Gravitational field

Intermediate

Force per unit mass at a point.

Key relationE = F/m = −GM/r²

The gravitational field g(r) = F/m is the force per unit mass at a point, directed toward the source. For a point mass |g| = GM/r².

Worked example

The field at the Moon's surface due to the Moon is 1.6 N/kg.

Common mistake

Field is a vector; add vectorially.

In more detail

A gravitational field describes the force per unit mass at each point in space. For a point mass, it is g = GM/r², pointing towards the mass.

Spacecraft trajectories are planned using gravitational fields of planets.
Geophysicists map Earth's gravitational field to find dense rock deposits.
Space mission planners map the gravitational field around a planet to see where a spacecraft will be pulled and how strongly.

What are the units of gravitational field?

Newtons per kilogram, which is also metres per second squared.

Does the field have direction?

Yes. It points towards the source mass.

Is the field the same as the force?

The field is the force per unit mass, so the force on any object is its mass times the field strength at that point.