Kepler's laws

Newton discovered his law of gravity around 1665. This gave finally an explanation of the motion of planets around the sun. Before Newton several quantitative descriptive models were given. First there was the Greek geocentric model using epicycles, a very complicated model, but highly successful in predicting the positions of planets for over 2000 years. Copernicus gave a heliocentric model, still insisting that planets move on circles. The most concise of these descriptive models was given around 1600 by Johannes Kepler. Precise observations by Tycho Brahe in the second half of the 16th century dispelled the myth of circular motion. Based on these observations Kepler spelled out the following laws:

1. Planets move around the sun in elliptic orbits with the sun located at one focus of the ellipse.
2. As the planet moves in its orbit around the sun, equal areas as measured from the focus are swept out in equal times.
3. The square of the period of the orbit is proportional to the cube of the semimajor axis of the ellipse.

We will prove these laws from Newton's laws later in the course. Kepler's laws are purely descriptive and make no attempt to explain the motion. For this reason they are a more practical tool to study the motions of bodies in a gravitational field. Kepler's laws still allow for circular motions, however, they are not restricted to these motions. Nevertheless, most of the planets, the moon and many artificial satellites actually travel along nearly circular orbits.