About Johannes Kepler

Johannes Kepler was born on 27th Dec 1571 in Weil der Stadt, Württemberg and died on the 15th Nov 1630 in Regensburg, both towns currently in Germany.  He moved to Leonberg with his parents when he was five. His father was lost in a battle in the Netherlands the same year and never returned leaving Johannes to be brought up by his mother and grandmother.

Kepler attended a local school and then to a nearby seminary, where he originally intended to become ordained as a Lutheran minister. He then enrolled at Tübingen University where he took classes in arithmetic, geometry, astronomy and music.

Traditional astronomy in those days was based on the Ptolemaic or geocentric system where the known planets were assumed to circle the earth and ever more increasingly difficult and arbitrary concepts such as 'epicycles' were invented to account for annoying differences with their measured orbits.  When Kepler was first introduced to the Copernican or heliocentric model where all the planets, including the earth, revolve around the sun, he immediately adopted it as describing physical reality.  He then began work on measuring the orbits with sufficient accuracy to deduce a theory of planetary motion in mathematical terms.

Far from being hounded mercilessly by the religious authorities for 'heresy' (compare this with Galileo in Italy at the same time), it would seem that the worst that happened to Kepler was that he was encouraged to give up aspirations for ordination and later excommunicated from the Lutheran church.  Even this seemed to be more to do with his somewhat outspoken opinions on religious matters, rather than his views on cosmology.  Notwithstanding this, he remained a devoutly religious man for his entire life.

Kepler's first model of the solar system in 1596 attempted to account for the exact distances of the six known planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn) from the sun by enclosing the orbits between them (assumed to be circular) with the five known regular solids (tetrahedron, octahedron, hexahedron, icosahedron, dodecahedron). 

Kepler's planetary modelThe model nearly worked, in fact it is accurate to within about 10% which is remarkably good: however not quite good enough for Kepler. In particular, it was the orbit of Mars that was especially troublesome.  With this in mind, he concluded that his observations were in error and set about obtaining more accurate data.  He applied for and received the post of mathematical assistant to the Prague astronomer Tycho Brahe, knowing that Brahe kept by far the most detailed and accurate observations then existing of the planetary positions.  Keep in mind that Galileo had not yet invented the telescope and all observations were essentially naked eye with the help of very simple measuring instruments.  

Brahe treated Kepler very much like an assistant and jealously guarded his data, doling out only what he thought was absolutely necessary.  However, after Brahe's death in 1601, Kepler took over his position and finally had unrestricted access to all of the observational data.  Eventually, he came to the conclusion that the orbit of Mars was not a circle but an ellipse.  Following that, he confirmed that, indeed, all the planetary orbits were ellipses and that his original theory could never be more than an idealised approximation.

The ease with which Kepler abandoned a theory of many years because it did not fit the observed data, is perhaps one of the finest indictments of him as a scientist and he rigorously put together his 'new' theory of the cosmos: one based around his three laws of planetary motion.  Not that any of this was easy, as well over 1000 pages of meticulous calculation will testify.

Here are Kepler's three laws:

  1. The orbit of each planet is an ellipse with the sun at one of its foci.
  2. An imaginary line joining the planet to the Sun sweeps out equal areas in equal periods of time as the planet revolves around the Sun.  A corollary to this is that the planet moves faster when it is closer to the Sun and slower when it is further out.
  3. For any given two planets, the ratio of the squares of their periods of revolution equals the ratio of the cubes of their mean orbital radii. 

This last law was by far the most difficult to deduce and was not published until 1619, some 10 years after the first two.

The landmark publication The Harmony of the World , in which this appeared is also noted for its extensive treatment of music theory in relation to planetary orbits.  In an endeavour to unify all aspects of this topic among the different mathematical sciences, including music, Kepler spent many chapters discussing the ratios of the planetary orbits and periods and relating them to the various intervals of the different musical scales in use during the 17th Century.  In fact, he even makes references to a book on music theory by Vincenzo Galilei, father of the great Galileo, which Kepler was said to have read during a journey to defend his mother who was tried for witchcraft.

Other firsts for which Kepler is noted are listed below:

  • Explained refraction within the eye, how both eyes are used for depth perception and how lenses might be used to correct nearsightedness and farsightedness
  • Described real, virtual and inverted images, magnification and the exact theory behind the telescope
  • Discovered and described total internal reflection
  • Suggested that the tides are caused by the Moon
  • Suggest that the Sun rotates about its own axis
  • Derived the currently-accepted birth year of Christ
  • Coined the word "satellite" to describe the moons of Jupiter
  • Devised a mathematical treatment of the close packing of equal spheres
  • Published of a method for devising volumes of resolution for solids
  • Discovered two new regular polyhedra
  • Proved how logarithms worked and calculated them to eight decimal places in a set of tables which were used to correctly predict planetary positions for many decades

Kepler died in Regensburg aged 59, after suffering a short illness.  He was buried in the local church, but this was later destroyed during the Thirty Years' War and nothing now remains at the site.

Johannes Kepler was always deeply religious and all his papers and books are prefaced by thanks to God for granting him any insights he made have had.  For him, science and religion were one, the gift of a Creator who expected mankind to discover His divine ways through the rational application of logic and mathematics, not by unchanging dogma and blind faith.

© Wayne Madden 2006

© Kepler Ensemble 2014