Calculations Using Kepler's Third Law

A convenient unit of measurement for periods is in Earth years, and a convenient unit of measurement for distances is the average separation of the Earth from the Sun, which is termed an astronomical unit and is abbreviated as AU. If these units are used in Kepler's 3rd Law, the denominators in the preceding equation are numerically equal to unity and it may be written in the simple form

This equation may then be solved for the period P of the planet, given the length of the semimajor axis,


or for the length of the semimajor axis, given the period of the planet,