Derive an expression for the gravitational potential energy of a body . Give the difference between gravitational potential and gravitational potential energy.

Explanation

Gravitational potential at a point is the amount of work to transfer unit mass of a body form infinity to that point in a gravitational field.
`int_(0)^(v)dV=int_(oo)^(r)(GM)/(x^(2))dx`
i.e., `V=GM[1/oo-1/r]`
i.e., `V=(-GM)/(r)`
Gravitational P.e at a point is defined as the energy acquired by the mass body placed at that point in a gravitational field.
i.e., `U=(-GMm)/(r)`
where M = mass of the Earth , m = mass of a body above the surface of the Earth , r = R + h where r = radius of the Earth , h = height of the mass body above the surface of the Earth.