# Gravitation – Potential and Potential Energy

## Gravitational Potential and Potential Energy

Gravitational potential at a point is the amount of work needed to bring a unit mass from infinity to that point.

Gravitational potential is defined to be negative since gravity is attractive in nature. A negative potential means that no external work is needed to bring a unit mass from infinity to that point, since the gravity-producing mass would be doing the work to pull the unit mass to that point.

Mathematically,

Note that potential is a scalar quantity. Hence, the potential at a point is simply the algebraic sum of the potential of the different masses at that point.

Similarly, gravitational potential energy is defined as

Gravitational potential energy of a mass at a point is the amount of work needed to bring the mass from infinity to that point.

You may find this concept similar to gravitational force and field strength. Both gravitational force and potential energy invloves the product of two masses while field strength and potential involves just the gravity-producing mass .

## Gravitational Potential vs Field Strength

It is easy to compare the relative values of potential and field strength because of the similar form of equations.

## GPE = mgh

In many junior Physics text, gravitational potential energy is quoted with the formula

This formula assumes that the change in height in insignificant compare to the radius of the Earth. This formula also calculates the change in the potential energy due to a change in position.

The formula calculates the actual amount of potential energy a mass possess due to its position. This formula does not calculate the change in potential energy. To calculate the change in potential energy,

If ,

From this, we have our old formula

### Summary

- Gravitational potential at a point is the amount of work needed to bring a unit mass from infinity to that point.
- Gravitational potential energy of a mass at a point is the amount of work needed to bring the mass from infinity to that point.
- The gravitational potential has a larger magnitude than the field strength.
- When the change in height is small, we may use