An extended body can be treated as a point mass when its size and internal mass distribution have a negligible effect on the gravitational interaction. This is exact for the external gravitational field of a spherically symmetric body and approximate when the body's dimensions are much smaller than the relevant separation.
The Reasoning
An extended body has mass distributed through a finite volume. The point-mass model simplifies it by concentrating its entire mass at one point, normally its centre of mass.
In IB Physics D.1 Gravitational fields, this allows Newton's universal law of gravitation to be applied:
Here, is the distance between the bodies' centres of mass, not between their surfaces.
| Situation | Is the point-mass model valid? |
|---|---|
| Spherically symmetric body; field point outside it | Yes. Its external field equals that of its mass concentrated at its centre. |
| Body much smaller than the separation | Yes, approximately. Distance variations across the body are negligible. |
| Irregular body close to the other body | Usually not. Shape and mass distribution affect the field significantly. |
| Bodies overlap, or the field point is inside an extended body | The simple external point-mass model is generally invalid. |
| Rotation, torque, or deformation matters | No. A point mass has no size, orientation, or rotational structure. |
For example, Earth can be modelled as a point mass when calculating the gravitational force on a satellite because Earth is approximately spherically symmetric and the satellite is outside it. Use , where is the satellite's altitude.
A common misconception is that every extended body can always be replaced by a point mass at its centre. This is false: spherical symmetry or a separation much larger than the body's dimensions is required.
Exam Technique
This is SL and HL content under D.1.3. In an Explain response, state the relevant condition, identify the centre-to-centre distance, and link the approximation to spherical symmetry or negligible dimensions relative to separation.
