Gravitational Potential Energy.   

     

The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force.

This work done is stored inside the body as its gravitational potential energy

∴ U = - (GMm/r)

Note:

 (i) Potential energy is a scalar quantity.

(ii) Unit : Joule

(iii) Dimension : [ML²T^–2]

(iv) Gravitational potential energy is always negative in the gravitational field because the force is always attractive in nature.

(v) As the distance r increases, the gravitational potential energy becomes less negative i.e., it increases.

(vi) If r = ∞ then it becomes zero (maximum)

For discrete distribution of masses

Gravitational potential energy

Relation between gravitational potential energy and potential U = - (GMm/r) = m [-Gm/r]

∴                                  U = mV