# Gravitational Potential Energy Formula

**Gravitational Potential Energy Formula**

The energy possessed by an object because of its position in the gravitational field is called Gravitational potential energy. The most common application of gravitational potential energy can be applied to the objects that are over the Earth’s surface where the gravitational acceleration can be assumed to be constant at 9.8 m/s^{2}.

The zero of gravitational potential energy can be chosen at any point like zero of a coordinate system, the potential energy at a height h above the point is the amount of work required to lift the object to the desired height with no net change in kinetic energy. Since the force needed to lift is equal to its weight, it uses that gravitational potential energy which is equal to the weight times the height to which it is lifted.

The Gravitational potential energy of the object of mass m is defined as the work done in moving that object from infinity to a particular point by the effect of gravity.

Gravitational Potential Energy Formula is expressed as

Where,

U is Gravitational Potential energy,

G is gravitational constant,

M is Mass of body 1,

m is Mass of body 2,

r is the distance between two bodies.

Gravitational Potential energy formula on earth’s surface is expressed as

Where,

m is the mass of the body

g is acceleration due to gravity

h is height.

Gravitational Potential Energy is usually expressed in Joules (J).

Calculate the potential energy of a body of mass 10Kg and is 25m above the ground.

**Solution:**

Given:

Mass m = 10Kg,

Height h = 25 m,

The Potential energy is given as

U = mgh

= 10 Kg × 9.8 m/s^{2} × 25 m

= 2450 J

**Example 2**

If mass of earth is 5.98 ×10^{24} Kgs and mass of sun is 1.99 × 10^{30} Kgs and earth is 160 million Kms away from sun.** Calculate** the gravitational Potential energy of the earth.

**Solution:**

Given:

Mass of earth m = 5.98 × 10^{24} Kgs,

Mass of sun M = 1.99 × 10^{30} Kgs

The Gravitational potential energy is given by

U = Gm / r

= 6.673×10^{−11}×1.99×10^{30} / 160×10^{9}

= 8.29 x 10^{8} J