Teach Astronomy - Kepler's Laws of Planetary Motion

http://www.teachastronomy.com/ Kepler deduced three laws of planetary motion that are applied to all the objects in the solar system. The first law says that the planets move in elliptical orbits with the sun at one focus. There is nothing at the other focus of the ellipse. We characterize an ellipse in terms of the semi-major axis. When the ellipticity, or amount by which the ellipse is squashed, goes to zero the ellipse turns into a circle and the semi-major axis into the radius. The second law says that in terms of the line between the planet and the sun planets sweep out equal areas in equal times. In an elliptical orbit this means that a planet moves faster when it is closer to the sun than when it is further away. An extreme version of this would be a comet that sweeps through the inner solar system rapidly and spends the large majority of its orbit in the distant reaches of space far from the sun. The third law of planetary motion relates the semi-major axis, or mean distance of a planet from the sun, to the orbital period and states that the cube of the semi-major axis is proportional to the square of the orbital period. This mathematical relationship accurately describes all the planets in the solar system.