Introduction to Gravitational Fields

Introduction

Gravitational fields are regions in space where bodies with mass will experience a force caused by gravity.

Newton's Law of Gravitation

Newton’s law describes the forces of bodies with mass, when they’re placed within a gravitational field.

  • “For two masses placed a distance apart, the gravitational force of attraction of
    one mass on the other is directly proportional to the product of the two masses
    and inversely proportional to the square of the distance between them.”

This states that $F \propto \frac{m_1 m_2}{r^2}$, where $F$ is the force, $m_1$ and $m_2$ are the masses of the two bodies, and $r$ is the distance between them.

Therefore, this can be seen as an equation, $F=\frac{Gm_1 m_2}{r^2}$, where $G=6.67 \times 10^{-11}Nm^2 kg^{-2}$ is the gravitational constant.

Gravitational Fields

Gravitational fields come in two different forms: radial and uniform.

A radial field is one where all forces are acting towards a single point. Here the magnitude of the force falls rapidly as distance increases.

A uniform field comes from a flat surface and is used to approximate gravity on the surface of a large source such as the Earth. Here the magnitude of the force is equal across the entire field.

radial field
Radial gravitational field
uniform gravitational field
Uniform gravitational field

Gravitational Field Strength

Gravitational field strength, $g$, is defined as the force per unit mass experienced by a body when it is placed within a gravitational field. Therefore $g=\frac{F}{m}$, and thus it has units of Newtons per kilogram, $Nkg^{-1}$.

Because $F=ma$, it follows that gravitational field strength can also be thought of as the acceleration due to gravity. Hence the units of metres per second squared, $ms^{-2}$, can also be used.

Commonly, there is one small body near a body with a much greater mass; thus set $m_1=m$ the small mass and $m_2=M$ the larger mass. Therefore, the gravitational field strength (experienced by the small mass) is $g=\frac{GMm}{mr^2}$ and hence $g=\frac{GM}{r^2}$.