Kepler's Three Laws of Planetary Motion

In the 16th century, the Polish astronomer Nicolaus Copernicus replaced the traditional Earth-centered view of planetary motion with one in which the Sun is at the center and the planets move around it in circles. Although the Copernican model came quite close to correctly predicting planetary motion, discrepancies existed. This became particularly evident in the case of the planet Mars, whose orbit was very accurately measured by the Danish astronomer Tycho Brahe.

The problem was solved by the German mathematician Johannes Kepler, who found that planetary orbits are not circles, but ellipses. Kepler described planetary motion according to three laws. Each of these laws is illustrated by an applet.

Law I: Each planet revolves around the Sun in an elliptical path, with the Sun occupying one of the foci of the ellipse.

Law II: The straight line joining the Sun and a planet sweeps out equal areas in equal intervals of time.

Law III: The squares of the planets' orbital periods are proportional to the cubes of the semimajor axes of their orbits.

Kepler's laws apply not just to planets orbiting the Sun, but to all cases in which one celestial body orbits another under the influence of gravitation -- moons orbiting planets, artificial satellites orbiting the Earth and other solar system bodies, and stars orbiting each other.