## Math in the Physical Sciences## Astronomy and Math |

## What are Kepler’s Laws of Planetary Motion? |

A great deal of mathematics went into the formulation of Kepler’s Laws of Planetary Motion. These laws were devised by German astronomer and mathematician (and Danish astronomer Tycho Brahe’s [1546-1601] assistant) Johannes Kepler (1571–1630). He presented the first and second laws in his work *Astronomia nova (New Astronomy)* in 1609; the third law was published in 1619 in *Harmonice mundi.* The three laws are as follows:

*Kepler’s first law* (or law of elliptic orbits)—Each planet moves about the Sun in an orbit that is an ellipse, with the Sun at one of the two foci of the ellipse.

*Kepler’s second law* (or the law of areas)—An imaginary straight line joining a planet to the Sun will sweep out equal areas of the ellipse in equal periods of time.

*Kepler’s third law* (or the harmonic law)—The square of the period of a planet’s revolution is directly proportionate to the cube of the semi-major axis of its orbit.