Kepler describes the orbits

The story

The perfect circle

Since ancient times astronomers had a fixed idea: the sky is perfect, and perfect things move along the most perfect shape, the circle. This is why Ptolemy, and Copernicus too, had imagined that the planets moved in circles, or in circles on top of other circles. The system worked only in part, and to make it match the observations it always needed new corrections.

Johannes Kepler was born in 1571 in Weil der Stadt, in Germany, into a modest family. He was a frail, sickly child, but very good at school, and he reached university thanks to a scholarship. He had a passion for mathematics and astronomy, and when he came across Copernicus's idea, that it is the Earth that goes around the Sun, he was struck by it.

Tycho and Mars

In 1600 Kepler moved to Prague, the capital of Emperor Rudolf II, to work with the Danish astronomer Tycho Brahe. Tycho was an exceptional observer: for decades he had measured the positions of the planets with a precision never reached before, with the naked eye, using large instruments he had designed himself. He did not trust Copernicus's system, but his data was a treasure. Tycho died in 1601, and Kepler inherited his tables and his post as imperial mathematician.

Kepler was given the hardest problem: the orbit of Mars, the planet that would not fit into circles. For years he tried different combinations of circles, with enormous calculations by hand. In the end he found one that agreed with the observations almost perfectly, but it was wrong by eight arcminutes, a tiny fraction, about a quarter of the width of the full Moon. Another astronomer would have let it go. Kepler reasoned that Tycho could not have been wrong by so much, and that it was the model that was wrong.

The ellipse

For a time Kepler was almost in despair: he wrote that he felt he had been “waging a war against Mars”. After very many attempts, he discovered that the orbit of Mars is not a circle but an ellipse, that is, a sort of squashed circle, and that the Sun is not at the centre, but at one of the two special points called foci. This is Kepler's first law. The second law says that a planet moves faster when it is closer to the Sun and slower when it is farther away, so that the line joining it to the Sun sweeps out equal areas in equal times.

Kepler published these two laws in 1609 in the “Astronomia nova”, that is, “New Astronomy”, a long book full of calculations, in which he also tells of his mistakes and false trails. Ten years later, in the “Harmony of the World”, he added the third law: the farther planets take longer to make one circuit, and there is a precise mathematical rule linking time and distance.

A hard life

Kepler's life was not easy. He always worked for emperors who paid him little or late; he lost his first wife and some of his children; and he was caught up in the wars of religion, because he was a Lutheran in a mostly Catholic country. His mother, Katharina, was accused of witchcraft in a trial that lasted years, and Kepler had to put aside his studies to defend her: in the end she was acquitted, in 1621. He also wrote a work of fantasy, the “Somnium”, in which a man travels to the Moon.

In 1627 he published the “Rudolphine Tables”, the most accurate planetary tables ever made, which used his laws. He died in Regensburg in 1630, during a journey to recover unpaid wages.