Obtain an expression of gravitational potential at a point in the gravitational field of earth. Give the relation between gravitational potential and gravitational potential energy.

Explanation

`implies` Work done in bringing a body of mass m from infinite distance in gravitational field of earth to a point at a distance `r (r gt R_E)` from the centre of earth.
`W=- (GM_Em)/r " "....(1)`
`implies` Gravitational potential at distance r from the centre of earth .
`V = W/ m`
`:. V = (GM_E)/R_E" "...(2)`
`implies` On the surface of earth `r = R_E`
`:. V_E =- (GM_E)/(R_E) " "...(3)`
`implies` Relation between gravitational potential and gravitational potential energy:
Gravitational potential energy at distance r from the centre of earth,
`U=-(GM_Em)/r`
`=(-(GM_E)/r)m`
`:. U = V . m " "...(4)`
Gravitational potential energy = (Gravitational potential) `xx` mass