Johannes Kepler

Johannes Kepler (Weil der Stadt 1571 - Regensburg 1630) was an astronomer whose name lives on in his three laws on the motion of the planets orbiting the sun. Kepler was a genuine Copernican, in contrast to most of his contemporaries, who still adhered to the geocentric system of Ptolemy.

Career

After the death of Tycho Brahe in 1601 Kepler became the Mathematicus Imperialis at the court of emperor Rudolph II in Prague. He stayed at the court until the abdication of Rudolph in 1612. During this period he wrote Astronomia Nova after an analysis of Tycho's detailed observations of the Martian orbit. It took Kepler eight years to discover that an elliptic orbit was needed to fit these data. In 1612 Kepler accepted a position in Linz (Austria).

Kepler lived and worked amid the great religious wars raging all over Europe. Kepler was Lutheran and had to flee several times during his lifetime from the Catholics. Belief in witchcraft was still widespread among both Catholics and Protestants. Between 1615 and 1621 it took Kepler much time, money, and use of his influence as Imperial Mathematician to get his mother absolved of the accusation of being a witch.

Theories

Johannes Kepler is sometimes described as a somewhat uddleheaded mystic. Usually, one then refers to the planetary theory that Kepler proposed at the age of twenty-four. He then put forward that the six planets: Mercury, Venus, Earth, Mars, Jupiter, and Saturn (the only ones then known) move on surfaces of spheres that envelop the five regular polyhedrons. By imposing the order, octahedron, icosahedron, dodecahedron, tetrahedron, cube, Kepler found that the planets moving on the respective spheres, had the correct relative distances to the Sun. He was able to develop this theory as these Platonic solids can be inscribed and circumscribed by spheres. For a while Kepler was very enthusiastic about his idea, because he believed that he had found the symmetries that had guided the creation. However, when he discovered that his theory was only qualitatively correct, but not quantitatively, he dropped it.

Three laws

Kepler's first law states that the planetary orbits are ellipses not circles. He surmounted here a great psychological barrier that, for instance, Copernicus had not been able to overcome. Since the days of Aristotle it was thought that the planetary motion was perfect, that is on circles or on spheres. Kepler's second law is known as the law of equal areas: A line joining a planet and the sun sweeps out equal areas during equal intervals of time. The first and second law were published in Kepler's book Astronomia Nova (1609).

Kepler's third law (published in the book Harmonice Mundi 1619) states that the squares of the orbital periods T of all planets are directly proportional to the cubes of the semi-major axis a of the orbits, $\scriptstyle T^{2}=a^{3}~$ (when the right units for a and T are chosen). Kepler himself pointed out the example of Saturn which is nine times further removed from the sun than the earth, and hence a Saturn year takes 27 earth years. (Kepler's third law is a first approximation, in reality the Saturn year takes 29.46 earth year).