Mercury's orbit nicely illustrates all three of Kepler's laws.

Mercury's orbit is a good example of Law I. As you can see, the orbit is not a circle, and the Sun, indicated by the black dot, is offset to one side. The other focus of the ellipse, indicated by the `+' sign, is empty. |

The shaded triangles shown at right represent the areas swept out in a time equal to 4% of Mercury's orbital period (about 3.5 days). These two triangles must have equal areas; as a result, Mercury moves about 50% faster at perihelion (closest to the Sun) than at aphelion (furthest from the Sun). |

**Law III.** The relationship between a planet's orbital period
*P* and the semimajor axis of its orbit *a* is

Given that Mercury's orbit has a semimajor axis *a* = 0.3871
AU, its orbital period *P* can be calculated:

Joshua E. Barnes (barnes@ifa.hawaii.edu) Last modified: September 30, 1999