# 7.2.1 Gravitational Field Strength

A gravitational field is a region of space where gravitational forces are exerted on masses. In other words, if a mass is situated in a gravitational field, it is going to experience a gravitational force.

The gravitational field strength g (at a point in a gravitational field) is defined as the gravitational force per unit mass (at that point). In theory, we can test the strength of the field at a particular position by placing a test mass m at that position. If the mass experiences a gravitational force Fg, then g can be calculated as

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

The direction of g is also defined by the direction of Fg.

Conversely, if a mass m is situated at a position where the gravitational field strength is g, it will experience a gravitational force of magnitude

${{F}_{g}}=mg$

in the direction of g.

Gravitational Acceleration

Since a mass experiences a gravitational force of ${{F}_{g}}=mg$, it’s acceleration due to gravity is $\displaystyle a=\frac{{{{F}_{g}}}}{m}=\frac{{mg}}{m}=g$. So gravitational field strength and gravitational acceleration are the exact same thing. In fact, N kg-1 and m s-2 are equivalent units.

Example

A 580 kg asteroid travelling in outer space experiences a gravitational force of 810 N.

a) Calculate the gravitational field strength at the asteroid position.

b) Calculate the gravitational force experienced by a 290 kg asteroid at the same location.

c) Calculate the acceleration of the asteroids.

Solution

a) $\displaystyle g=\frac{{{{F}_{g}}}}{m}=810\div 580=1.40\text{ N k}{{\text{g}}^{{-1}}}$

b) ${{F}_{g}}=mg=290\times 1.40=406\text{ N}$

c) 1.40 m s-2