The Mechanics of The Mechanics of the Solar Systemthe Solar System

(Part I)(Part I)

David McDonald, M.Ed.David McDonald, M.Ed.

Director of EducationDirector of Education

The McAuliffe-Shepard Discovery The McAuliffe-Shepard Discovery CenterCenter

Basic Inner Planet Basic Inner Planet VocabularyVocabulary

Inferior PlanetInferior Planet Superior PlanetSuperior Planet ConjunctionConjunction Inferior Conjunction Inferior Conjunction (Mercury – January (Mercury – January

5, 2010)5, 2010) Transit Transit (Venus – June 6, 2012; Mercury – May 10, (Venus – June 6, 2012; Mercury – May 10,

2016)2016)

Superior Conjunction Superior Conjunction (Venus – January (Venus – January 12, 2010)12, 2010)

Opposition Opposition (Mars – January 29, 2010)(Mars – January 29, 2010)

Vocabulary ContinuedVocabulary Continued

EclipticEcliptic Greatest ElongationGreatest Elongation Greatest Western Elongation of Greatest Western Elongation of

Mercury January 27, 2010Mercury January 27, 2010 Greatest Eastern Elongation of Greatest Eastern Elongation of

Venus August 20, 2010Venus August 20, 2010 PhasesPhases

Solar System DistancesSolar System Distances

Bode’s LawBode’s Law Geometric series 0, 3, 6, 12, 24, 48, 96, Geometric series 0, 3, 6, 12, 24, 48, 96,

192, 384, 768192, 384, 768 Add 4 and divide by 10Add 4 and divide by 10 .4, .7, 1.0, 1.6, 2.8, 5.2, 10, 19.6, 38.4, .4, .7, 1.0, 1.6, 2.8, 5.2, 10, 19.6, 38.4,

7777 .4, .7, 1.0, 1.5, 2.8, 5.2, 9.5, 19.2, 30, .4, .7, 1.0, 1.5, 2.8, 5.2, 9.5, 19.2, 30,

39.539.5 Scale models (ball park)Scale models (ball park)

Astronomers of the PastAstronomers of the Past

Aristotle – Geocentric universe of nested Aristotle – Geocentric universe of nested spheres.spheres.

Ptolemy – Followed Aristotle’s ideas but Ptolemy – Followed Aristotle’s ideas but with some adjustment. Interested in a with some adjustment. Interested in a mathematical description of the motion mathematical description of the motion of the planets.of the planets.

Many followed Ptolemy and tried to solve Many followed Ptolemy and tried to solve the “Problem of the Planets” making the “Problem of the Planets” making various adjustments in the epicycles.various adjustments in the epicycles.

This is a problem

Ptolemy’s UniversePtolemy’s Universe

Copernicus: Copernicus: Heliocentric ModelHeliocentric Model

De Revolutionibus (1530)De Revolutionibus (1530) Sun at centerSun at center Not any more accurateNot any more accurate Uniform circular motionUniform circular motion Small epicycles neededSmall epicycles needed Total change in thinkingTotal change in thinking

Tycho BraheTycho Brahe

Danish NoblemanDanish Nobleman 1572 – A new star 1572 – A new star Precise Precise

measurements of measurements of the stars.the stars.

Heavens DO changeHeavens DO change New Geocentric New Geocentric

modelmodel Died 1601 - tables Died 1601 - tables

“given” to Kepler“given” to Kepler

Johannes KeplerJohannes Kepler

Believer in Believer in Copernican theoryCopernican theory

Five regular solidsFive regular solids Rudolphine TablesRudolphine Tables 1606 Mars has 1606 Mars has

elliptical orbitelliptical orbit Different speedsDifferent speeds 1609 “Astronomia 1609 “Astronomia

Nova”Nova”

Kepler’s Laws of Planetary Kepler’s Laws of Planetary MotionMotion

1. The orbits of the planets are ellipses 1. The orbits of the planets are ellipses with the sun at one focus.with the sun at one focus.

2. A line from a planet to the sun sweeps 2. A line from a planet to the sun sweeps over equal areas in equal intervals of over equal areas in equal intervals of time.time.

3. A planet’s orbital period squared is 3. A planet’s orbital period squared is proportional to its average distance from proportional to its average distance from the sun cubedthe sun cubed

PP2 2 = a = a33 P in years; a in AUs P in years; a in AUs

A Little MathA Little Math If Jupiter’s average distance from the sun If Jupiter’s average distance from the sun

is 5.2 AU, what is the period of Jupiter’s is 5.2 AU, what is the period of Jupiter’s orbit around the sun?orbit around the sun?

PP2 2 = a = a33

5.2 cubed is about 140.6. Take the square 5.2 cubed is about 140.6. Take the square root of that and you get about 11.8 yearsroot of that and you get about 11.8 years

Pluto orbits the sun with a period of 247.7 Pluto orbits the sun with a period of 247.7 years; what is its average distance from years; what is its average distance from the sun?the sun?

39.5 AU39.5 AU

Galileo GalileiGalileo Galilei

First to systematically study the heavens First to systematically study the heavens with a telescope he built (1609).with a telescope he built (1609).

Saw mountains and valleys on the moonSaw mountains and valleys on the moon Saw four moons around Jupiter in January Saw four moons around Jupiter in January

1610 (supported Copernican Theory)1610 (supported Copernican Theory) Saw sun spots (not perfect – problem)Saw sun spots (not perfect – problem) Saw Venus had phases – went around the Saw Venus had phases – went around the

sunsun

Phases of Venus Support Phases of Venus Support CopernicusCopernicus

A Brief History TimelineA Brief History Timeline

And that’s just the start And that’s just the start of getting into trouble - of getting into trouble - stay tuned for Newton stay tuned for Newton

and Einstein in and Einstein in “Mechanics of the Solar “Mechanics of the Solar

System Part Deux” System Part Deux” (April 14, 2010 at a (April 14, 2010 at a

Discovery Center near Discovery Center near you)!you)!Think about that and have a Think about that and have a

nice day!nice day!