The year was 1571. Copernicus had been dead for 28 years and his great idea of a heliocentric universe had received virtually no public support. Tycho Brahe was a young man of 25. Galileo and Shakespeare were both 7 years old. And Johannes Kepler was born, on 27 December (at 2.30 in the afternoon, according to a horoscope that he later cast for himself), the first child of Heinrich and Katharina Kepler. Kepler was born in Weil der Stadt in Germany. The main square now has a monument to its most famous son (figure 3), and the Kepler Museum on the corner stands on the site of the Kepler household. Much of what is known about his early life comes from his own writings (Caspar 1993).
Kepler's statue in Weil der Stadt, Germany.
Johannes Kepler had an unhappy childhood. He described his father as “an immoral, rough and quarrelsome soldier”, and his mother as “small, thin, dark-complexioned, garrulous, quarrelsome and generally unpleasant”. He himself was not a particularly healthy child; he nearly died of smallpox, aged three. His father, the mercenary, left to fight in yet another war when Kepler was in his mid-teens, and was never seen by the family again.
Kepler did recollect, however, a few happy moments in his early life. In 1577, when he was five, his mother took him out one night to see the bright comet of that year. This was the same comet that was being observed in far-away Denmark by Tycho Brahe, who concluded that — contrary to Aristotelian doctrine — it lay beyond the sphere of the Moon. He also notes that, in 1580, his father called him outdoors to look at an eclipse of the Moon.
Kepler was a bright child who did very well at school. In 1589 he had no difficulty in getting into the Protestant stronghold of Tubingen University, where he intended to train to become a Lutheran clergyman. It was here he met Michael Maestlin, professor of mathematics and astronomy, and one of the few people who recognized that the Copernican system was correct.
The initial tone of the Protestant reaction to Copernicus was epitomized by his contemporary Martin Luther who declared: “This fool [Copernicus] wishes to reverse the entire science of astronomy; but sacred scripture tells us that Joshua commanded the Sun to stand still, and not the Earth.” Other Protestant leaders expressed similar views. Maestlin, as a member of a staunchly Protestant university, was required to teach the Ptolemaic system to his pupils. But in addition, perhaps only privately, he also taught them about the Copernican system, and the simplifications and greater explanatory power which — in principle — it had in comparison with Ptolemy.
Going to Graz
Thanks to Maestlin, Kepler became an early and very public convert to Copernican ideas, although he still intended to become a Lutheran clergyman. But the whole direction of his life changed suddenly, by chance, in 1594. A maths teacher at an obscure Lutheran school in Graz died, and the school authorities turned to Tubingen University for advice on a successor. Kepler was the obvious choice. Not only was he a brilliant student, but he had also shown some regrettably unorthodox tendencies, in both his Copernicanism and his approach to Calvinism. These hardly suited him to the job of a Lutheran minister of religion. Kepler was initially unwilling to move, but eventually saw the benefit of the position.
So Kepler travelled to Graz, where he took up the posts both of maths teacher and district mathematician. Three astronomical problems particularly fascinated him at that time: why were there only six planets; why were they at the distances that they were from the Sun; and why did they travel more slowly the further they were from the Sun? He could not possibly have known that the first and second questions were fruitless, but that the third would — 25 years later — lead him to his third law of planetary motion.
But it was the first two questions that initially fired his imagination and led him on a totally false path, although it did in the end lead to his first two laws of planetary motion. During one of his classes he realized that an equilateral triangle could be placed — more or less exactly — between the orbits of Jupiter and Saturn, as a result of the fact that the radius of the orbit of Jupiter is half the radius of the orbit of Saturn (give or take a few percent, or perhaps it would fit exactly if only he had more accurate figures than those used by Copernicus?). This was the moment of Kepler's revelation. It was clear to him that God had created orbits of this size so that a geometrical figure could be fitted exactly between them. The triangle was not, of course, literally there, but it was present in the mind of God, Kepler reasoned.
He tried to find other two-dimensional shapes to fit between the other planetary orbits, without success. However, by judicious choosing, he found he could achieve his purpose with three-dimensional shapes (the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron). Euclid had proved that there were five and only five perfect solids, so Kepler reasoned that there were six planets, only, precisely because there were five perfect solids to fit between the five pairs of orbits of the six planets. Again, the match was not exact, but Kepler put this down to the quality of his data. He knew that better data was held by Tycho Brahe, the great observational astronomer.
Into print
The eager young Kepler rushed to publish a book setting out his discovery. Mysterium Cosmographicum was published in 1597, when he was 25. It was a beautiful theory, and totally incorrect. Kepler circulated the book widely and gained a reputation as a bright theoretical astronomer. It is also noteworthy that, 54 years after the publication of De Revolutionibus, this was almost the first book to come out publicly in favour of the Copernican universe, albeit Kepler's own version of this cosmology.
Kepler's life was plagued by both religious intolerance and family tragedy. In 1597 he married Barbara Muller who, although only 23, had already been married and widowed twice. She brought a daughter, Regina, to the marriage. Religious intolerance first showed itself in the decree of September 1598 that all Protestant preachers and teachers were to leave Graz, ruled by the devoutly Catholic Archduke Ferdinand, who had declared: “I would rather rule a country ruined than a country damned.” Kepler was among the many thrown out, but he was alone in being allowed back only a month later, perhaps because of his official role as district mathematician, perhaps because he had friends in high places. However, he knew that he would not be able to stay in Graz for much longer.
Kepler tried and failed to get a job at his old university in Tubingen; his tendency towards unorthodox views meant that he was not acceptable there. At this time he also received a letter from Tycho Brahe thanking him for a copy of his book, and expressing the hope that he would soon apply the ideas in it to the Tychonic system, and that Kepler would one day call in on him. The Tychonic system was a compromise between those of Ptolemy and Copernicus, in which the Earth retained its central position in the universe, with the Sun and the Moon in orbit about it, but the five planets orbited the Sun. Kepler demolished it very effectively in his later writings.
To Prague and Tycho Brahe
In January 1600, at the age of 28, Kepler set off for Prague to see if Brahe would offer him employment. The two met in February. It was a meeting of opposites who needed each other. Brahe was a rich nobleman, whereas Kepler had come from a much humbler background. Brahe was primarily an observer, Kepler a theoretician. Brahe wanted Kepler to demonstrate the truth of his Tychonic view of the universe, and Kepler wanted Brahe's observations to verify his own version of the Copernican theory.
Things did not start off at all well. Kepler was unhappy with his conditions of service. In April, he had a blazing row with Brahe, and walked out. He soon realized what a mistake he had made, begged Tycho's forgiveness, and was received back into the fold. In June he returned to Graz to collect his wife and possessions, and to settle his affairs there — just in time. In August all Protestants in the city — not just preachers and teachers — were required to convert to Catholicism or get out. Kepler got out and returned to Prague to work for Brahe. Just over one year later, in October 1601, Brahe died, and Kepler was appointed Imperial Mathematician to the eccentric Rudolph II in his place.
Good years
At this point in the story we can say goodbye to Kepler the mystical speculator, and instead concentrate on Kepler the scientific genius — although it has to be said that Kepler's mystical side never left him. The years from the time he started working for Brahe to the publication of his first two laws, in 1609, were highly productive. He showed his genius in his fundamental approach to the problem of working out planetary orbits. Before Kepler, everybody — including Copernicus — had looked at the problem of planetary orbits as purely a problem in geometry. If you could find a geometrical model that replicated the movements of the planets, then you had done your job. There was no need to look for physical causes. Kepler felt that this approach was wrong. He suggested that there was some sort of force coming out of the Sun that dragged the planets round. The force faded with distance, which was why the outer planets moved more slowly than the inner planets. And the force was magnetic, or something like it in its effects. Kepler was the person who single-handedly moved astronomy from geometry to physics.
His idea had an immediate practical consequence. He decided that he should measure all planetary positions, angles and distances from the Sun, rather than from the centre of planetary orbits. He also had the good fortune to be given the orbit of Mars to study. Mars, of course, has the highest eccentricity of all the planets except for Mercury, which is hard to observe. If you can crack the orbit of Mars, you can crack the orbit of any of the other planets.
His initial approach was conventional. He assumed a circular orbit, with the Sun and the equant — the point from which the planet would be seen to move at a constant angular rate — offset from the centre. The idea of the equant came from Ptolemy, who introduced it as an ingenious fudge to help align theory and observation.
Brahe had a huge collection of Mars observations, including 10 observations at opposition, to which Kepler later added two more of his own. His task was to find an orbit that fitted the opposition observations. This was a lengthy and tedious trial and error exercise, involving a series of ever closer approximations. Eventually he succeeded in finding a circular orbit for Mars that fitted all the opposition observations, to within 2 arcminutes, the level of accuracy of Tycho's pre-telescopic observations. Anybody else might have stopped there, but not Kepler. He checked his orbit further, against more of Tycho's observations, and found that it did not fit. At worst, it was out by a full 8 arcminutes — an error that simply could not be neglected. He realized that he would have to throw out the assumptions of his predecessors, and start all over again. As he himself later put it: “These 8 minutes showed the way to a renovation of the whole of astronomy.”
“Kepler was the person who single-handedly moved astronomy from geometry to physics.”
He recognized that he was going to have to throw out in particular the assumption of circular motion that had been at the core of astronomical thinking for the past 2000 years. But first, and more fundamentally, he was going to have to check the Earth's orbit; if the Earth did not move at a uniform rate round the Sun, then observations made from Earth based on this assumption would be wrong.
But how do you find out whether the Earth moves at a uniform rate? Kepler's solution was, as Einstein put it, “an idea of true genius” (Baumgardt 1951). He measured the Earth's orbit as it would be seen by an observer on Mars. He noted the position of Mars relative to Earth (and therefore the position of Earth relative to Mars) every 687 days — the orbital period of Mars. A succession of Tycho's observations at 687-day intervals, when Mars was at the same place, enabled Kepler to plot the true position of Earth at various times in its orbit. He concluded that the Earth does not revolve round the Sun at a uniform rate, and that the Sun is not at the centre of the Earth's orbit. This led him to the fact that the Earth and the other planets sweep out equal areas in equal times, his second law, which he discovered before his first law.
Having established this, he moved back to the shape of the orbit of Mars. As he explained: “The conclusion is quite simply that the planet's path is not a circle — it curves inwards on both sides and outward again at opposite ends … The orbit is not a circle, but an oval.” He battled with the shape until the spring of 1605, when he finally realized that the oval was in fact an ellipse — his first law. The other part of his first law — that the Sun was at one focus of this ellipse — was only explicitly stated in his Epitome, published some 10 years later.
Both laws had to wait four more years for publication. There were two reasons for the delay. First, the Emperor Rudolph II had no funds available and, secondly, Brahe's heirs were creating difficulties. Eventually, in 1609, the laws appeared in Kepler's book Astronomia Nova.
In the spring of 1610, news reached him that Galileo had discovered four new planets. Kepler immediately realized that these could not be planets in their own right, but must be satellites of a known planet, for he had proved in Mysterium Cosmographicum that there could only be six planets. And sure enough, it soon emerged that the new planets were satellites of Jupiter.
Bad years
The year 1611 was a disastrous one for the 39-year old Kepler. Rudolph II, his patron, was far from secure on his throne. And early in the year, Kepler's favourite child, Friedrich, died of smallpox at the age of six. Kepler decided that it was time to leave Prague, partly for the sake of his homesick wife, and accepted a job as maths teacher in Linz, in Austria. Later that year, his wife also died.
Once settled in Linz, Kepler married for the second time. His new wife was Susanna Reuttinger, some 17 years his junior. The marriage seems to have been happier, except for the deaths of more of his children. Kepler had twelve children, but eight of them died in infancy or early childhood (figure 2). A further family problem came in 1615, when Kepler's mother was accused of witchcraft. It was six years before the charge was finally dropped, but defending her took a significant slice of Kepler's time.
Kepler's family tree, showing childhood deaths.
The year 1619 saw the publication of Harmonice Mundi, which contained Kepler's third law of planetary motion: that for any two planets, the ratio of the cube of the mean distance from the Sun to the square of the period is the same. It is not generally realized that, in his Epitome of Copernican [i.e. Keplerian] Astronomy, published in instalments in the years 1618–1621, Kepler extended this law to include the four newly discovered satellites of Jupiter. The constant of proportionality was of course different, and the distances and periods that Kepler quotes were (unsurprisingly) not totally accurate, but table 1 shows that his third law held up well, given the inevitable inaccuracies in his figures.
Portrait of Kepler aged 38, artist unknown.
Kepler's legacy
1634 Kepler's Somnium, the story of a journey to the Moon, is published posthumously.
1638 Kepler's second wife, Susanna, dies in poverty at the age of 49.
1687 Newton publishes Principia, which includes his gravitational inverse square law, from which he derives Kepler's three laws.
2009 The Kepler mission is launched, to search for Earth-like planets around other stars.
A fitting conclusion
Arguably, the culmination of all Kepler's work was the publication in 1627 of the Rudolphine Tables, dedicated to the late Rudolph II. Based on his laws of planetary motion, these enabled the prediction of planetary positions well into the future. It was the fact that they were more accurate than any other tables that led to the gradual and no doubt reluctant acceptance of Kepler's ellipses. This took some time — for example, Galileo's Dialogue on the Two Chief World Systems, published in 1632, contains no mention of elliptical orbits, even though he must have been fully aware of Kepler's discoveries.
The frontispiece to the tables was drawn up according to Kepler's instructions, and shows a gathering of astronomers — a Babylonian, Hipparchus, Ptolemy, Copernicus and Tycho. On the base, on the left, is a picture of Kepler, working away. Above hovers an eagle, the symbol of the emperor, dropping coins, perhaps symbolizing the fact that poor Kepler was still owed substantial sums of money for his efforts.
The forecast in the tables that there would be a transit of Mercury across the face of the Sun in 1631 was duly observed by the French astronomer Pierre Gassendi. Sadly, Kepler himself did not live to see or hear about this. One can only hope that his last year of life brought some happiness — his oldest daughter, Susanna, was married in March 1630, and his youngest daughter, Anna Maria, was born in April. Kepler himself was passing through Regensburg when he fell ill, and later died on 15 November 1630. In 1632 the churchyard where he was buried was destroyed during the 30 Years' War. So we can visit the tombs of Galileo and Newton, but not that of Kepler. The inscription he had arranged to have placed on his tombstone is, however, known:
“I measured the skies, now the shadows I measure.
Sky-bound was the mind, earth-bound the body rests.”
David Love gives an introduction to the life and achievements of Johannes Kepler, who published his first two laws of planetary motion 400 years ago, in 1609.
References
Further reading
Max Caspar's excellent and detailed biography provided much of the biographical information, but a shorter and more readable account is Arthur Koestler's The Watershed (part of The Sleepwalkers), published by Heinemann in 1961.
Information about science and the church in Kepler's time comes from Andrew D White's A History of the Warfare of Science with Theology, chapter III (1993, Prometheus) and Owen Chadwick's The Penguin History of the Church, Vol. 3 — The Reformation (1964, Penguin).
A summary of Kepler's arguments is given in Selections from Kepler's Astronomia Nova by William H Donahue (2004, Green Lion Press), who is currently preparing a new and revised translation of the complete Astronomia Nova. Essential further reading on this topic are Kepler's Physical Astronomy by Bruce Stephenson (1987, Princeton University Press) and The Composition of Kepler's Astronomia Nova by James R Voelkel (2001, Princeton University Press).
