Two demonstrations of Kepler's third law for elliptical orbits are presented. Both assume the validity of Kepler's first two laws and a few simple facts concerning the geometry of the ellipse; one directly employs conservation of energy, the other the centripetal-force relation. But neither involves an elaborate use of the calculus.

Kepler's third law for elliptical orbits can be demonstrated using conservation of energy and the centripetal-force relation, without needing elaborate calculus.

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Kepler's Third Law for Elliptical Orbits

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