# Kepler's Laws

In the latter part of the sixteenth century Tycho Brahe was the astronomer royal to the King of Denmark. He worked at the observatory on the island of Uraniborg making twenty years of observations of the positions of the planets. He used giant protractors and sighting devices because the telescope had only just been invented and was not used for astronomy until years after his death.

He had a very bright pupil, Johannes Kepler who, in about 1610, suggested the first real laws describing the way in which the planets moved around the Sun.

(Kepler image courtesy of: Sternwarte Kremsmuenster Upper-Austria)

Kepler proposed three laws.

1. The planets move in ellipses with the Sun at one focus – this means that the distance between a planet and the Sun changes during the year. For example the Earth is about five million km closer to Sun at its nearest point than it is at its furthest point. This may seem a lot but remember that the average distance of the Earth from the Sun is about 150 million km.

You can prove this by measuring the diameter of a projected image of the Sun at different times of the year.
(NB although the Earth does move in an elliptical orbit this orbit is every nearly circular. The only planet with a very elliptical orbit is Pluto.)

2. A line drawn from the planet to the Sun sweeps out equal areas in equal times
This means that planets (and other objects) move faster when they are closer to the Sun and slower when they are further away. The best examples of this are the long period comets. They spend only a few months close to the Sun before moving off into deep space – not returning for maybe many hundreds of years.

3. The ratio of the square of the period (T) of the planet about the Sun to the cube of the mean orbit radius (r) is a constant.

This means that if you work out the square of the period of one planet (the time it takes to go once round the Sun) and divide that number by the cube of its distance from the Sun the result that you get will be the sane for all the other planets.

Remember that Kepler only suggested HOW the planets moved and not WHY! It was left for Newton and his law of gravitation to do this.

### schoolphysics: Kepler's laws animation

To see an animation of Kepler's second law click on the animation link.

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB