Gravitational Potential
At a point in a gravitational field, potential V is defined as negative of work done per unit mass in shifting a test mass from some reference point (usually at infinity) to the given point i.e.,
[as F/m = I]
âˆ´
i.e., negative gradient of potential gives intensity of field, or potential is a scalar function of position whose space derivative gives intensity. Negative sign indicates that the direction of intensity is in the direction where the potential decreases.
âˆ´ Gravitational potential produced by a point mass
Gravitational Potential for Different Bodies
Potential due to uniform ring
At a point on its axis

At the center



Fig. 9
Potential due to spherical shell
Outside the surface
r > R

On the surface
r = R

Inside the surface
r < R




Fig. 10
â€‹Potential due to uniform solid sphere
Outside the surface r > R 
On the surface r = R 
Inside the surface r < R 


At the center (r = 0)

Fig. 11