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 done to transfer unit mass of a body from 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= hight of the mass body above the surface of the Earth.