- #1

Saitama

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## Homework Statement

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 is ##R##. Making use of Kepler's laws, find its period of revolution.

(Ans: ##\pi \sqrt{(r+R)^3/(2GM)}##)

## Homework Equations

Kepler's laws:

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.

2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

## The Attempt at a Solution

From the third law, ##T^2 \propto R^3## but according to the answer there should be a ##(r+R)^3## and also, I don't know how would I determine the constants here.

Any help is appreciated. Thanks!