Kepler’s simple, brilliant equation
and in 1593 the Roman Inquisition passed down a charge of heresy. He was burned at the stake.
When Kepler was 6 his mother, who made a living as a healer and herbalist, took him to a hilltop to observe The Great Comet of 1577. This astronomical event clearly had an effect on him and, in combination with his talent for mathematics and later his strong religious beliefs, cemented his ambition to become an astronomer and mathematician.
Kepler’s science and indeed the science of his age was one in which there was no clear distinction between astronomy and astrology – fate and the motions of the stars and planets were one and the same.
In 1615, a woman claimed that Kepler’s mother Katharina, had made her ill with one of her herbal remedies and accused her of being a witch.
Katharina was imprisoned for 14 months and released in large part due to the defence put forward by her famous son.
An insight into the 17th century legal process was given whilst she was in detention. In an attempt to unsettle her, a detailed description was read in her presence of exactly what torture she would be subjected to if found guilty.
The process was clearly routine enough for it to have a formal legal name – territio verbalis.
Kepler had a reputation for being an accomplished astrologer and was quick to dismiss the efforts of other practitioners. He was asked by Emperor Rudolph II to prepare the Rudolphine Tables, a series of tables used to establish the positions of the planets against the fixed stars for astrological purposes, such as writing horoscopes. It isn’t clear how committed to astrology Kepler was but it paid his wages.
Kepler wanted to demonstrate in his work, as he saw it, that God had created the Universe according to a plan that could be accessed by inquisitive humans. He exhaustively analysed the magnificent recorded observations left by the late Tycho Brahe (1546-1601) of the orbits of the six known planets of that time.
Brahe was by far the greatest astronomer before the invention of the telescope. The accuracy of his astronomical measurements is stunning.
Armed with this treasure trove of information, Kepler set about his work. The result was one of the greatest legacies in science – his three laws of planetary motion. Of these, perhaps the most rewarding for him was his third law, in which he discovered a beautiful mathematical relationship arising from the orbits of the planets.
If T is the time in years for any planet to orbit the Sun and D is half the sum of the planet’s furthest and nearest distances from the Sun, if that distance is in Astronomical Units (AU) where 1AU is the distance from the Earth to the Sun, then T x T divided by D x D x D is the number 1 for every planet.
For example, for the planet Mercury, T is 0.24 years and D is 0.39 AU, so TXT is 0.06 and DXDXD is 0.06. Dividing the two gives 1.This result must have confirmed his belief that the Universe was constructed by a rational God.
After his death in 1630, with the advent of Newtonian mechanics, the source of this powerful result was explained, but Kepler’s contribution to the mathematics of astronomy and planetary orbits in particular was huge.