Question

Let the period of revolution of a planet at a distance 2R from a star be T. Prove that if it
was at a distance of 8R from the star, its period of revolution will be 8T.​

Answer 1

According to Kepler's third law, The square of orbital period of revolution T of a planet around a star is directly proportional to the cube of the mean distance R of the planet from the star. Thus, for a planet, at a distance of 2R from the star, its period of revolution will be √8 T.