Kepler's Third Law, the Law of Periods.

Definition

The square of the period of any planet about the Sun is proportional to the cube of the planet’s mean distance from the Sun.

Let’s first prove this for circular orbits. Relating Newton’s Law of Gravitation to Centripetal Force:

Replace for where is the rotational period.

When we do the same for elliptical orbits, is replaced with the semimajor axis .

Note that is a constant, proving Kepler’s Third Law. We can also say that the ratio is a constant for every planet orbiting the sun.