Kepler’s 3rd Law of Planetary Motion

Kepler’s 3rd law states:

Since the right hand side equates to a constant for a given central mass, it implies that the square of the period of orbit, T, of any object orbiting the central mass is proportional to the cube of its orbital radius, R.

Derivation of Kepler’s 3rd law

Kepler’s 3rd law can be easily derived if you consider the gravitational force exerted on a planet by the central mass to be equal to the centripetal force which causes the planet to orbit the central mass.