1. The Mechanics of theThe Mechanics of the
Solar SystemSolar System
(Part I)(Part I)
David McDonald, M.Ed.David McDonald, M.Ed.
Director of EducationDirector of Education
The McAuliffe-Shepard Discovery CenterThe McAuliffe-Shepard Discovery Center

2. Basic Inner Planet VocabularyBasic Inner Planet Vocabulary
 Inferior PlanetInferior Planet
 Superior PlanetSuperior Planet
 ConjunctionConjunction
 Inferior ConjunctionInferior Conjunction (Mercury – January 5, 2010)(Mercury – January 5, 2010)
 TransitTransit (Venus – June 6, 2012; Mercury – May 10, 2016)(Venus – June 6, 2012; Mercury – May 10, 2016)
 Superior ConjunctionSuperior Conjunction (Venus – January 12, 2010)(Venus – January 12, 2010)
 OppositionOpposition (Mars – January 29, 2010)(Mars – January 29, 2010)

3. Vocabulary ContinuedVocabulary Continued
 EclipticEcliptic
 Greatest ElongationGreatest Elongation
 Greatest Western Elongation of MercuryGreatest Western Elongation of Mercury
January 27, 2010January 27, 2010
 Greatest Eastern Elongation of VenusGreatest Eastern Elongation of Venus
August 20, 2010August 20, 2010
 PhasesPhases

4. Solar System DistancesSolar System Distances
 Bode’s LawBode’s Law
 Geometric series 0, 3, 6, 12, 24, 48, 96, 192, 384,Geometric series 0, 3, 6, 12, 24, 48, 96, 192, 384,
768768
 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, 77.4, .7, 1.0, 1.6, 2.8, 5.2, 10, 19.6, 38.4, 77
 .4, .7, 1.0, 1.5, 2.8, 5.2, 9.5, 19.2, 30, 39.5.4, .7, 1.0, 1.5, 2.8, 5.2, 9.5, 19.2, 30, 39.5
 Scale models (ball park)Scale models (ball park)

5. Astronomers of the PastAstronomers of the Past
 Aristotle – Geocentric universe of nestedAristotle – Geocentric universe of nested
spheres.spheres.
 Ptolemy – Followed Aristotle’s ideas but withPtolemy – Followed Aristotle’s ideas but with
some adjustment. Interested in a mathematicalsome adjustment. Interested in a mathematical
description of the motion of the planets.description of the motion of the planets.
 Many followed Ptolemy and tried to solve theMany followed Ptolemy and tried to solve the
“Problem of the Planets” making various“Problem of the Planets” making various
adjustments in the epicycles.adjustments in the epicycles.

6. This is a problem

7. Ptolemy’s UniversePtolemy’s Universe

9. 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

10. Tycho BraheTycho Brahe
 Danish NoblemanDanish Nobleman
 1572 – A new star1572 – A new star
 Precise measurementsPrecise measurements
of the stars.of the stars.
 Heavens DO changeHeavens DO change
 New Geocentric modelNew Geocentric model
 Died 1601 - tablesDied 1601 - tables
“given” to Kepler“given” to Kepler

11. Johannes KeplerJohannes Kepler
 Believer in CopernicanBeliever in Copernican
theorytheory
 Five regular solidsFive regular solids
 Rudolphine TablesRudolphine Tables
 1606 Mars has elliptical1606 Mars has elliptical
orbitorbit
 Different speedsDifferent speeds
 1609 “Astronomia1609 “Astronomia
Nova”Nova”

12. Kepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion
 1. The orbits of the planets are ellipses with the1. The orbits of the planets are ellipses with the
sun at one focus.sun at one focus.
 2. A line from a planet to the sun sweeps over2. A line from a planet to the sun sweeps over
equal areas in equal intervals of time.equal areas in equal intervals of time.
 3. A planet’s orbital period squared is3. A planet’s orbital period squared is
proportional to its average distance from the sunproportional to its average distance from the sun
cubedcubed
PP22
= a= a33
P in years; a in AUsP in years; a in AUs

13. A Little MathA Little Math
 If Jupiter’s average distance from the sun is 5.2If Jupiter’s average distance from the sun is 5.2
AU, what is the period of Jupiter’s orbit aroundAU, what is the period of Jupiter’s orbit around
the sun?the sun?
 PP22
= a= a33
 5.2 cubed is about 140.6. Take the square root5.2 cubed is about 140.6. Take the square root
of that and you get about 11.8 yearsof that and you get about 11.8 years
 Pluto orbits the sun with a period of 247.7 years;Pluto orbits the sun with a period of 247.7 years;
what is its average distance from the sun?what is its average distance from the sun?
 39.5 AU39.5 AU

14. Galileo GalileiGalileo Galilei
 First to systematically study the heavens with aFirst to systematically study the heavens with a
telescope he built (1609).telescope he built (1609).
 Saw mountains and valleys on the moonSaw mountains and valleys on the moon
 Saw four moons around Jupiter in January 1610Saw four moons around Jupiter in January 1610
(supported Copernican Theory)(supported Copernican Theory)
 Saw sun spots (not perfect – problem)Saw sun spots (not perfect – problem)
 Saw Venus had phases – went around the sunSaw Venus had phases – went around the sun

15. Phases of Venus Support CopernicusPhases of Venus Support Copernicus

16. A Brief History TimelineA Brief History Timeline

17. And that’s just the start ofAnd that’s just the start of
getting into trouble - stay tunedgetting into trouble - stay tuned
for Newton and Einstein infor Newton and Einstein in
“Mechanics of the Solar System“Mechanics of the Solar System
Part Deux” (April 14, 2010 at aPart Deux” (April 14, 2010 at a
Discovery Center near you)!Discovery Center near you)!
Think about that and have a nice day!Think about that and have a nice day!
