Gravitational potential at a point can be defined as the workdone required to take a unit mass from infinity to that point.

In classical mechanics, the gravitational potential at a point in space is equal to the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point.

Thus, the gravitational potential is the work done per unit mass by some externally applied force to bring a mass from zero potential to infinity. The formula is given by;
V = -GM/r
Here V is the Gravitational potential due to gravity, M is the mass of the source and r is the distance between the source and unit mass.

1. Gravitational potential is the work per unit mass by an external force to bring a unit mass to a point from a position of zero potential or infinity
2. If the field is caused by an isolated massive point object (or any object of limited size), the potential is usually defined as zero at an infinite distance from the object; it is negative everywhere else since the gravitational force is always attractive.
3. Gravitational Potential (J/kg) is a scalar quantity with a negative value.

Gravitational Potential Energy (G.P.E) is defined as the energy stored in an object due to its height above the earth. The amount of gravitational potential energy depends on the mass and height of an object.

G.P.E = U = mgh

Example 1: What is the gravitational potential at a point on the surface of the earth if G = 6.67 × 10^-11Nm²kg^-2 and the radius and mass of the earth are respectively 6.4 × 10⁶m and 5.98 × 10²⁴kg?

Example 2: Find the gravitational potential energy of 2.5 kg mass kept at a height of 15 m above the ground. The force of gravity on mass 1 kg is 10 N.

G.P.E = U
U = mgh
where m = 2.5kg
h = 15m
But g = force/mass
:. g = 10m/s²
U = 2.5 × 10 × 15
G.P.E = 3.75 × 10²J