What is meant by gravitational potential ? Extablish the formula for the same.

Explanation

Gravitational potential : The work done in bringing a unit mass from infinity to a point in the gravitational field is called the .gravitational potential. at that point.
`V=(W)/(m)" J/kg"`
Derivation : Suppose a point mass M is situated at a point O. Let A be a point in the gravitational field of mass M, distance r from O, at which gravitational potential is to be determined. For this let a unit mass be placed at the point A. Then the gravitational force acting on it due to M is given by :

Now suppose the unit mass moves against this force from A to B through a small distance dr then work done
`"dW = F.dr"=("GM")/(r^(2))"dr"`
the work done in taking the unit mass from A to infinity
`W=int_(r)^(oo)("GM")/(r)dr=GM[-(1)/(r)]_(r)^(oo)=(GM)/(r)`
Hence the work done when the unit mass moves from infinity to A will be `-(GM)/(r)`
`V=-(GM)/(r)`