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Assume that the elliptical orbit ed r = 1 + e cos is in the xy-plane, with L along the z-axis. Prove that d ||L| = = r2 . dt

Assume that the elliptical orbit ed r = 1 + e cos is in the xy-plane, with L along the z-axis. Prove that d ||L| = = r2 . dt

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Assume that each planet moves in an orbit given by the vectorvalued function r. Let r = || r||, let G represent the universal gravitational constant, let M represent the mass of the sun, and let m represent the mass of the planet. Prove Kepler’s Second Law: Each ray from the sun to a planet sweeps out equal areas of the ellipse in equal times.

Assume that the elliptical orbit ed r = 1 + e cos is in the xy-plane, with L along the z-axis. Prove that d ||L| = = r2 . dt
Transcribed Image Text:Assume that the elliptical orbit ed r = 1 + e cos is in the xy-plane, with L along the z-axis. Prove that d ||L| = = r2 . dt
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