At the surface of a certain planet the free–fall acceleration is measured to be 7.5ms−2, and the minimum speed required to escape from its surface is found to be 6.0kms−1. Assume the planet to be a perfect sphere of uniform density.
(i) Show how the planet’s radius R may be expressed in terms of the given escape speed ve and the surface acceleration due to gravity g.
(ii) Hence determine the numerical values of (a) the planet’s radius and (b) its mass.