# Gravitational Fields

## Definition

A gravitational field, similar to an electric field or a magnetic field, is a region where masses experience a gravitational force. Just as with electric and magnetic fields, we can draw gravitational field diagrams with gravitational field lines which indicate the path a test mass would take.

## Gravitational Field Strength

Gravitational field strength is the gravitational force acting on an object per unit of mass. It is analogous to electric field strength for electric fields.

The gravitational field strength can be calculated at a point, if the mass and force acting on a test mass at that point is known:

Formula

$g=\frac{F}{m}$

Variable Key

• $g$ is the gravitational field strength, in newtons per kilogram.
• $F$ is the #Gravitational Force acting on the object, in newtons.
• $m$ is the mass of the object being acted on, in kilograms.

## Gravitational Force

Gravitational force is simply the proper name for weight, but is a more universally applicable term - especially when considering interplanetary scales. We can calculate the gravitational force between two masses using Newton's law of universal gravitation, an inverse-square law which suggests that as the distance between two masses doubles, the force between them is four times weaker.

The equivalent for an electric field is Coulomb's Law, which is used to calculate the electrostatic force between two charges.

Formula

$F=\frac{GMm}{{r}^{2}}$

Variable Key

• $F$ is the gravitational force between the masses, in newtons.
• $G$ is the gravitational constant, approximately .
• $M$ and $m$ are the masses of the two objects, in kilograms.
• $r$ is the distance between the masses, in metres.

## Gravitational Potential

Gravitational potential at a point in a gravitational field is a scalar which represents gravitational potential energy (the gravitational counterpart to electric potential energy) per unit of mass. The formal definition of gravitational potential at a point is the energy required to move a 1 kilogram test mass to that point from an infinitely far location, where the gravitational field strength would be zero. For this reason, gravitational potential is always negative - moving a mass in the same direction as it is being pulled by gravitational force is equivalent to negative work done.

Gravitational potential is the gravitational counterpart to electric potential, and both use the symbol $V$.

Formula

$V=\frac{GW}{m}$

Variable Key

• $V$ is the gravitational potential at a point, in joules per kilogram.
• $G$ is the gravitational constant, approximately .
• $W$ is the work done bringing a test mass from infinity, in joules.
• $m$ is the mass of the object brought to the point, in kilograms.