# Gravitational field strength – formula, definition, & derivation

Last updated on December 2nd, 2022 at 05:08 pm

A gravitational field is a region where you find gravity. More precisely, the gravitational field is defined as a region of space where a mass experiences a force because of its mass. In this post, we will find out more about the Gravitational field strength with its definition, derivation, and formula.

## What is the gravitational field strength? | define gravitational field strength

Gravitational field strength gives a measure of how much force a body will experience in the gravitational field. It is defined as the gravitational force per unit mass experienced by a small test mass placed in the gravitational field.

So if a test mass, m, experiences a force F at some point in space, then the field strength, g, at that point is given by g = F/m

Unit: The unit of Gravitational field strength g is N/kg, and it is a vector quantity. See how to get the Dimensional formula of gravitational field strength.

## Gravitational field strength formula derivation | Derivation of Gravitational field strength formula

Let’s consider the Gravitational field around a spherical object of mass M.

The gravitational force experienced by the mass, m is given by F = G Mm/r^2

So the field strength at this point in space, g = Gravitational force per unit mass =F/m
So, g = G M/r^2. This is the formula of Gravitational field strength.

## Write down the formula of Gravitational field strength

The gravitational field strength at a point in a gravitational field = g = G M/r^2
G = Universal Gravitational constant
M is the mass that is the source of the gravitational field
r is the distance of the test point from the source mass

Suggested readingcalculate the value of the Gravitational field strength.