Kepler's Three Laws

1. The planets move in elliptical orbits. The sun sits at one of the foci.

   

2. The radius vector, measured from the sun to the planet has a very neat property. The area swept out by the radius vector, covers equal areas in equal times.

   

3. The period $T$ of orbit is simple related to $R ~=~ (r_{min}+r_{max})/2$. ($R$ is half of the major axis of the ellipse). It is that $T^2$ is proportional to $R^3$.

These laws seemed to describe the motion of the planets very accurately but since Newton hadn't given us classical mechanics, people were at a loss to come up with a reasonable explanation. In fact, Newton's three laws are not enough to explain Kepler's. You still have to figure out what the force is between the sun and a planet.

Newton was a mighty smart fellow and once a form of this gravitational force was proposed, he could easily whip through pages of his newly invented calculus to figure out if it was consistent with Kepler's laws. It is debatable whether he actually came up with the correct form. Some say it was Robert Hooke, who has been largely overlooked by historians because of poor political skills, and just plain bad luck. But whatever the truth, the gravitational force has become known as Newton's law of gravity, or Newton's inverse square law, or Newton this, or Newton that. Next you might be wondering who really invented those cookies with figs inside of them.