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

(N/A) The work done in bringing a body of mass $m$ from an infinite distance in the gravitational field of the Earth to a point at a distance $r$ $(r > R_{E})$ from the center of the Earth is given by the gravitational potential energy $U = -\frac{GM_{E}m}{r}$.
Gravitational potential $V$ at a point is defined as the work done per unit mass to bring a body from infinity to that point:
$V = \frac{W}{m} = \frac{U}{m}$
Substituting the expression for $U$:
$V = \frac{-GM_{E}m/r}{m} = -\frac{GM_{E}}{r}$
On the surface of the Earth,where $r = R_{E}$,the gravitational potential is:
$V_{E} = -\frac{GM_{E}}{R_{E}}$
Relation between gravitational potential and gravitational potential energy:
Since $U = -\frac{GM_{E}m}{r}$ and $V = -\frac{GM_{E}}{r}$,we can write:
$U = V \cdot m$
Therefore,Gravitational potential energy = (Gravitational potential) $\times$ (mass).