What is the Gravitational Potential Energy?

Gravitational Potential Energy

Consider a block of mass m kept near the surface of the earth and suppose it is raised through a height h. COnsider "the earth + the block" as the system. The gravitational force between the earth and the block is conservative and we can define a potential energy corresponding to this force. The earth is very heavy as compared to theblock and so one can neglect its acceleration. Thus, if we take our reference frame attached to the earth, it will still be very nearly an inertial frame.

The work done y the gravitational force due to the block on the earth is zero in this frame. The force mg on the block dooes work if the block ascends through a height h and hence the potential energy is increased by mgh. Thus, if a block of mass m ascends a height  h above the earth's surface, the potentail energy of the "earth + block" system increases by mgh. If  the block descends by a height h, the potential energy decreases by mgh.

Since the earth almost remains fixed, it is customary to call the potential energy of the block - earth system as the potential energy of the block only. We then say that the gravitational potential energy of the "block" is increased by an amount mgh when it is raised through a height h above the earth's surface.