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day04keplerlaws - K s&& = R 3 T 2 = Gm s&& 4 ±...

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Kepler’s Laws 1. The planets move about the sun in elliptical orbits, with the sun at one focus. 2. The straight line joining the sun and a given planet sweeps out equal areas in equal intervals of time. 3. The square of the period of revolution of a planet about the sun is proportional to the cube of its mean distance from the sun. For the Earth: (Derivation) F c = F g m s & ( 4 ± 2 R T 2 ) = Gm E m s & R 2 (for circular orbits) (* s = satellite) K E = R 3 T 2 = Gm E 4 ± 2 = 1.01 x 10 13 m 3 / s 2 For sun satellites ( e.g. planets, asteroids, etc.)
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