon by a torque..

The direction of motion of the axis is such thatit causes the direction of spin of the gyroscope totend to coincide with that of the impressed torque.The horizontal component of precession is called"drift," and the vertical component is called "topple."

Precession of the EquinoxesThe conical motion of theearth's axis about the vertical to the plane of theecliptic, caused by the attractive force of the sun,moon, and other planets on the equatorial pro-tuberance of the earth.

Pressure (abbr p)As measured in a vacuum system,the quantity measured at a specified time by a so-called vacuum gage, whose sensing element is locatedin a cavity (gage tube) with an opening orientedin a specified direction at a specified point within thesystem, assuming a specified calibration factor.

The sensitivity of the sensing element is in generalnot the same for all molecular species, but the gagereading is frequently reported using the calibrationfactor for air regardless of the composition of thegas. The opening to the gage tube is often carelesslyoriented with respect to mass-flow vectors in thegas (which is seldom at rest), and errors due tovariations in wall temperatures of tube and systemare frequently neglected. The actual total pressurein a high-vacuum system cannot usually be measuredby a single gage, but in vacuum technology the term"total pressure" is sometimes used to refer to thereading of a single untrapped gage which respondsto condensable vapors as well as permanent gases.

Pressure SuitA garment designed to provide the humanbody an environment above ambient pressure so thatrespiratory and circulatory functions may continuenormally, or nearly so, under low-pressure conditions,such as occur at high altitudes or in space withoutbenefit of a pressurized cabin.

PressurizedContaining air, or other gas, at a pressurethat is higher than the pressure outside the container.

PrestageA step in the action of igniting a large liquidrocket taken prior to the ignition of the full flow,and consisting of igniting a partial flow of propel-lants into the thrust chamber.

PrimaryI. Short for "primary body." 2. Short for"primary cosmic ray."

Primary BodyThe spatial body about which a satelliteor other body orbits, or from which it is escaping,or towards which it is falling.

The primary body of the moon is the earth; theprimary body of the earth is the sun.

Primary Cosmic RaysHigh energy particles or;ginatingoutside the earth's atmosphere.

Primary cosmic rays appear to come from alldirections in space. Their energy appears to rangeYrom 10' to more than 10" electron volts. .

Pre sable Error (abbr pe)In statistics, that value e, forwhich there exists an even probability (0.5) thatthe actual error exceeds ep. The probable error e, is0.6745 times the standard deviation o,

The probable error is not "probable" in the normalsense of the word.

ProbabilityThe chance that a prescribed event willoccur. represented as a number greater than zerobut less than one. The probability of an impossibleevent is zero, and that of an inevitable event is one.

ProbeAny devi( ,t inserted in an environment for thepurpose of obtaining information about, the environ-ment. Specifically, an instrumented vehicle movingthrough the upper atmosphere or space or landingupon another celestial body in order to obtain infor-mation about the specific environment.

Almost any instrumented spacecraft can 6e con-sidered a probe. However, earth satellites are notusually referred to as "probes." Also, almost anyinstrumented rocket can be considered a probe. Inpractice, rockets which attain an altitude of less thanone earth radius (4000 miles) are called "soundingrockets," those which attain an altitude of morethan one earth radius are called "probes" or "spaceprobes." Spacecraft which enter into orbit aroundthe sun are called "deep-sp,..ce probes." Spacecraftwhich enter into orbit around the sun are called"deep-space probes." Spacecraft designed to passnear or land on :mother celestial body are often des-ignated "lunar probe," "Martian probe," "Venusprobe," etc.

ProminenceA filament .e protuberance from thechromosphere of the bun.

Prominem_es can be observed (optically) whencerthe sun's disk is masked., as during an eclipse orusing a coronagraph; and can be observed instru-mentally by filtering in certain wavelengths, as witha spectroheliograph. A typical prominence is 6,000to 12,000 km thick, 60,000 1 m high, and 200,000 kmlong.

PropellantShort for "rocket propellant."ProspectorThe successor to the Surveyor program with

the mission of obtaining detailed photographs of thelunar surface, SOFT-LANDING mobile, automatedlaboratories on the moon, and returning lunar soilsamples to the earth for analysis.

ProtonA positively-charged subatomic particle havinga mass slightly less than that of a neutron but about1847 times greater than that of an electron. Es-sentially, the proton is the nucleus of the hydrogenisotope (ordinary hydrogen stripped of its orbitalelectron.) its electric charge (+4.8025 x 10-'° esu)is numerically equal, but opposite in sign, to thatof the electron.

Protons and neutrons comprise atomic nuclei; theyare both classed as "nucleons."

PrototypeSpacecraft or element thereof which is under-going or has passed environmental and other testswhich qualify design for fabrication of flight unitsor elements thereof.

Proving StandA test stand for reaction engines,especially rocket engines.

PurgeTo rid a line or tank of residual fluid, especiallyof fuel or oxygen in the tanks or lines of a rocketafter a test firing or simulated test firing.

q = Dynamic Pressure.QuantizationThe process of converting from continuous

values of information to a finite number of discretevalues.

Quantum theoryThe theory (first stated by Max Planckbefore the Physical Society of Berlin on December14, 1900) that all electromagnetic radiation is emittedand absorbed in "quanta" each of magnitude 3w,h being Planck's constant and v the frequency of theradiation.

Quiet SunSee "Year of the Quiet Sun."

R

Radar AstronomyThe development of powerful radartransmitters, large antennas, and very sensitivereceivers allows the detection of high frequency radiowaves (radar) reflected off the nearby members ofthe solar system. Signals reflected from the moonwere first detected in 1945, while the first signalsfrom Venus were unambiguously received in 1961.A careful analysis of the reflected signal gives in-formation as to the distance, velocity of approachor recession, surface roughness, rate of rotation, anddielectric constant of the planet. A large antennawith an aperture of 1000 feet under corn' ruction inPuerto Rico should allow radar detection of Mercury,Mars, some of the asteroids, the satellites of Jupiter,and tha platiet Jupiter itself, if the dense Jovianatmosphere does not absorb all of the incident radarsignal.

RadiationShort for "electromagnetic radiation," "Ma-clear radiation."

Radiation BeltsSee VA 4 ALLEN BELTS, MAGNE-TOSPHERE.

Radiation Pressure (abbr Pr)Pressure exerted uponany material body when electromagnetic radiation isincident upon body.

This pressure is manifested whenever the electro-magnetic momentum in a radiation field is changed,and is exactly twice as great when the radiation isreflected at normal incidence as it is when the radia-tion is entirely absorbed at normal incidence. Themagnitude of any radiation pressure effect is directlyproportional to the intensity of the radiation, andis very small by most standards.

On a perfectly reflecting surface Pr = v/3 wherev = radiation density the amount of radiativeenergy per unit volume in the space above the sur-face. Radiation pressure has perceptible effect onthe orbit of earth satellites, especially those with alarge reflecting surface such as Echo.

Radiation 0.leld-1. A device used on certain types ofinstruments to prevent unwar:fiej radiation frombiasing the measurement of a quantity. 2. A deviceused to protect bodies from the harmful effects ofnuclear radiation, cosmic radiation, or the like.

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RadiatorI. Any source of radiant energy, especiallyelectromagnetic radiation. 2. A device that dissipatesheat from something, as from water or oil, not neces-sarily by radiation only.

Generally, the application of the terms "radiator"(in sense 2) or "heat exchanger" to a particular ap-paratus depends upon the point of view: If theemphasis is upon merely getting rid of heat, "radia-tor" is most of ten used, or sometimes "cooler"; ifthe emphasis is upon transferring heat, "heat ex-changer" is usedbut these distinctions do notalways hold true.

Radio AstronomyThe earth's atmosphere is transparentto electromagnetic radiation in only two frequencybands, or "windows". The familiar "optical window"lies in the wavelength interval from 3000 A to afew MICRONS. Practically all astronomy and astro-physics prior to thirty years ago was based on theinformation received through this window. Sincethat time, the development or sensitive electronicreceivers and the construction of large antennas hasallowed the detection of radio waves from astro-nomical sources which pass through the atmo erein the "radio window," from a wavelength of rtmillimeters to a few tens of meters. Radio astron-omy has furnished information about the moon, theplanets, the sun, the interstellar medium (in particu-lar the distribution of atomic hydrogen), supernovafragments, and the structure of galaxies.

Radiometer--A device used to measure some property ofelectromagnetic radiation. In the visible and ultra-violet regions of the spectrum, a photocell or photo-graphic plate may be thought of as a radiometer.I': the infrared, solid state detectors such as photo-conductors, lead sulfide cells and thermocouples areused, while in the radio and microwave regions,vacuum tube receivers, often with parametric ormaser preamplifiers, are the most sensitive detectorsof electromagnetic radiation.

Radio MeteorA meteor detected by the reilection of aradio signal from the meteor trail of relatively highion density (ion column).

Such an ion column is left behind a meteoroidwhen it reaches the region of the upper atmospherebetween about 80 and 120 km, although occasionallyradio meteors are detected at higher altitudes.

RadiosondeA balloon-borne instrument for the simul-taneous measurement and transmission of meteor-ological data.

Radio TelescopeA device for receiving, amplifying, andmeasuring the intensity of radio waves originatingoutside the earth's atmosphere.

RangerThe initial United States program for the in-vestigation of the moon, and the region between themoon and the earth. Errly versions of the Rangerare designed to provide croseup television photo-graphs of the lunar surface, and to rough-land seis-mographs on the moon.

Rarefied Gas DynamicsThe study of the phenomena.elated to the molecular or noncontinuum nature ofgas flow at low densities.

Rayleigh-Jeans LawAn approximation to PLANCICSLAW for blackbody radiation valid in the limit of

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long wavelengths. It is almost always of sufficientaccuracy in the radio and microwave regions of thespectrum.

Reaction Control System--A system of controlling theattitude of a craft when outside the atmosphere byusing jets of gas in lieu of aerodynamic control sur-faces.

Reaction EngineAn engine that develops thrust by itsreaction to ejection of a substance from it; specifi-cally, such an engine that ejects a jet or stream ofgases created by the burning of fuel within the en-gine.

A reaction engine operates in accordance withNewton's third law of motion, i.T., to every action(force) Mere is an equal and 4.vposite reaction. Rothracket engines and jet engines are reaction engines.

ReadoutI. The action of a radio transmitter transmit-ting data either instantaneously with the acquisitionof the data or by play of a magnetic tape uponwhich the data have been recorded. 2. In computeroperations to extract information from storage.

Readout StationA recording or receiving radio stationat which data are received from a transmitter in aprobe, satellite, or other spacecraft.

Real TimeTime in which reporting on events or re-cording of events is simultaneous with the events.

For example, the real time of a satellite is thattime in which it simultaneously reports its environ-ment as it encounters it; the real time of a computeris that time during which it is accepting data.

RecombinationThe process by which a positive and anegative ion join to form a neutral molecule or otherneutral particle.

RecoveryThe procedure or action that obtains when thewhole of a satellite, or a satellite instrumentationpackage, or other part ,>f a rocket vehicle is recov-ered after a launch; the result of this procedure.

Recycle-4n a countdown: To stop the count and to re-turn to in earlier point in the countdown, as in "wehave recycled, -DW at T minus 80 and counting."Compare hold. In besting: to repeat a group orseries of tests,

Red ShiftIn astronomy, the displacement of observedspectral lines toward the longer wavelengths of thered end of the spectrum. Compare space reddening.

The "red shift" in the spectrum of distant galaxieshas been interpreted as evidence that the universe isexpanding.

ReentryThe event occurring when a spacecraft or otherobject comes back into the sensible atmosphere afterbeing rocketed to altitudes abate the sensible atmo-sphere; the action involved in this event.

Reentry VehicleA space vehicle designed to return withits payload to earth through the sensible atmosphere.

Reentry WindowThe area at the limits of the earth'satmosphere through which a spacecraft in a giventrajectory can pass to accomplish a successful re-entry.

Regenerative CoolingThe cooling of a part of an engineby the propellant being delivered to the combustionchamber; specifically, the cooling of a rocketengine

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combustion chamber or nozzle by circulating the fuelor oxidizer, or both, al-ound the part tic,be cooled.

RegeneratorA device used in a thermodynamic processfor capturing and returning to the process heat thatwould otherwise be lost. Also called "a heat ex-changer"

Relative Humidity (abbr rh)The (dimensionless) ratioof the actual vapor pressure of the air to the satura-tion vapor pressure.

Relativibtic Particle Ir general, pertaining to material,as a subatomic particle, moving at speeds which arean appreciable fractfo.n of the speed of light.

RelativityA principle that posttulates the equivalenceof the description of the universe, in terms of physi-cal laws, by various observers, or for various framesof reference.

RendezvousThe event of two or more objects meetingat a preconceived time and place.

A rendezvous would be involved, for example, inservicing or resuppfyirt* (a space station.

ResonanceI. The pheamtnon of amplification of afree wave or °a-ciliation of a system by a forcedwave or oteillation of exactly equal period. Theforced wave may arise from an impressed force uponthe system or from a boundary condition. The growthof the resonant amplitude is characteristically linearin time. 2. Of a system in forced osculation, thecondition which exists when any change, howeversmall, in the frequency of excitation causes a de-crease in the response of the system.

Resonance FrequencyA frequency at which resonanceexists. Also called "resonant frequency."

In case of possible confusioa, the type of resonancemust be indicated; as "velocity resonance frequency."

Retrorocket(From aretroacting'.) A rocket on orin a spacecraft, satellite, or the like to produce thrustopposed to forward motion.

ReiolutionMotion of a celestial bod: in its orbit; circu-lar motion about an axis usually external to thebody.

In some contexts the terms "revolution" and "rota-tion" are used interchangeably; but with referenceto the motions of a celestial body, "revolution" refersto the motion t.. an orbit or about an axis externalto the body. while "rotation" refers to motion aboutan axis within the body. Thus, the earth revolvesabout the sun annually and rotates about its axisdaily.

RillsNarrow, sharply-defined features that extendacross the surfaces of the lunar MARIA. They maybe cracks or wrinkles in the lava beds.

RoCketI. A projectile, pyrotechnic device, or flying ye-hick propelled by a rocket engine. 2. A riAk e t en-gine.

Rocket Engine--A reaction engine that contains withinitself, or carries along with itself, all the substancesnecessary for its operation or for the consumptionor combustion of its fuel, not requiring intake of anyoutside substance and hence capable of ...peration inouter space. Also called "Rocket Motor."

Rocket PropellantAny agent used for consumption orcombustion in a. rocket and from which the rocketderives its thrust, such as a fuel, oxidizer, additive,catalyst, or any compound or mixture of these."Rocket propellant" is often shortened to "pro-pellant."

Rocketsonde--Meteorological rocket.

Roe koonA high-altitude sounding system consisting ofa small solid-propellant research rocket launchedfrom a large plastic balloon.

The rocket is fired near the maximum alt;tude ofthe balloon flight. It is a ,natively mobile rocketsounding system, and has been used extensively fromshipboard.

ReerttgenThat amount of x or gamma radiation suffi-cient to produce ions carrying one electrostatic unitof charge in one cm' of air. The term is loosely usedto signify that amount of any ionizing radiationwhich produces the same effect as one roentgen ofgamma rays. The average person receives about 0.1roentgen per year of total body radiation fromCOSMIC RAYS and the radioactivity of the earth.Five hundred roentgens of full body radiation is fatalto most people.

RollThe rotations: or oscillatory movement of an air-craft or similar body which takes place about alongitudinal axis through the bodycalled "roll" forany amount of such rotation.

Rotatit.nTurning of a body about an ax' within thebody, as the daily rotation If the earth. See Revo-lution.

RumbleA form of combustion instability, especially ina liquid-propellant !rocket trrgine, characterized bya low-pitched, low-frequency rumbling noise; thenoise made in this kind of combustion.

S

Satellite-1. An attendant body that revolves about an-other body, the primary; especially in the solar 14.tem, a secondary body, ur moon, that revolves abouta planet. 2. A man made object that revolves abouta spatial body, such as Explorer I orbiting about theearth.

Scale HeightA measure of the relationship betweendensity and temperature at any point in an atmos-phere; the thickness of a homogeneous atmospherewhich would give the observed temperature or pres-sure.

Schlieren(German, "streaks," "striae.") 1. Regions ofdifferent density in a fluid, especially as shown byspecial apparatus. 2. A method or apparatus forvisualizing or photograiling regions of varyingdensity in a field of flow.

ScreamingA form of combustion instability, especiallyin a liquid-propellant rocket engine, of relatively highfrequency and characterized by a high-pitched noise.

ScrubTo cancel a scheduled rocket firing, either be-fore or during countdown.

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Secondary, Cosmic RaysSecondary emission in the at-mosphere stimulated by primary cosmic rays.

SeeingA blanket term long used by astronomers forthe disturbing effects produced by the atmosphereupon the image quality of an observed astronomicalbody.

SelenocentricRelating to the center of the moon; re-fer.ring to the moon as a center.

Selenographic-1. Of or pertaining to the physicalgeography of the moon. 2. Specifically, referring topositions on the noon measured in latitt..e.e from.themoon's equator and in longitude from a referencemeridian.

Semicircular CanalsTubes located in the inner earwhich play a part in the mechanism of balance andorientation.

Sensible AtmosphereThat part of the atmosphere thatoffers resistance to a body passing through it. SeeEffective Atmosphere.

SensorThe component of an instrument that convertsan input signal into a quantity which is measuredby another part of the instrument. Also called"sensing dement."

Service TowefGantry Scaffold.ShadowgraphA picture or image in which steep density

gradients in the flow about a body are made visible,the body itself being presented in silhouette.

ShakerAn electromagnetic device capable of impartingknown, and/or controlled vibratory acceleration toa given ,object.

.ShieldShort for "radiation shield"; "heat shield."Shock TubeA relatively long tube or pipe in which very

brief high-speed gas flows are produced by the sud-den release of gas at very high pressure into a low-pressure portion of the tube; the high-speed flowmoves into the region of low pressure behind ashock wave.

The shock tulle is used as a tool in the study ofgases or as a kind of intermittent wind tunnel.

Shock WavesThe phenomena in compressible fluid flowwhere a positive pressure disturbance propagatesand eventually steepens into a shock front. In thelimit of a perfect fluid conductor, such variables asvelocity, pressure density, temperatore, end mag-netic field can change discontinuously across a shockfront. A high-velocity shock can be driven by pass-ing a large electric current through a highly ionizedPLASMA. Highly ionized shocks which propagatethrough a magnetic field are called MAGNETOHY-DRODYNAMIC (MHD) shock waves.

Shoran(From "short range navigation.") A precision. electronic position fixing syttem using a pulse trans-

mitter and receiver and two transponder beacons atfixed points.

ShotAn act or instance of firing a rocket, especiallyfor the earth's surface, as "the shot carried therocket 200 miles."

ShroudThe nosecone of a space vehicle whers it i.. usedonly as a shield for passage through the atmospherefrom launch to orbit. It is usually jettisoned .whenorbital speed is achieved.

SiderealOf or pertaining to the stars.SloshingThe back-and-forth splashing of a liquid fuel

in its tank, creating-problems of stability and controlin the vehicle.

SlugA unit of mass; the mass of a free body which ifacted upon by a force of 1 pound would experiencean acceleration of 1 foot per second per second.

SlurryA suspension of fine solid particles in a liquid.Soft RadiationRadiation which is absorbed by an

absorber equivalent to 10 centimeters of lead or less.Radiation which can penetrate more than 10 centi-

meters of lead is termed "hard radiation."

Solar Atmospheric TideVertical motion of the atmos-phere due to thermal or gravitational action of thesun.

Solar CellA photovoltaic device that converts sunlightdirectly into electrical energy.

Solar ConstantThe rate at which solar radiation isreceived on a surface perpendicular to the incidentradiation and at the earth's mean distance from thesun, but outside the earth's atmosphere.

Solar CycleThe observed fluctuation from maximum tominimum of the incidence of SUNSPOTS, and theactivity of SOLAR FLARES and prominences, witha mean period of 11.2 years. There is also evidencethat the overall magnetic held of the sun fluctuateswith the same period.

Solar FlareSudden local increase in the intensity of thelight of hydrogen on the sun. Some solar flares areassociated with the expulsion of charged particlesand the production of radio bursts.

Solar PlasmaSee Solar Wind.Solar RadiationThe total electromagnetic radiation

emitted by the sun.

Solar WindA stream of protons constantly movingoutward from the sun. Synonymous with solarplasma.

Solid PropellantSpecifically, a rocket propellant insolid form, usUally containing both fuel and oxidizercombined or mixed and formed into a monolithic(not powdered or granulated) grain. See RocketPropellant and Grain.

Solid-Propellant Rocket EngineA rocket engine using asolid propellant. Such engines consist essentially ofa combustion chamber containing the propellant, anda nozzle for the exahust jet, although they oftencontain other components, as grids, liners, etc. SeeRocket Engine and Solid Propellant.

Sonic-1. Aerodynamics: Of or pertMrting to the speedof sound; that moves at the speed of sound, as in

"sonic flow"; designed to operate or perform at thespeed of slund, as in "sonic leading edge." 2. Of orpertaining to sound, as in "sonic amplifier".

Sonic BoomA noise caused by the shock wave thatemanates from an aircraft or other object travelingin the atmosphere at or above the speed of sound.

Sonic SpeedThe speed of sound; by extension, the speedof a body traveling at Mach 1.

Sound travels at different speeds through different

mediums and at different speeds through any givenmedium. under different conditions of temperature,etc. In the standard atmosphere at sea level, sonicspeed is approximately 760 miles per hour.

Sounding-1. In geophysics, any penetration of thenatural enviroment for scientific observation. 2. Inmeteorology, same as upper-air observation. How-ever, a common connotation is that of a single com-plete radiosonde observation.

Sounding RocketA rocket designed to explore the at-mosphere within 4,000 miles of the th's surface.

Space-1. Specifically, the part of the universe lying out-side the limits of the earth's atmosphere. 2. Moregenerally, the volume in which all spatial bodies,including the earth, move.

Space-Air VehicleA vehicle that may be operatedeither within or above the sensible atmosphere.

SpacecraftDevices, manned or unmanned, which aredesigned to be placed into an orbit about the earthor into a trajectory to another celestial body.

Space EquivalentA condition within the earth's atmos-phere that is virtually identical,. in terms of a partic-ular function, with a condition in outer space.

For example, at 50,000 feet the low air pressureand the scarcity of oxygen create a condition, so faras respiration is concerned, that is equivalent to acondition in outer space where no appreciable oxygenis present; thus, a physiological space equivalent ispresent in the atmosphere.,

Space MedicineA branch of aerospace medicine con-cerned specifically with the health .,f persons whomake, or expect to make, flights into space beyondthe sensible atmosphere.

Space ProbeSee Probe.Space ReddeningThe observed reddening, or absorp-

tion of shorter wavelengths, of the light from distantcelestial bodies caused by scattering by small par-ticles in interelellar space.. Compare red shift.

Space Simulator=-A device which simulates some condi-tion or conditions existing in spz. t and used fortesting equipment, or in training programs.

Spate SystemA system ,vrisisting of launch vehicle(s),spacecraft and ground support equipment.

Space VehicleA launch vehicle and its associated space-craft.

Spatial Pertaining to space.

SpatioA combining farm meaning "space."

Specific ImpulseA performance parameter of a rocket.propellant, expressed in seconds, and equal to thrust(in pounds) divided by weight flow vate (in poundsper second). .See Thrust.

SpectrometerAn instrument which measures somecharacteristics such as intensity, of electromagneticradiation as a function of wavelength or frequency.

Spectrum-1. In physics, any series of energies arrangedaccording to wavelength (or frequency); specifically,the series of images produced when a beam of radi-

ant energy, such as sunlight, is dispersed by a prismor a reflecting grating. 2. Short for "electromagneticspectrum" or for any part of it used for a specific pur-pose as the 'radio spectrum' (10 kilocycles to 300,000megacycles).

SputteringDislocation of surface atoms of a materialbombarded by high-energy atomic particles.

StageA propulsion unit e a rocket, especially one unitof a multistage rocket, including its own fuel andtanks.

Stage-and-a-HalfA liquid-rocket propulsion unit ofwhich only part falls away fre-xl the rocket vehicledaring flight, as in the case of tyoster rockets fallingaway to leave the sustainer engine to consume re-maining fuel.

Standard Atmospheret. A hypothetical vertical dis-tribution of atmospheric temperature, pressure, anddensity which, by agreement, is taken to be repre-sentative of the atmosphere for purposes of pressurealtimeter cajhrations, aircraft performance calcula-tions, aircraft and rocket design, ballistic tables, etc.2. A standard unit of atmospheric pressure exertedby a 760 mm column of mercury at gravity (980 S5cm/sec') at temperature 0°C.

One standard atmosphere - 760 mm Hg29.9213 in. Hg1013.250 mb

Stationary OrbitAn orbit in which an equatorial satel-lite revolves about the primary at the same angularrat- as the primary rotates on its axis. From theprimary, the satellite thus appears to be stationaryover a pointon the primary.

Stefan-Boltzmann Law.=One of the radiation laws whichstates that the amount of energy radiated per unittime from a unit surface area of an Ideal black ho.i,is proportional to the fourth power of the absolutetemperature of the black body.

Stoichiometric7-Of a combustible mixture, have the exactproportions required for complete combustion.

StratoriphereThe region of the atmosphere lying on-the average between about 12 and 60 kilometers; ithas a temperature which is either constant or in-creases with altitude, and is therefore stable againstconvection. The upper part of the stratosphere isat a temperature of about 260°K, and is heated bythe absorption of ultraviolet light by OZONE.

SubassemblyAn assembly within a larger assembly.

Subatomic. ParticleA component of an atom, such asan electron, a proton, a meson, etrk.

SubsonicIn aerodynamics, dealing with speeds less thanthe speed of sound (see sonic speed), as in "sub-sonk aerodynamics."

SubsystemA functioning entity within a major system(launch vehicle, spacecraft, etc.) of a space systemsuch as plopulSiw subsystem of a launch vehicle orattitude control subsystem of a spacecraft. Alsoconsidered a system.

Sudden Ionospheric Disturbance(Often abbreviatedSID). A complex .combination of sudden changes in-

the condition of the ionosphere, and the effects ofthese changes.

SunspotA relatively dark area on the surface of thesun, consisting of a dark central umbra surroundedby a penumbra which is interm, .liate in brightnessbetween the umbra and the surrounding photosphere.

Sunspots usually occur in pairs with oppositemagnetic polarities. They have a lifetime rangingfrom a few days to several months. Their occurrenceexhibits approximately an eleven year period (thesunspot cycle).

Sunspot CycleA cycle with an average length os. 1...1years, but varying between about 7 and 17 years, inthe number and area of sunspots, as given by therelative sunspot number. This number rises from aminimum of 0-10 to a maximum of 50-140 aboutfour years later, and then declin s more slowly.

An approximate 11-year cycle has been found orsuggested in geomagnetism, frequency of aurora,and other ionospheric characterisacs.

Eleven-year cycles have been suggested for vari-ous tropospheric phenomena, but none of these hasbeen substantiated.

SupersonicPertaining to speeds g-eater than the speedof sound. Compare ultrasonic.

SurveyorThe United States program for the scientificexploration of the surface and subsurface of themoon, following the RANGER program. SurveyorA, designed to make SOFT LANDINGS on the moon,will enplore the physical, chemica;, and mineralogicalproperties of the moon at the landing site. It isexpected to be launched using an ATLAS-Centaur inthe last half of 1964. Surveyor B will be placedin a stable orbit about. 60 miles above the lunarsurface. it will allow a scan by television of thevisit? and hidden faces of the moon, and will beused for a preliminary selection of APOLLO land-ing sites, as well as permit studies of radiationnear the lunar surface, and the gravity and massdistribution of the moon. The launching of a totalof seven Surveyor A's and 5 Surveyor B's is cur-rently planned.

Sustainer EngineAn engine that maintains the velocityof a missile rocket vehicle once it has achieved itsprogrammed velocity by use of booster or otherengine.

This term is applied, for example, to the remain-ing engine of the Atlas after the two booster engineshave been jettisoned. The term is also applied to arocket engine used on an orbital glider to providethe small amount of thrust now and then requiredto ,compensate for the drag imparted by air particlesin the upper atmosphere.

SweepThe motion of the visible dot across the face ofa cathode-ray tube, as a result of scanning deflectionof the electron beam.

Synchronous RotationRotation of a planet or satel-lite about its axis with the same period as its revolu-tion about a parent body, with the axis of rotationassumed perpendicular to the plane of the orbit. Aconsequence of this type of rotation is that the planetor satellite always presents the same side or faceto the parent body. The moon rotates synchronouslywith respect to the earth, and Mercury with respect

t' the sun. There is some evidence that Venus alsorotates synchronously with respect to the sun, or atleast has a day comparable in length to its year.Synchronous rotation is usually assumed to becaused by TIDAL RAG acting during the planet'spast.

Synchrotron RadiationElectromagnetic radiation gen-erated by the acceleration of charged relativisticparticles (usually electrons) in a magnetic ikld.Radiation of this kind was first encountered inparticle acceJerator called the synchrotron. it is animportant mechanism for the generation of non-themal. continuous radio waves in supernova frag-ments and galactic halos.

Synchronous SatelliteAn equatorial west-to-east satel-lite orbiting the earth at an al'itude of 22,300 statutemiles at which altitude it makes one revolution in24 hours, synchronous with the earth's rotation.

Synergic CurveA curve plotted for the ascent of arocket, space-air vehicle, or space vehicle calculatedto give the vehicle an optimum economy in fuel withan optimum velocity.

This curve, plotted to minimize air resistanre,starts of vertically, but bends towards the horizontalbetween 20 and 60 miles altitude.

System-1. An organi2.ed arrangement in which the op-erational results of two or more functioning entitiescan be predicted.

2. Used in term, space system, to mean the launchvehicle, s. 1...ecraft and ground support used in aspace launch and flight.

8. One of major subdivisions of a space system,such as 'aunch vehicle, spacecraft, or ground supportsystem.

4. One of major functioning entities within amajor subdivision of a space system, such as theguidance system of a launch vehicle or the attitudecontrd system of a spacecraft.

In sense 4, synonymous with subs):.-tehi,

Systems IntergrotionThe management process by whichthe systems of a project for example, the launchvehicle, the spacecraft, and its supporting groundequipment and opera' onal procedures) are madecompatible, in order i,o achieve the purpose of theprojec. or the given flight mission.

TTektiteA small glassy body containing no crystals,

probably of meteoritic origin, and bearing no ant(cedent relation to the geological formation in whichit occurs.

Tektites are found in certain large areas called"strewn fields" They are named as minerals withthe suffix "ite," as "australite," found in Australia;"billitOnite," "indochinite," and "rizalite," found inSoutheast Asia; "bediasite" from Texas, and "molda-vite" front Bohemia and Moravia.

TelemetryThe science of measuring a quantity or quan-tities, transmitting the measun'l value to a distantstation, and there interpreting, indicating, or record-ing the quantities measured.

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TerminatorThe line separating illuminated and darkportions of a nonluminous body, as the moon.

TerrestrialPertaining to the earth.Thermal RadiationThe electromagnetic radiation emit-

ted by a hot blackbody, such as the filament of alamp. The distribution of energy with frequency ofthermal radiation is given by PLANCK'S LAW. Thesue r-adiates approximately as a blackbody with atemperature of about 5700°K. (See NONTHERMALRADIATION.)

ThermocoupleA temperature- sensing element whichconverts thermal e .ergy directly into electricalenergy. In its basic form it consists of two dissimilarmetallic electrical conductor:- connected in a closedloop. Each junction forms a thermocouple.

If one thermocouple is maintained at a temperaturedifferent from that of the other, an electrical currentproportional to this temperature difference will flowin the circuit; the value of this proportionality varieswith materials used. For meteorological purposes,couples of copper and constantan are frequently usedwhich generate approximately 90 microvolts per °Cof couple temperature difference.

ThermodynamicPertaining to the flow of heat or tothermoCynamics.

ThermodynamicsThe study of the relationships betweenhe"t and mechanical energy.

ThermonuclearPertaining t. a nuclear reaction that istriggered by particles of high thermal energy.

ThermosphereThe gion of the atmosphere, above theMESOSPHERE. which there is strong heating andincreasing temperature, resulting from the PHOTO-DISSOCIATION of 0, and the PHOTOIONIZATIONof N, N2 and 0. It extends roughly from an altitudeof 90 to 600 kilometers.

Thrust-1. The pushing force developed by an aircraftengine or a rocket engil e. 2. Specifically, in rocketry,the product of propellanc mass flow rate and exhaustvelocity relative to the vehicle.

Thrust-to-Weight Ratio-1 he ratio of the engineTHRUST of a rocket to the total vehicle weight.This ratio must be greater than one to lift the vehicleoff th,. ground.

Tidal DragThe damping of a planet or satellite's rota-tion produced by frictional losses associated withtides raised either in the solid body of the planet orsatellite, or in seas upon its surface. (See SYN-CHRONOUS ROTATION.)

TirosA series of United States meteorological satellitesdesigned to observe the cloud coverage of the earthand measure the heat radix lon emitt..-d by the earthin the infrared.

Topside] SounderA' satellite designed to measure ionconcentration in the ionosphere from above the iono-sphere.

Tore or TorusIn geometry the surface described by aConic section, especially a circle, rotating about astraight line in its own plane or the solid of revolu-tion enclosed by such a surface. Hence, the extendedsections of a manned space laboratory, having a

generally circular configuration and rotating arounda stationary central section.

Torr. (From Torricelli)Suggested international stand-ard term to replace the English term "millimeter ofmercury" and :is abbreviation "mm of Hg" (or theFrench "mm de Hg").

Both "Tor" and "Torr" have been used in Germany,the latter spelling being more common and the oneofficially adopted by the German Standards Associa-tion. The "Torr" is defined as 1/760 of a standardatmosphere or 1,013,250/760 dynes per square centi-meter. This is equivalent to defining the "Torr" as1?-33.22 micro' ars and differs by orly one part inseven million from the International Standard milli-meter of mercury. It is recommended that "Torr" notbe abbreviated. Jowever. the abbreviation T hasbeen used. The prefixes "milli" and "micro" are at-tached it hyphenation.

TrackingThe p-ocess of following the movement ofa satellite or rocket by radar, radio, and photographicobservations.

TrajectoryIn general, the path traced by any body, asa rocket, moving as a result of externally appliedforces.

Trajectory is loosely used to mean "flight path" or"orbit."

TransducerA device capable of being actuated by en-ergy from one or more transmission systems ormedia, as a microphone, a thermocouple, etc.

Transfer OrbitIn interplanetary travel an ellipticaltrajectory tangent to the orbits of both the departureplanet and the target planet.

Transit-1. The passage of a celestial body across acelestial meriaian; usualiy called "meridian transit."2. The apparent passage of a celestial body acrossthe face of another celestial body or across any point,area, or line.

TranslunarOf or pertaining to space outside the moon'sorbit about the earth.

TransponderA combined receiver and transmitter whosefunction is to transmit signals automatically .hentriggered by an interrogatng signal.

;rider BeaconA beacon having a transponder.

T-TlmeAny specific time, minus or plus, as referencedto "zero," or "launch" time, during a countdown se-quence that is intended to result in the firing of arocket propulsion unit that launches a rocket vehicleor missile.

TroposphereThat portion of the atmosphere from theearth's surface to the tropopause; that is, the lowest10 to 20 km of the atmosphere. The troposphere ischaracterized by decreasing temperature with height,appreciable vertical wind motion, appreciable watervapor content, and weather. Dynamically, the tropo-sphere can be divided into the following layers:surface boundary layer, Ekman layer, and freeatmosphere.

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Ultage The amount that a :Nantainer, such as a Lueltank, lacks of being full.

UltrasonicOf .or pertaining to frequencies. above thosethat affect the human ear, i.e., more than 20,000vibrations per second.

The term "ultmsonie" may be used as ar 400dififT toindicate a dei'iee or syNient intended to operate at if14nitrasorrk f requency.

Although "supersonic" WMx formerly used in (WOW:-lien mon siy wit h "uft rason Jtsitg, isarab rag

Ultraviolet RadiationElectromagnetic radiation shorterin wavelength than visible radiation but, longer than'X4ays; roughly, radiation in the wavelength intervalbetween 10 and 4000 angstroms.

Ultmiolet radiation from the sun is responsiblefor many complex photochemiral reactions VbilrUCter-'bill(' of the fa,i)per tifinovher, e.g., the formation ofthe OZOTle layer through Oraciokt dissociation ofoxygen molecules followed by recombination to formozone.

Umbiical CordAny of the servicing electrical or fluidlines bet teen the ground Or a tower and an uprightrocket missile or vehicle before the launch. Oftenshorteti6d to 'umbilical'.

Upper-Air.ObservationA measurement. of atmosphericconditions aloft, above the effective range of a sur-face weather observation. Also called "sounding,""upper-air sounding."

VVan Allen Belt, Van Allen Radiation Belt[For James

A. Van Allen, 1915-.] The zone of high-intensityradiation-- surrounding the earth beginning at alti-tudes- of approximately 1000 kilometers.

The radiation of the Van Allen belt is composedof protons and electrons, temporarily trapped in theearth's magnetic field. The intensity of radiation-varies with the- distance from the earth, thus theVan Allen belt is often considered as two belts orzones, with maxima of intensity jai approximately2600 kilometers and 16,000 kilometers.

VehicleSpecifically, a structure, machine, or device,such as an: aircraft or rocket, designed to carry aburden 'through air or spac6,; more restrictively, arocket craft.

This -word has itcqyi7ed its specific meaning owingto the need for a term '.40 embrace all flying craft,including aircraft and rockets.

Vehicle Control SystemA system, incorporating controlsurfaces or other devices, which adjusts and main-tains the altitude and heading, and sometimes speed,of the vehicle in accordance with signals receivedfrom a guidance system.

The essential difference between a control systemand a guidance system is that'the control systempoints the vehicle and the guidance system gives the

'191

4ids which tell the control system where topoint. However, the control system maintains theinstantaneous orientation of the vehicle withoutspecific commands from the guidance system.

Vernier EngineA rocket engine of small thrust usedprimarily to obtain a fine adjustment in the velocityand tra,iectory of a ballistic missile or space vehiclejust after the thrust cutoff of the last propulsionengine, and used secondarily to add thrust to abooster or sustainer engine. Also called 'vernierrocket'.

VerticalThe direction in which the force of gravity acts.

Visible Radiation J lectromagnetie radiation lying withinthe wr,elength interval to which the h'unan eye issensitive, which is from approximately 0.4 to 0.7mivron (4000 to 7000 angstroms). This portion ofthe electromagnetic spectrum is bounded on theshortwavelength end by ultraviolet radiation/and onthe longwavelength end by infrared radiation.

VoyagerA series of spacecraft which will be launchedby the United States as a successor to theMARINER program. Voyager craft, launched usingthe Saturn, will be directed into stable orbits aroundMars and Venus, and will attempt to SOFT-LANDinstrumented payloads on both these planets. Othersmay be used for flyby studies of Mercury andJupiter.

WaveguideA system of material boundaries capable ofguiding electromagnetic waves.

WeightThe force with which an earth-bound body isattracted toward the earth.

Weightlessness=A condition in which no acceleration,whether of grz.-Oity or other force, can be detectedby an observer within the system in question.

Any object falling freely in a vacuum .is weight-less, tints an unaccelera.ted satellite, orbiting the earthis "weightless" although gravity affects its orbit.Weightlessness can be produced within the atmo-sphere in aircraft flying a parabolic flight path.

WaiverGranted use or acceptance of an article,whichdoes not meet, specified requirements.

WhistlerA radio-frequencY electroniagnetic "signalsometimes generated by lightning discharges.

This signal apparently propagates along a geo-magnetic line cf force, and- often "bounces". severaltimes between the Northern and Southern Hemi-spheres. Its name derives from the sound heard onradio receivers.

X-Ray--Electromagnetic radiation of very shor -ave-length, lying within the wavelength interval of 0.1to 100 angstroms (between gamma rays and ultra-violet radiation', 'Roentgen ray).

X-rays penetrate various thickness of all s- - -icesand they at upon photographic plates in the same.manner as light. Secondary X-rays are producedwhenever X-rays are absorbed by a Rube lance, ;athe case of absorption by a y_..4s, this results sn

Y

Yaw-1. The lateral rotational or oscillatory movementof an aircraft, rocket, or the like about a transverseaccis. 2. The amount of this movement, i.e., the angleof yaw.

Year of the Quiet SunEleven year low period in solaractivity which is expected between April, 1964 andDecember, 1965. The international program formaximum observation and research in this intervalis termed International Year of the Quiet Stnt(IQSY).

ZenithThat point of the celestial sphere vertically ov..,r-head. The point 180° from the zenith is called the"nadir."

Zero G=We33htlessness.

192GOVERNMENT PRINTING OFFICE 1966 0-771.606