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As simple as Newton's equation of gravity looks, if you massage it long enough

with enough calculus and geometry, all of Kepler's laws fall out of it.

Those mathematical results include the facts that the planets have to travel in

elliptical orbits, with the sun at one focus, and that the number equal to

(square of the orbital period) divided by (cube of the semi-major axis)

has to be the same number for every object that orbits the sun.

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Q: Why do all orbits with the same semi-major axis have the same period?
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