LAWS OF KEPLER DESCRIBE PLANETARY MOTION

by Knut Jørgen Røed Ødegaard

For hundreds of years astronomers studied the planets moving around in the sky with increasing intensity. It was not easy to describe their paths mathematically. We see the planets projected onto the sky and cannot easily see how they move in space - towards or away from us.

In 1619 Johannes Kepler (1571 - 1630) published the third and last of his laws describing planetary motions around the Sun. They are simply called the laws of kepler.

1. Alle planets have elliptic orbits with the Sun at one focal point.
2. An imaginary line connecting the Sun an a planet sweeps out equal areas in equal intervals of time as the planet revolves in its orbit.
   
3. The square of the periods of the planets are proportional to the cubes of their mean distances from the Sun.

A planet being close to the Sun in its orbit will move fast. The increased speed compensate for the short distance from the Sun, so that the area sweeped out in say one day is equal to that sweeped out in one day when the planet is far from the Sun (law 2).

Law number 3 gives their relative distances from the Sun when their orbital periods are known.

If we use the units terrestrial years and 1 Astronomical Unit (the mean distance from the Earth to the Sun), the ratio between the square of the period and the cube of the mean distance equal to one for all planets!!

This table gives an example:

	Mercury	Venus	Earth	Mars	Jupiter	Saturn
Square of period	0.058	0.378	1	3.54	140.7	867.7
Mean distance cubed	0.058	0.378	1	3.54	140.8	867.9

The value in the first line divided by the value in the second line is always 1. The small dviations are due to inaccurate observations and round off errors.

THE TRUE DISTANCE?

Keplers discovery implies that if we can measure the real distance between the Sun and one planet, for example the Earth, we will immediately know the real distances between the Sun and all the planets and therefore also the distances between the planets!

The only extra need is knowledge of the periods and they were quite well known.

During the 19th century the distances to the nearest stars were measured by triangulation. A parallax method similar to that giving us the solar distance with the aid of the transit of Venus in 1769, was used.

In 6 months time the earth move around 300 million kilometers relative to the Sun and the surrounding Universe. This base line cause the nearest stars to change their position slightly compared to distant stars.

The phenomenon is the same as we experience if we hold our arm straight and look with only the left and then with only the right eye. The hand seems to move a little compared to the background. Try it!
The base line of our eyes is only a few centimenters while the base line of the earth is 300 million kilometers.

The determination of the distance to the Sun in 1769 was necessary to find out the size of the whole universe. It was an extremely important breakthrough in the understanding and study of space, but also demonstrated how insignificant humans are when compared to the gigantic universe.

CONTACT INFORMATION - PRESS CONTACT