Mercury's orbit nicely illustrates all three of Kepler's laws.
|
Law I. Planets move in elliptical orbits with the Sun at one focus of the ellipse. 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. |
 |
|
Law II. A line between the Sun and a planet sweeps out equal areas in equal times. 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
where P is measured in years and a is measured in AU.
Given that Mercury's orbit has a semimajor axis a = 0.3871 AU, its orbital period P can be calculated:
(0.38713) =
0.05801 = 0.2408 year.