All Problems Universal Gravitation
Problem 1.202
A planet of mass \(M\) moves around the Sun along an ellipse so that its minimum distance from the Sun is equal to \(r\) and the maximum distance to \(R\). Making use of Kepler's laws, find its period of revolution around the Sun.
1.202. \(T=\pi V(r+R)^{3} / 2 \gamma M .\) 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. \((r+R) / 2,\) since in accordance with \(\mathrm{Kepler}^{\prime} \mathrm{s}\) laws the period of revolution is the same.