Shannonside Astronomy Club

[Simon Kenny]

Great astronomers: Johannes Kepler (Article174)

Johannes Kepler was a seventeenth century mathematician who laid the theoretical foundations for planetary motion.

When Kepler was born near Stuttgart in 1571, the Earth was still considered the centre of the universe. Copernicus’s theory that the Sun occupied its centre was a novel, even shocking idea to conservative minds. Kepler supported the Copernican theory and for this and his Calvinist faith, he often had an insecure and wandering existence in a strife-torn Europe after the Reformation.

Kepler’s mathematical brilliance was noticed by Tycho Brahe, the greatest observational astronomer of his day. In one of the most productive collaborations in history, Kepler worked for Tycho from 1600 until Tycho’s death a year later. Tycho was famously quarrelsome, as evidenced from a damaged nose from a duel in his student days, and difficult to work with. Tycho seemed envious of his talented assistant and jealously kept his astronomical observations to himself. However, Tycho gradually released some of his observations, which were crucially important to Kepler in developing his laws of planetary motion.

Following Tycho’s death in 1601, Kepler took his observation log books, an action that caused a lengthy legal conflict with the heirs to Tycho’s estate. Finally, Kepler was permitted to study them and use Tycho’s observations to develop and test his theories of planetary motion. Kepler’s laws were built on these and on Copernicus’s Sun-centred model of the Solar System, but with one radical difference. Copernicus, like all before him, assumed that planets moved in perfectly circular orbits. Tycho’s observations confirmed Kepler’s suspicion that all planets had elliptical orbits. Unlike circles, ellipses have two ‘centres’ or foci. The motion of Mars in the sky, for example, could be accurately explained if Mars followed an elliptical path around the Sun, with the Sun positioned at one of the ‘centres’ or foci of the ellipse. From this he derived his first law of planetary motion:
· The orbit of every planet is an ellipse, with the Sun at one of its foci.

In his second law, Kepler rejected the old belief that planets travel at a constant velocity. He found that in its elliptical path, a planet travels faster as it gets closer to the Sun and slows down as the distance between them increases. He states this observation in his second law of planetary motion as follows:
· A line joining the planet and the Sun traces out equal areas during equal intervals of time as the planet travels along its orbit.

His third law states that the further a planet is from the Sun, the longer it takes to make a full orbit and the slower it moves in its orbit. It is stated (rather abstractly!) as follows:
· The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axes.

Like Tycho, Kepler too has a crater named after him west of centre of the full Moon.