# Kepler's Laws of Planetary Motion

History of the Laws:

Johannes Kepler was a German astronomer and mathematician of the late sixteenth and early seventeenth centuries. His work was largely based on the work of his mentor, Tycho Brahe. Kepler was able to use Bahe's precise measurements (made before telescopes) to determine, mostly by trial and error, three laws that described the motion of the five planets then known.

First Law: Kepler's Elliptical Orbit Law:

Each planet moves in an elliptical orbit, with the sun at one focus of the ellipse.

Second Law: Kepler's Equal-Area Law:

A line from the sun to each planet sweeps out equal areas in equal time.

The picture to the right depicts this law.

Third Law: Kepler's Law of Periods:

The periods of the planets (T) are proportional to the 3/2 powers of the major axis lengths of their orbits (L).

Expressed mathematically, then, this says that:

T is proportional to L3/2
or
T2is proportional to L3

Proving Kepler's Laws:

Though they fit with observation and certainly seemed to work, he had no theoretical basis for explaining why they were true. The theoretical framework came in the form of Newton's Law of Gravity, nearly a century later. Newton's universal gravitation can be used to prove that Kepler's Laws do indeed describe the motion of planetary bodies in orbit.