The gravitational potential energy of an object placed at earth's surface is U1=−RGMm where, G= gravitational constant, M= Mass of earth, m= mass of object and R= radius of the earth The negative sign in the above relation indicates that it is the work done in bringing the object from infinity to a distance R. The gravitational potential energy of object at a height habove the surface of earth is U2=−(R+h)GMm So, the change in potential energy is ΔU=U2−U1=−R+hGMm−(−RGMm)=−GMm[(R+h)1−R1]=−GMm(−R(R+h)h)=R(R+h)GMmh