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 *F _{g}*, then

*g*can be calculated as

The direction of *g* is also defined by the direction of *F*_{g}.

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

in the direction of *g*.

Gravitational Acceleration

Since a mass experiences a gravitational force of , it’s acceleration due to gravity is . 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)

b)

c) 1.40 m s^{-2}