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Universal Gravitation

Problem 1.202

A planet of mass MM moves around the Sun along an ellipse so that its minimum distance from the Sun is equal to rr and the maximum distance to RR. Making use of Kepler's laws, find its period of revolution around the Sun.

Reveal Answer
1.202. T=πV(r+R)3/2γM.T=\pi V(r+R)^{3} / 2 \gamma M . It is sufficient to consider the motion along the circle whose radius is equal to the major semi-axis of the given ellipse, i.e. (r+R)/2,(r+R) / 2, since in accordance with Kepler′s\mathrm{Kepler}^{\prime} \mathrm{s} laws the period of revolution is the same.
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