For a satellite of mass m moving in a circular orbit of radius r around a planet of mass M
a. (i) Using the condition for uniform circular motion, prove that the kinetic energy of the satellite is equal to one-half the magnitude of its gravitational potential energy.
b. (ii) Hence derive an expression for the total mechanical energy of the satellite in terms of G, M, m and r.
c. (iii) What fraction of the gravitational potential energy of the system is converted into the satellite’s kinetic energy in such an orbit?