## Gravitational field

Glossary Definition for 16-19

#### Description

A gravitational field exists in any region where a particle is subject to a force that depends only on the particle’s mass and position.

The gravitational field at a point is a vector quantity usually represented by the symbol ** g**.

The gravitational field at a point is defined as the force per unit mass that would act on a particle located at that point.

If a test mass *m* is subject to a force ** F** at some point, and

**depends only on the particle’s mass and position, then the gravitational field at that point is defined as**

*F***=**

*g*

*F**m*

#### Discussion

Gravitational field is sometimes referred to as gravitational field strength; this glossary avoids that term because it might be confused with the magnitude of the gravitational field.

The force in the description is known as a gravitational force and is often called weight, but the latter term is to be avoided as it is ambiguous.

Historically, *g* was sometimes referred to as the acceleration due to gravity

as it is numerically equal to the acceleration experienced by a free-falling object in a gravitational field.

#### SI unit

newton per kilogram, N kg^{-1}

#### Expressed in SI base units

m s^{-2}

#### Other commonly unsed unit(s)

gal ( 1 gal = 0.01 N kg^{-1})

#### Mathematical expressions

- if a mass
*m*experiences a gravitational force, then the gravitational field at that point is*F*

=*g**F**m* - The magnitude of the gravitational field
*g*on the Earth's surface is related to the universal gravitational constant*G*

*g*=

*G*

*M*

*R*_{E}^{ 2}

where

*M*is the Earth's mass and

*R*

_{E}its radius.

#### Related entries

- Electrostatic field
- Gravitational potential
- Weight

#### In context

The magnitude of the gravitational field at the surface of the earth is around 9.8 N kg^{-1}.

The value of *g* varies from place to place on the Earth’s surface. One reason for this is that *g* depends on distance from the Earth’s centre, and Earth is not a perfect sphere – Earth’s radius is smaller at the poles than at the equator. Also, the Earth’s density is not uniform so Earth’s mass is not equally distributed.

Gravimetry, involving measurements of surface gravitational field, can provide information about the nature of the materials in the Earth’s interior, e.g. oil deposits. Variations in Gravimetry, involving measurements of surface gravitational field, can provide information about the nature of the materials in the Earth’s interior, e.g. oil deposits. Variations in *g* of the order of ~ 10^{-8} N kg^{-1} can be detected using sensitive instruments.

The acceleration of free fall on Earth, as measured for example in a simple pendulum experiment or by timing a falling object, is affected by the Earth’s rotation as well as by the local gravitational field. The effects of rotation are greatest at low latitudes (close to the equator), but even at the equator rotational effects reduce the acceleration of free fall by only about 3 × 10^{-2} m s^{-1} so such effects can often be ignored