‘Month of Equations’: What Does Kepler’s Third Law Really Mean?

                                              October 3: Kepler’s Third Law

3. Kepler's laws

Meaning of Equation: “Farther a planet from its orbiting star, more time it takes to complete one revolution around it” 

The equation of Kepler’s third law is easy to comprehend. The time period T is directly proportional to 1.5th power of the semi major axis of the elliptical orbit of the planet. Here the semi major axis represents the distance between the centres of the star and the planet which can be roughly replaced by the distance between the star and the planet. Now since the dependence of T on a is governed by the power of 1.5 in the exponent, as a will increase, T will increase. Hence we can deduce that farther a planet, more time will it take to complete its orbit around its parent star.

Kepler derived this law empirically, by using the data of the mean period of a planet and its distance from the Sun. Upon finding this pattern, Kepler quoted:

“I first believed I was dreaming…But it is absolutely certain and exact that the ratio which exists between the period times of any two planets is precisely the ratio of the 3/2th power of the mean distance.” translated from “Harmonies of the World” by Kepler (1619)

The graph between T^2 and a^3 will be a straight line. (Image: hyperphysics)