The Copernican The Copernican RevolutionRevolution

Figure 2-1Figure 2-1StonehengeStonehenge

Figure 2-2Figure 2-2Observatories in the AmericasObservatories in the Americas

The Greek Frame of MindThe Greek Frame of Mind

Much of the Greek method of thinking Much of the Greek method of thinking revolved around philosophy instead of revolved around philosophy instead of scientific reasoningscientific reasoning

Greeks valued perfection and therefore Greeks valued perfection and therefore any model of the universe should involve any model of the universe should involve the perfect shape, the circlethe perfect shape, the circle

Greek also had no reason to believe that Greek also had no reason to believe that the Earth was not the center of the the Earth was not the center of the universe. Egotistical, yes - but universe. Egotistical, yes - but completely reasonable at the timecompletely reasonable at the time

The only 'scientific' data they had The only 'scientific' data they had available to them was the motion of the available to them was the motion of the Sun, Moon, and planets, which were Sun, Moon, and planets, which were monitored heavily at the timemonitored heavily at the time

Ptolemy ~140 AD

What is this?What is this?

Retrograde Motion within a Planetarium Ceiling – We will do this!

The Motion of the PlanetsThe Motion of the PlanetsRetrograde MotionRetrograde Motion

A model of the universe A model of the universe would be very simple except would be very simple except for the fact that the planets for the fact that the planets undergo a looping motion in undergo a looping motion in their orbitstheir orbits

Remember, in one night, all Remember, in one night, all planets still rise in the east planets still rise in the east and set in the westand set in the west

However, if you keep track However, if you keep track of the planet's position of the planet's position versus the background stars versus the background stars night to night, you will see night to night, you will see the planet 'move'the planet 'move'

The word 'planet' means The word 'planet' means wanderer in Greekwanderer in Greek

Retrograde Motion

Jupiter and Saturn (6/2000 - 5/2001)

Figure 2-5Figure 2-5Inferior and Superior OrbitsInferior and Superior Orbits

Ptolemaic ModelPtolemaic Model

In order to produce the In order to produce the retrograde motion of the retrograde motion of the planets, Ptolemy created a planets, Ptolemy created a model with epicyclesmodel with epicycles

All the planets orbited the Earth All the planets orbited the Earth in a perfect circlein a perfect circle

The planet itself made a smaller The planet itself made a smaller orbit centered upon the larger orbit centered upon the larger orbit around the Earthorbit around the Earth

With the right timing, this model With the right timing, this model can reproduce the retrograde can reproduce the retrograde motion seen from Earthmotion seen from Earth

Deferent = larger circular orbit around EarthEpicycle = smaller circular orbit around the deferent

Ptolemaic ModelPtolemaic Model In Ptolemy's complete In Ptolemy's complete

model, each planet had its model, each planet had its own orbit around the Earth own orbit around the Earth with its own epicyclewith its own epicycle• By changing the period of the By changing the period of the

orbit and the epicycle, the orbit and the epicycle, the model could match model could match observations relatively wellobservations relatively well

The Sun and the Moon The Sun and the Moon traveled around the Earth traveled around the Earth in perfect circlesin perfect circles

The entire model was The entire model was composed of more than 80 composed of more than 80 circles and was very circles and was very complicatedcomplicated

Simplified Ptolemaic Model

The Ptolemaic Model SurvivesThe Ptolemaic Model Survives Since the Ptolemaic model matched observations sufficiently Since the Ptolemaic model matched observations sufficiently

and no contrary evidence was produced, it was supported for and no contrary evidence was produced, it was supported for nearly 1,500 years!nearly 1,500 years!

After all, if the Earth was moving, shouldn't we feel it?After all, if the Earth was moving, shouldn't we feel it?

Also, the Greeks were smart enough to realize that if the Earth Also, the Greeks were smart enough to realize that if the Earth was orbiting the Sun, it would produce stellar parallaxwas orbiting the Sun, it would produce stellar parallax• The Greeks didn't believe it existed because they didn't have The Greeks didn't believe it existed because they didn't have

telescopes to observe such small variations in a star's telescopes to observe such small variations in a star's positionposition

On top of all this, the Dark Ages provided relatively little On top of all this, the Dark Ages provided relatively little advance in any sciences for Europeadvance in any sciences for Europe

The Copernican RevolutionThe Copernican Revolution

At the end of the Dark Ages, a At the end of the Dark Ages, a Polish cleric name Copernicus Polish cleric name Copernicus devised a new model of the devised a new model of the universe where the Earth was no universe where the Earth was no longer at the centerlonger at the center

The heliocentric (Sun centered) The heliocentric (Sun centered) model placed the Earth out of its model placed the Earth out of its central position, yet still central position, yet still maintained many of the maintained many of the observations we seeobservations we see

The beauty in his model was its The beauty in his model was its simplicity over the Ptolemaicsimplicity over the Ptolemaic• Occam's RazorOccam's Razor

The simplest solution is the The simplest solution is the bestbest Nicolaus Copernicus (1473-1543)

The Copernican ModelThe Copernican Model

In the Copernican model, retrograde motion is an apparent effect caused by the Earth 'overtaking' an outer planet in its orbit

The Copernican RevolutionThe Copernican Revolution

Despite the fact that the Copernican model was a Despite the fact that the Copernican model was a better representation of the solar system, it was not better representation of the solar system, it was not widely acceptedwidely accepted

While it did provide a much simpler description While it did provide a much simpler description compared to Ptolemy, it did not necessarily improve compared to Ptolemy, it did not necessarily improve the predictive power of the modelthe predictive power of the model

The religious dogma of the time insisted upon Earth The religious dogma of the time insisted upon Earth being the center of the universebeing the center of the universe

Copernicus published his works in Latin, which was Copernicus published his works in Latin, which was unreadable by the common publicunreadable by the common public

Galileo - The ObserverGalileo - The Observer

A century after Copernicus' A century after Copernicus' work, other scientists began to work, other scientists began to make strides toward make strides toward popularizing the heliocentric popularizing the heliocentric modelmodel

Galileo was the first to use a Galileo was the first to use a telescope to make detailed telescope to make detailed observations of the skyobservations of the sky

Though he did not invent the Though he did not invent the telescope, he made many telescope, he made many working prototypes and trained working prototypes and trained them on a variety of celestial them on a variety of celestial bodiesbodies

Galileo Galilei (1564-1642)

Galileo's Observations - IGalileo's Observations - I Galileo used his telescopes to Galileo used his telescopes to

make observations of many make observations of many heavenly objectsheavenly objects

The sketch to the right shows The sketch to the right shows Galileo's observations of the Galileo's observations of the moons of Jupitermoons of Jupiter

He noticed that the position of He noticed that the position of these four moons changed night these four moons changed night to night, as if they were rotating to night, as if they were rotating around Jupiteraround Jupiter

These moons now bear his nameThese moons now bear his name• The Galilean moons are:The Galilean moons are:

IoIo EuropaEuropa GanymedeGanymede CallistoCallisto

Galileo's Observations - IIGalileo's Observations - II Galileo also noticed that Galileo also noticed that

Venus was not simply a Venus was not simply a point of light, but point of light, but actually a diskactually a disk

He watched Venus go He watched Venus go through complete through complete phases, just like the phases, just like the MoonMoon

This cycle of phases can This cycle of phases can only be satisfied by the only be satisfied by the heliocentric model, not heliocentric model, not the geocentricthe geocentric

The phases of Venus

Galileo's Observations - IIIGalileo's Observations - III Galileo also pointed his Galileo also pointed his

telescope toward the Suntelescope toward the Sun• NEVER DO THISNEVER DO THIS

He discovered that the He discovered that the disk of the Sun was not disk of the Sun was not perfect and was perfect and was occasionally dotted with occasionally dotted with small black spotssmall black spots

By making daily sketches By making daily sketches of these spots, he was of these spots, he was able to determine that the able to determine that the Sun itself was rotatingSun itself was rotating

Galileo - Galileo - Acceleration of GravityAcceleration of Gravity

Galileo discovered that the higher an object is Galileo discovered that the higher an object is dropped, the greater its dropped, the greater its speedspeed when it reaches when it reaches the groundthe ground

All falling objects near the surface of the Earth All falling objects near the surface of the Earth have the have the same accelerationsame acceleration (9.8 m/s (9.8 m/s22))

The acceleration of gravity on the surface of The acceleration of gravity on the surface of other solar-system bodies depends on their other solar-system bodies depends on their mass and radiusmass and radius• Mars and the Moon have a smaller acceleration of Mars and the Moon have a smaller acceleration of

gravitygravity• Saturn is about the same as EarthSaturn is about the same as Earth• Jupiter is more than EarthJupiter is more than Earth

Astronaut Alan BeanAstronaut Alan Bean

Performed Galileo’s experiment on the Moon

Galileo's ConclusionGalileo's Conclusion All of Galileo's observations were All of Galileo's observations were

pointing towards a heliocentric view of pointing towards a heliocentric view of the universethe universe

Galileo published his observations and Galileo published his observations and conclusions in multiple works, conclusions in multiple works, including some published in Italian to including some published in Italian to appeal to a wider audienceappeal to a wider audience

Galileo was threatened with torture, Galileo was threatened with torture, forced to deny his beliefs in the forced to deny his beliefs in the heliocentric model, and sentenced to heliocentric model, and sentenced to house arrest for the rest of his lifehouse arrest for the rest of his life

The seeds of the Copernican The seeds of the Copernican Revolution had been planted Revolution had been planted

You makin’ that up

!!!

Tycho Brahe - An ObserverTycho Brahe - An Observer

Tycho Brahe was a Tycho Brahe was a prominent scholar and prominent scholar and aristocrat in Denmark in aristocrat in Denmark in the mid-late 1500'sthe mid-late 1500's

He made a huge number He made a huge number of observations of the of observations of the stars and planets, all stars and planets, all with the naked eyewith the naked eye• Even without a telescope, Even without a telescope,

he was very accurate in his he was very accurate in his measurementsmeasurements

Also recorded the Also recorded the appearance of comets appearance of comets and supernovaeand supernovae

Tycho (1546-1601)

Brahe’s ModelBrahe’s Model

Geo-HeliocentricGeo-Heliocentric

Wanted to please the Wanted to please the church and his church and his observations observations simultaneously.simultaneously.

Let Earth still be most Let Earth still be most important with other important with other planets orbiting sun.planets orbiting sun.

Johannes Kepler - A TheoristJohannes Kepler - A Theorist Shortly before his death, Shortly before his death,

Tycho began working Tycho began working with another scientist with another scientist named Keplernamed Kepler

Kepler was put to the Kepler was put to the task of creating a model task of creating a model to fit all of Tycho's to fit all of Tycho's planetary dataplanetary data

Kepler spent the Kepler spent the remainder of his life remainder of his life formulating a set of laws formulating a set of laws that explained the that explained the motion of the planetsmotion of the planets Kepler (1571 - 1630)

Kepler's First LawKepler's First Law Kepler first noted that the Kepler first noted that the

orbital path of a planet around orbital path of a planet around the Sun is an ellipse, not a the Sun is an ellipse, not a perfect circleperfect circle

The Sun lies at one of the foci The Sun lies at one of the foci of the ellipseof the ellipse

The eccentricity of an ellipse is The eccentricity of an ellipse is a measure of how 'squished' a measure of how 'squished' from a circle the shape isfrom a circle the shape is

Most planets in the Solar Most planets in the Solar System are very close to a System are very close to a perfect circleperfect circle• Eccentricity, Eccentricity, ee ~ 0 for a circle ~ 0 for a circle

Focus Focus

Kepler's 1st Law: The orbital paths of the planets are elliptical

with the Sun at one focus.

Kepler's First LawKepler's First Law

=closest to the Sun=farthest from the Sun

Kepler's Second LawKepler's Second Law

Kepler also noticed that Kepler also noticed that the planets sweep out the planets sweep out equal areas in their orbit equal areas in their orbit over equal timesover equal times

Notice that this means Notice that this means the planet must speed up the planet must speed up and slow down at and slow down at different pointsdifferent points

If it takes the same If it takes the same amount of time to go amount of time to go through A as it does C, at through A as it does C, at what point is it moving what point is it moving faster?faster?• C, when it is closest to C, when it is closest to

the Sunthe Sun

Kepler's 2nd Law: An imaginary line connecting the Sun to any planet

sweeps out equal areas of the ellipse over equal intervals of time.

Kepler's Third LawKepler's Third Law Finally, Kepler noticed Finally, Kepler noticed

that the period of that the period of planet's orbit squared is planet's orbit squared is proportional to the cube proportional to the cube of its semi major axisof its semi major axis

This law allowed the This law allowed the orbits of all the planets orbits of all the planets to be calculatedto be calculated

It also allowed for the It also allowed for the prediction of the prediction of the location of other location of other possible planetspossible planets

32 aT Kepler's 3rd Law Simplified

NOTE: In order to use the equation as shown, you must be talking about a planet in the Solar System, T must be in years, and

a must be in A.U. !!!

Kepler's Third Law - ExamplesKepler's Third Law - Examples

Suppose you found a new planet in the Suppose you found a new planet in the Solar System with a semi major axis of Solar System with a semi major axis of 3.8 A.U.3.8 A.U.

A planet with a semi major axis of 3.8 A planet with a semi major axis of 3.8 A.U. would have an orbital period of A.U. would have an orbital period of 7.41 years7.41 years

32 aT

872.548.3 32 T

41.7872.54872.54 21

T years

Kepler's Third Law - ExamplesKepler's Third Law - Examples

Suppose you want to know the semi Suppose you want to know the semi major axis of a comet with a period of major axis of a comet with a period of 25 years25 years

A planet with an orbital period of 25 A planet with an orbital period of 25 years would have a semi major axis of years would have a semi major axis of 8.55 A.U.8.55 A.U.

23 Ta

6252523 a

55.8625625 331

a A.U.

Isaac NewtonIsaac Newton Kepler's Laws were a Kepler's Laws were a

revolution in regards to revolution in regards to understanding planetary understanding planetary motion, but there was no motion, but there was no explanation explanation whywhy they worked they worked

That explanation would have That explanation would have to wait until Isaac Newton to wait until Isaac Newton formulated his laws of motion formulated his laws of motion and the concept of gravityand the concept of gravity

Newton's discoveries were Newton's discoveries were important because they important because they applied to actions on Earth applied to actions on Earth and in spaceand in space

Besides motion and gravity, Besides motion and gravity, Newton also developed Newton also developed calculuscalculus

Newton (1642-1727)

Newton and the Apple - GravityNewton and the Apple - Gravity

After formulating his three After formulating his three laws of motion, Newton laws of motion, Newton realized that there must realized that there must be some force governing be some force governing the motion of the planets the motion of the planets around the Sunaround the Sun

Amazingly, Newton was Amazingly, Newton was able to connect the able to connect the motion of the planets to motion of the planets to motions here on Earth motions here on Earth through gravitythrough gravity

Gravity is the attractive Gravity is the attractive force two objects place force two objects place upon one anotherupon one another

Gravitational ForceGravitational Force

• The gravitational The gravitational force is always force is always attractiveattractive

• The strength of the The strength of the attraction decreases attraction decreases with increasing with increasing distancedistance

The Gravitational ForceThe Gravitational Force

GG is the gravitational constant is the gravitational constant • GG = 6.67 x 10 = 6.67 x 10-11-11 N m N m22/kg/kg22

mm11 and and mm22 are the masses of the two are the masses of the two bodies in questionbodies in question

rr is the distance between the two bodies is the distance between the two bodies

221

r

mGmFg

Gravity - ExamplesGravity - Examples Weight is the force you feel due to the gravitational Weight is the force you feel due to the gravitational

force between your body and the Earthforce between your body and the Earth• We can calculate this force since we know all the variablesWe can calculate this force since we know all the variables

26

242

211

221

)10378.6(

)1097.5)(72)(1067.6(

m

kgkgkgmN

r

mGmFg

NFg 7051 Newton is approximately 0.22 pounds

lbsN

lbsNFg 155

1

22.0705

Gravity - ExamplesGravity - Examples If gravity works on any two bodies in the universe, If gravity works on any two bodies in the universe,

why don't we all cling to each other?why don't we all cling to each other?• Replace the from previous examples with two people and the Replace the from previous examples with two people and the

distance with 5 metersdistance with 5 meters

2

2

211

221

)5(

)65)(72)(1067.6(

m

kgkgkgmN

r

mGmFg

NNFg81025.10000000125.0

1 Newton is approximately 0.22 pounds

lbsN

lbsNFg

98 1075.21

22.01025.1

Orbit of Earth around SunOrbit of Earth around Sun

OrbitsOrbits The law of universal The law of universal gravitation accounts for gravitation accounts for planets not falling into the planets not falling into the Sun nor the Moon Sun nor the Moon crashing into the Earthcrashing into the Earth

Paths A, B, and C do not Paths A, B, and C do not have enough horizontal have enough horizontal velocity to escape Earth’s velocity to escape Earth’s surface whereas Paths D, surface whereas Paths D, E, and F do.E, and F do.

Path E is where the Path E is where the horizontal velocity is horizontal velocity is exactly what is needed so exactly what is needed so its orbit matches the its orbit matches the circular curve of the Earthcircular curve of the Earth

PTYS/ASTR 206 Keplers Laws and Gravity 2 1/27/09

The same concept holds for planetary The same concept holds for planetary orbits about the Sunorbits about the Sun

Galilean Satellites and Kepler’s LawsGalilean Satellites and Kepler’s Laws

Newton derived Kepler’s third law using Newton derived Kepler’s third law using physics and his universal law of physics and his universal law of gravitation. His form of Kepler’s 3gravitation. His form of Kepler’s 3rdrd law law for the orbits of the planets about the Sun for the orbits of the planets about the Sun is:is:

The EARTHThe EARTH

Is just a tiny planet

The Earth The Earth has a moonhas a moon

The Earth and Moon together, as seen from the departing Galileo space probe

The SunThe Sun

Mass 2x1030 kg

Radius 7x105 km

Central temperature 15 million K

Surface temperature 5780 K

Composition 75% hydrogen(by mass) 25% helium

Our Planet is Pretty BigOur Planet is Pretty Big

Planets are Pretty Big…..Right?Planets are Pretty Big…..Right?

Our sun is Pretty BigOur sun is Pretty Big

Our sun is Pretty Big … Right?Our sun is Pretty Big … Right?

Our sun is Pretty Big … Right?Our sun is Pretty Big … Right?

……and our star is one of and our star is one of 200,000,000,000 in this…200,000,000,000 in this…

Which Looks Like This:Which Looks Like This:

……which is one of these…which is one of these…

……and there are about 40 and there are about 40 billion other galaxies in the billion other galaxies in the universe.universe.

How are we going to get a handle on this BIG Universe of ours???

Units of DistanceUnits of DistanceAstronomers use (and mix Astronomers use (and mix together) units of distance.together) units of distance.

Metric:Metric: 1 meter = 1 m1 meter = 1 m1 centimeter = 1cm1 centimeter = 1cm1 kilometer = 1 km1 kilometer = 1 km

Astronomical Unit (AU) – Earth-Sun distanceAstronomical Unit (AU) – Earth-Sun distance= 1.496 x 10= 1.496 x 1011 11 mm

Light Year – Distance light travels in 1 yearLight Year – Distance light travels in 1 year= 9.46 x 10= 9.46 x 1012 12 kmkm

Parsec (pc) = Parsec (pc) = = 3.08 x 10= 3.08 x 1016 16 mm…….kiloparsec (kpc), megaparsec (Mpc).kiloparsec (kpc), megaparsec (Mpc)

So…how big is IT anyway?So…how big is IT anyway?(the Universe that is….)(the Universe that is….)

……about 10 billion-billion-billion centimeters in diameterabout 10 billion-billion-billion centimeters in diameter

oror10,000,000,000,000,000,000,000,000,000 cm10,000,000,000,000,000,000,000,000,000 cm

oror10102828 cm cm

oror10 billion l-y10 billion l-y

oror6000 Mpc6000 Mpc

Where is the Shuttle?Where is the Shuttle?

Where is the Shuttle?Where is the Shuttle?

Where is the Shuttle?Where is the Shuttle?

=

12,800 km

10 cm

Scale of the UniverseScale of the Universe1) The Earth is the Size of a clenched fist1) The Earth is the Size of a clenched fist

- or…. 12,800 km = 10 cm- or…. 12,800 km = 10 cm

2) The Moon is 3500 km in Diameter2) The Moon is 3500 km in Diameter - or….the size of the tip of your THUMB- or….the size of the tip of your THUMB

3) The Moon is 384,000 km away3) The Moon is 384,000 km away- or…. 3 meters from the fistor…. 3 meters from the fist

4) The Sun is 1,400,000 km in diameter4) The Sun is 1,400,000 km in diameter - or…. 11 meters in diameter- or…. 11 meters in diameter

5) The Sun is 150,000,000 km away5) The Sun is 150,000,000 km away- or…. 1.2 km from the fist- or…. 1.2 km from the fist

The Earth and the SunThe Earth and the Sun

Earth Sun

Diameter 12800 km 1.5 million km (117x Earth)

Mass 6x1024 kg 2x1030 kg (333,000x Earth)

Composition rocks gas(75% hydrogen25% helium)

Rotation period =1 day ~25 days