Gravitational field strength (A-level only)

AQA·Physics·3.7.2.2

Gravitational field lines

Gravitational field lines are a way to represent the direction and relative strength of a gravitational field. They are drawn with arrows to show which way a mass placed in the field would be pulled.

Direction of gravitational field lines

At any point, the direction of the field line is the direction of the gravitational force on a mass placed there. The arrows point towards the attracting mass.

Around a point mass or a spherically symmetric mass, the field lines are radial: they run along straight lines towards the centre. A mass placed at any point in this field is pulled towards that centre.

Field-line spacing and strength

The spacing of the lines represents the field’s relative strength. Where lines are closer together, the gravitational field is stronger; where they are farther apart, it is weaker. Around a point mass or a spherically symmetric mass, radial lines spread farther apart with distance from the centre, showing that the field becomes weaker.

Gravitational field strength

A gravitational field exerts a force on a mass placed in it. Gravitational field strength at a point measures the force per unit mass at that point.

g=Fmg = \frac{F}{m}

Here, $$g$$ is gravitational field strength, $$F$$ is the gravitational force on the mass, and $$m$$ is the mass placed at the point. The unit of $$g$$ is $$\mathrm{N,kg^{-1}}$$.

Gravitational field strength has a direction as well as a magnitude. Its direction is the direction of the gravitational force on the mass placed at that point.

Field strength around a spherical mass

For a point mass, or at a point outside a spherically symmetric mass, the gravitational field is radial: its direction is towards the centre of the attracting mass. The magnitude of the field strength is:

g=GMr2g = \frac{GM}{r^2}

Here, $$G$$ is the gravitational constant, $$M$$ is the attracting mass, and $$r$$ is the distance from its centre to the point where the field strength is measured.

At a fixed distance, the field strength is proportional to the attracting mass: doubling $$M$$ doubles $$g$$. At a fixed attracting mass, field strength follows an inverse-square relationship with distance: doubling $$r$$ reduces $$g$$ to one quarter of its original value.