# Formula Kepler's Third Law (Orbital Periods, Semi-Major Axes)

## Orbital period of the 1st planet

Unit
Time it takes planet #1 to orbit a star (such as the Sun).

## Orbital period of the 2nd planet

Unit
Time a planet #2 needs to orbit the sun. So we need the data of two planets for the third Kepler law.

## Semi-major axis from 1st planet

Unit
Planets travel around the star on elliptical orbits. The corresponding ellipse has a large semi-axis. It corresponds to half of the long axis of the ellipse. The traversed elliptic orbit is different for different planets. Here $$a_1$$ is the semi-major axis of the elliptical orbit of planet #1.

## Semi-major axis from 2nd planet

Unit
Semi-major axis of another, second planet.