## Derivation of The Approximate Expression for the Gravitational Potential Energy

The equation (increase in) Gravitational Potential Energy=is only an approximation when is is small compared to the radius of the Earth. The graph of gravitational potentialagainstthe distance from the Earth's centre is shown below.To move from a distancesay, near to the Earth's surface to a distancewe need to put in an amount of energy per unit mass for the object being moved of

since

the acceleration due due gravity is given by the force of gravity on a 1 Kg mass at the Earth's surface.

The increase in Gravitational Potential is thenand the increase in gravitational potential energy for a massis