Kepler's Laws

Today we take for granted that our Earth and all other planets in our solar system move around the Sun on more or less circular orbits. But only about 500 years ago this was not the accepted view of the world. The Catholic Church claimed the Earth was the center of the universe, and all other objects in the sky revolved around the Earth. But then the telescope was invented, and more an more complete observations of the apparent motion of planets like Venus were made by people like Galileo Galilei, Tycho Brahe, and by Johannes Kepler. Galileo claimed that the Earth was moving around the Sun and was forced to recant in a show-trial. However, Kepler's careful analysis of the planetary motion found very simple and elegant equations of motion which were clearly superior to the epicycles of the geocentric model in their brilliant simplicity and clarity. This marked the turning point in the general acceptance of the heliocentric model, but much more important in the triumph of scientific reason over misguided religious doctrine.

First Law - law of orbits:
- Planets move in elliptical orbits with the Sun at one of the focal points.
Second Law - law of areas:
- A line from the Sun to a planet sweeps out equal areas in equal lengths of time (as is shown in the animation below.)
Third Law - law of periods:
- The square of the period of a planet is directly proportional to the cube of the average distance of the planet from the Sun, that is: T²/R³= constant = 4$\pi$²/(GM)
  where M is the mass of the Sun, and G is the universal gravitational constant.