1. Planetary Orbits The ancient Greeks (Aristotle and Plato) thought the only perfect shapes were the circle and line. All things fall in a line toward Earth, except things in Heaven (the stars and planets) which must move in a circle, with Earth at the center, in order to be “perfect”.

2. By the 3 rd Century B.C., astronomers could not explain the actual movement in the sky of the planets, if they moved in circles around the Earth. So they came up with a system of “epicycles”, planets moving around circles on circles, which sort of explained the motion.

3. As centuries passed, and instruments became more accurate, astronomers had more and more problems predicting exactly where the planets should be, and they added more and more epicycles.

4. One of the most obvious problems was Mars. Venus, Mercury and the Moon move in one direction across the sky. If you see it one night, the next night it will have moved a little bit over, the next a little more, and so on, all in the same direction. Mars will do that, but sometimes stops and goes backwards (retrograde motion), and then changes again.

5. In the early 1600s, German mathematician Johannes Kepler solved the problem with his Three Laws of Planetary Motion. Law 1: The orbit of the planets are ellipses with the Sun at one focus.

6. Eccentricity describes how circular or elliptical an orbit is. It is defined as “d ”, the distance between the foci, divided by “l ”, the length of the major axis (the widest part of the ellipse). foci d major axis

7. Law Two: A line from a planet to the Sun sweeps over equal areas in equal intervals of time.

8. Law Three: A planet’s orbital period squared (years) is proportional to its average distance to the Sun (AU) cubed. P y 2 = a AU 3