# Kepler's Laws of Planetary Motion

## Physical Laws

**Kepler's laws of planetary motion** are a set of three physical laws that describe the motion of planets in the solar system.

### First Law

### Second Law

### Third Law

- The square of the period of the orbit of a planet around the sun is proportional to the cube of its average distance from the sun.

## Source of Name

This entry was named for Johannes Kepler.

## Historical Note

Kepler derived his three laws of planetary motion in the early $1600$s from a concentrated study over the course of $20$ years of the colossal wealth of observational data which had been made previously by Tycho Brahe of the behavior of the planets of the solar system, and in particular Mars.

The first two of these results he published in his gigantic $1609$ work *Astronomia Nova*.

The third appears some ten years later in his *Harmonices Mundi* of $1619$.

It was Isaac Newton who managed to interpret these three laws and so work out what is now known as Newton's Law of Universal Gravitation, from which Kepler's laws can straightforwardly be derived.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.25$: Kepler's Laws and Newton's Law of Gravitation - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Kepler's laws** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Kepler's laws** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World: Kepler - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Kepler's laws of planetary motion**