# 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/s2.

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

Following is the formula of gravitational potential energy:

 $U=\frac{-GMm}{r}$

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

 U=m g h

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).

Following is the table explaining concepts related to gravity:

### Solved Examples

Example 1. 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,

Potential energy is given as
U = m g h

= 10 Kg × 9.8 m/s2 × 25 m = 2450 J

Example 2. If the mass of the earth is 5.98 ×1024 Kgs and the mass of the sun is 1.99 × 1030 Kgs and earth is 160 million Kms away from the sun.Calculate the gravitational Potential energy of the earth.

Solution:
Given:
Mass of earth m = 5.98 × 1024 Kgs,

Mass of sun M = 1.99 × 1030 Kgs

The Gravitational potential energy is given by:
$U=\frac{-GMm}{r}$

$U=\frac{6.673*10^{-11}*5.98*10^{24}*1.99*10^{30}}{160*10^{9}}$ = 8.29 x 108 J