If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

The gravitational potential energy of the body on earth's surfaceUR=GMmRAt a height h from the earth's surfaceUR+h=−GMm(R+h)=−GMm2R (∵h=R)Therefore, gain in potential energy=UR+h−U=−GMm2R−−GMmR=GMm2R=gmR22R=12mgR