Kepler's Third Law

Kepler's First Law

Kepler's Second Law

Statement of Kepler's Third Law

From observations collected over many centuries, and especially data compiled by the Danish astronomer Tycho Brahe, Kepler deduced a relationship between the orbital period and the radius of the orbit. Precisely:

the square of the period of an orbit is proportional to the cube of the semimajor axis length $a$.

Although Kepler never expressed the equation in this way, we can write down the constant of proportionality explicitly. In this form, Kepler's Third Law becomes the equation: \begin{equation} T^2 = \frac{4\pi^2 a^3}{GM} \end{equation} where $G$ is the Gravitational Constant that we shall encounter in Newton's Law, and $M$ is the mass about which the planet is rotating (usually the sun for our purposes). This relationship is extremely general and can be used to calculate rotational periods of binary star systems or the orbital periods of space shuttles around the earth.