Let U be the magnitude of the gravitational potential energy of the moon-earth system, assuming zero potential energy at an infinite separation. Let K denote the kinetic energy of the moon relative to the earth.

Step-by-step solution

The gravitational potential energy of the moon-earth system is given by V = - GMm r , where M is the mass of the earth, m is the mass of the moon, and r is the orbital radius. The magnitude of the gravitational potential energy is U = |V| = GMm r . For the moon revolving around the earth, the necessary centripetal force is provided by the gravitational force: mv^2 r = GMm r^2 mv^2 = GMm r The kinetic energy of the moon is K = 1 2 mv^2 = GMm 2r . Comparing U and K , we get U = 2K . Since K is a positive quantity, it