D.1.3—Point-mass approximation

Core idea

The point-mass model replaces an extended body by a single mass at a representative point, usually its centre of mass. It is suitable when the body’s size is negligible compared with the separation involved, or when the body is spherically symmetric and the point of interest is outside it.

Use spherical symmetry

A satellite orbiting a spherical planet of uniform density can be modelled as if the planet’s entire mass were concentrated at its centre. The gravitational force then depends on the centre-to-centre distance. The same approximation can be used for two spherically symmetric bodies when their separation is measured between centres.

Check the limit

The approximation is not automatically valid for nearby irregular bodies, for points inside an extended body, or when the object’s size is comparable with the separation. In those cases different parts of the mass are at significantly different distances and their contributions cannot be represented by one point without further justification.

Common trap

Do not justify the model only by saying that the planet is “large”. The relevant reasons are small satellite-to-planet size ratio and/or spherical symmetry with an external point of interest.