`implies` Gravitational potential energy :
"The work done in bringing a body of unit mass from infinite distance to the given point in gravitational field of other body is called the gravitational potential energy at that point".
`implies` Suppose, the mass of earth is Mp and radius RE: We have to determine the gravitational potential energy of mass m at point P from distancer from the centre of earth.
`implies` Suppose, at any instant body of mass m lying at point A at a distance x from the centre of earth OP = x
`implies` The gravitational force on the body at this point,
`F = (GM_(E) m)/x^2 " "...(1)`
`implies` The work done to move the body to small displacement from the centre of earth dW = Fdx
`:.dW = (GM_Em)/x^2dx" "...(2)`
`implies` Total work done to bring the body from infinite (D) distance to x distance
`implies W = intdW=int_(oo)^(r)(GM_Em)/x^2dx`
`implies W=GM_(E)"m"int_(oo)^(r) x^(-2) dx`
`implies W = GM_Em[-1/x]_(oo)^(r)`
`implies W=(GM_Em)[-1/r+1/oo]`
`:. W=-(GM_Em)/r" "...(3)`
`implies ` According to definition this work done is known as gravitational potential energy of a body of mass m at point P,
`U =-(GM_Em)/r" "...(4)`
If a body bring to at the surface of earth r = Re,
`U = - (GM_Em)/(R_E) " "....(5)`
