The gravitational potential (V) is the gravitational potential energy (U) per unit mass: where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
Gravitational Potential due to a point mass
Gravitational Potential due to a point mass is given by:
Field due to different arrangements of shells
Example: Two concentric shells of masses M1 and M2 are having radii r1 and r2. Find the expression of gravitational field in different regions of shells.
Solution: A uniform shell has no contribution to the gravitational field inside it from Gauss Law for Gravitation. Using this principle, gravitational field would be 0 for r<r1 gravitational field would be r2GM2 for r1<r<r2 gravitational field would be r2G(M1+M2) for r>r2
Calculation of Potential Energy
For an object having mass m having its center of gravity at height h and g be the acceleration due to gravity. P.E.=mgh