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# Kepler's laws of planetary motion

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### Kepler's laws of planetary motion

1. 1. MARSJOHANNES KEPLERTHE SOLAR SYSTEMMARSJOHANNES KEPLERTHE SOLAR SYSTEMLAWS OF PLANETARY MOTIONLAWS OF PLANETARY MOTION
2. 2. Danish astronomerTyco Brahe (1546-1601)had an islandobservatory and thebest measurements ofthe positions for allknown planets(Mercury, Venus, Mars,Jupiter, and Saturn)and the Moon.Picture of Brahe
3. 3. AustrianmathematicianJohannes Kepler(1571-1630),interested in howthe planets movearound the sun,went to Tyco’sisland to get theseaccuratemeasurements.
4. 4. At that time, many astronomersbelieved that planets orbited aroundthe sun in perfect circles, but Tyco’saccurate measurements for Marsdidn’t fit a circle.Instead, the mathematician JohannesKepler found that the orbit of Mars fitan ellipse the best…
5. 5. What is an ellipse?What is an ellipse?2 fociAn ellipse is ageometric shape with2 foci instead of 1central focus, as in acircle. The sun is atone focus withnothing at the otherfocus.FIRST LAW OF PLANETARY MOTION
6. 6. An ellipse also has……a major axis …and a minor axisSemi-major axisPerihelion AphelionPerihelion: When Mars or any another planetis closest to the sun.Aphelion: When Mars or any other planet isfarthest from the sun.
7. 7. Kepler also found that Mars changedspeed as it orbited around the sun:faster when closer to the sun, slowerwhen farther from the sun…A BBut, areas A and B,swept out by a linefrom the sun toMars, were equalover the sameamount of time.SECOND LAW OF PLANETARYMOTION
8. 8. Kepler found arelationship between thetime it took a planet togo completely aroundthe sun (T, siderealyear), and the averagedistance from the sun(R, semi-major axis)…R1R2T1T2T12R13T22R23=T 2= T x TR3= R x R x R( )THIRD LAW OF PLANETARY MOTION
9. 9. T2R2Earth’s sidereal year (T)and distance (R) bothequal 1. The averagedistance from the Earthto the sun (R) is called 1astronomical unit (AU).Kepler’s Third Law, then, changes toT12R13T12R13T22R231 1= =or or T12= R13
10. 10. Planet T(yrs) R(au) T2R3Venus 0.62 0.72 0.38 0.37Earth 1.00 1.00 1.00 1.00Mars 1.88 1.52 3.53 3.51Jupiter 11.86 5.20 141 141When we compare the orbitsof the planets…We find that T2and R3are essentially equal.
11. 11. Kepler’s Laws apply to any celestialbody orbiting any other celestialbody.• Any planet around a sun• The moon around the Earth• Any satellite around the Earth• The international space station• Any rings around any planet
12. 12. Later, Isaac Newton built upon Kepler’s Lawsto confirm his own Law of Gravitation.THE RED PLANET MARS IS FOREVERLINKED TO OUR UNDERSTANDING OFTHE SOLAR SYSTEM AND ONE OF THE4 BASIC FORCES OF NATURE.If it wasn’t for Mars and its complicatedtravels across the night sky, JohannesKepler may not have derived his Laws ofPlanetary Motion. Isaac Newton might nothave had a foundation for his Law ofGravitation...