Derby and District Astronomical Society
The Journal of the Derby and District Astronomical Society
September - December 2005
The Life and Laws of Johannes Kepler
By Maurice Batchelor
Portrait of Johannes Kepler by the author
Tycho of course, was in no danger at all, because up to the time of his death at the end of 1601, he still felt sure that the Sun moved around the Earth. He undoubtedly hoped that his pupil Johannes Kepler would use the Hven observatories on an island in the Baltic to prove the unlikely looking 'Tychonic' theory. Kepler began his work with an open mind. Fortunately he was as brilliant as a theorist as Tycho had been as an observer.
Johannes Kepler was born at Weil der Stadt, Württemburg (Germany) in 1571. In his early years he did not enjoy good health. A severe illness when he was four years old left him with a partially crippled hand, poor eyesight and a generally delicate constitution. It is therefore not surprising that he made very few astronomical observations himself. He went to Tubingen University planning to enter the Church, however, he soon turned his attention to astronomy.
In the year 1594 he accepted a lecturing post at the University of Grätz. His first book published two years later contained a measure of science mixed with a good deal of astrological superstition and some quite unsound ideas. Tycho Brahe, having read the book was highly impressed by it, with the result Tycho invited Kepler to join him as his assistant. Here surely was a man who would be able to make proper use of the Hven observations. Kepler was glad to accept as there were religious troubles in Grätz, so the young German mathematician joined the old Dane in Prague. Less than two years later Tycho died and Kepler succeeded him as Imperial Mathematician to Emperor Rudolph II.
Kepler now had the task of proving that the Earth moved round the Sun. He also looked into the question of the movements of various planets. This presented a problem as according to Tycho’s observations compared with his own results, the two could not be compared. He then made an important discovery. The planets move round the Sun indeed, but they do so in orbits which are not circles but ellipses.
How to draw an ellipse. Diagram by the author.
The planetary orbits were found to be ellipses of very slight eccentricity, but this was sufficient to explain the difference between his calculations and Tycho’s observations. To show what is meant the distance of Earth from the Sun varies by 1½ million miles. Actually we are closest to the Sun in December when the Northern Hemisphere is experiencing winter. Having ascertained these facts he went on to draw up his three famous laws of planetary motion.
This states that the planets move round the Sun in elliptical orbits, not in circles.
This states that a planet moves faster when it is closest to the Sun than when it is at its greatest distance. This is illustrated in the following diagram by the author. S represents the Sun, A, B, C and D a planet in four different positions in its orbit. According to Kepler’s Law, a planet moves at its quickest when at it closest to the Sun (i.e. between A and B).
This states that the square of the sidereal period for any planet, i.e. the time taken to complete one journey round the Sun, is proportional to the cube of its average distance from the Sun.
Having established these laws, it is worth mentioning that the third law was included in a book called Harmonies Mundi (The Harmonies of the World), a valuable book of scientific discoveries. Although not a true observer due to defective eyesight he was interested in the new telescopes invented in 1608. For instance he explained why the Moon appears coppery or reddish in colour during a total lunar eclipse. This is caused by the refraction of light in the Earth’s atmosphere so that a small amount of light falls onto the Moon’s surface.
He came upon financial difficulties due to the death of his benefactor, Emperor Rudolph II. He did not always receive his promised salary, so that in 1612 he moved Linz in Austria, taking up a lecturing post there in the University. The death of his wife and one of his three children added to his problems. To make matters worse, his Mother, Catherine Kepler was arrested on a charge of witchcraft. Although Kepler secured her acquittal and release from prison, she did not live long afterwards. He wrote a book dealing with the Copernican system as well as giving details about comets. Strangely perhaps, the Church authorities did not trouble him in this regard.
In conclusion, Kepler, was a very clever mathematician, well ahead of his time and it is worth remembering that the colouration of the Moon’s surface during a total eclipse due to refraction of the Sun’s light by the Earth’s atmosphere was first explained by Johannes Kepler, more than three hundred years ago.
Read Maurice's other article in this edition of Aries, on the distances to the stars by clicking here.