Kepler's third law

Statement of Kepler's third law, or the law of orbital periods: The square of the period of revolution is proportional to the cube of the distance from the Sun.

From Kepler's third law, the distance of a body from the Sun can be calculated if we know its period of revolution. The period is relatively easy to measure, unlike the distance.

By linking to classical mechanics Newton deduced the following formula:

Which approximates to

when

which makes it possible to find the constant of proportionality in Kepler's third law. The various parameters are:

• T the period of the body
• a semi-major axis of the elliptical trajectory;
• G the universal gravitational constant;
• M the mass of the body at the centre;
• m the mass of the body in orbit.

It applies to all binary systems, except for systems in the domain of quantum physics {electron, nucleus} for example.