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

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

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.