2. The Last Mystics, The Scientists

The movement of the planets – Tycho Brahe – Measuring star positions – Tycho’s supernova – Tycho observes comet – His model of the Universe – Johannes Kepler: Tycho’s assistant and inheritor – Kepler’s geometrical model of the Universe – New thoughts on the motion of planets: Kepler’s first and second laws – Kepler’s third law – Publication of the Rudolphine star tables – Kepler’s death

The person who most deserves the title of ‘first scientist’ was Galileo Galilei, who not only applied what is essentially the modern scientific method to his work, but fully understood what he was doing and laid down the ground rules clearly for others to follow. In addition, the work he did following those ground rules was of immense importance. In the late sixteenth century, there were others who met some of these criteria – but the ones who devoted their lives to what we now call science were often still stuck with a medieval mindset about the relevance of all or part of their work, while the ones who most clearly saw the, for want of a better word, philosophical significance of the new way of looking at the world were usually only part-time scientists and had little influence on the way others approached the investigation of the world. It was Galileo who first wrapped everything up in one package. But Galileo, like all scientists, built on what had gone before, and in this case the direct link is from Copernicus, the man who (himself drawing on the work of his predecessors such as Peuerbach and Regiomontanus) began the transformation of astronomy in the Renaissance, to Galileo, via Tycho Brahe and Johannes Kepler (and on, as we shall see, from Kepler and Galileo to Isaac Newton). Tycho, as he is usually known, also provides a particularly neat example of the way in which profoundly significant scientific work could still, at that time, be mixed up with distinctly old-fashioned and mystical interpretations of the significance of that work. Strictly speaking, Brahe and Kepler weren’t quite the last mystics – but they certainly were, in astronomy at least, transitional figures between the mysticism of the Ancients and the science of Galileo and his successors.

Tycho Brahe was born in Knudstrup, on the southern tip of the Scandinavian peninsula, on 14 December 1546. This is now in Sweden but was then part of Denmark. The baby was christened Tyge (he was even a transitional figure in the way that he later Latinized his first name, but not his surname). He came from an aristocratic family – his father, Otto, served the King as a Privy Counsellor, was the lieutenant of several counties in turn and ended his career as governor of Helsingborg Castle (opposite Elsinore, later made famous by William Shakespeare in Hamlet, first performed in 1600). As Otto’s second child but eldest son, Tycho was born with the proverbial silver spoon in his mouth, but his life almost immediately took a twist which might have come right out of a play. Otto had a brother, Joergen, an admiral in the Danish navy, who was married but childless. The brothers had agreed that if and when Otto had a son, he would hand the infant over to Joergen to raise as his own. When Tycho was born, Joergen reminded Otto of his promise, but received a frosty response. This may not have been unrelated to the fact that Tycho had a twin brother who was stillborn, and his parents may well have feared that Otto’s wife, Beate, might not be able to have more children. Biding his time, Joergen waited until Tycho’s first younger brother was born (only a little over a year later) and then kidnapped little Tycho and took him off to his home at Tostrup.

With another healthy baby boy to raise (Otto and Beate eventually produced five healthy sons and five healthy daughters) this was accepted by the family as a fait accompli, and Tycho was indeed raised by his paternal uncle. He received a thorough grounding in Latin as a child before being sent to the University of Copenhagen in April 1559, when he was not yet 13 years old – not unusually young in those days for the son of an aristocrat to begin the education aimed at fitting him for high office in the state or Church.

Joergen’s plans for Tycho to follow a career of service to the King in the political field began to fall apart almost at once, because on 21 August 1560 there was an eclipse of the Sun. Although total in Portugal, it was only a partial eclipse in Copenhagen. But what caught the imagination of 13-year-old Tycho Brahe was not the less-than-spectacular appearance of the eclipse, but the fact that the event had been predicted long before, from the tables of observations of the way the Moon seems to move among the stars – tables going back to ancient times but modified by later observations, particularly by Arabian astronomers. It seemed to him ‘as something divine that men could know the motions of the stars so accurately that they could long before foretell their places and relative positions’.¹

Tycho spent most of the rest of his time in Copenhagen (just over eighteen months) studying astronomy and mathematics, apparently indulged by his uncle as a phase he would grow out of. Among other things, he bought a copy of a Latin edition of the works of Ptolemy and made many notes in it (including one on the title page recording that he purchased the book, on the last day of November 1560, for two thaler).

In February 1562, Tycho left Denmark to complete his education abroad, part of the usual process intended to turn him into an adult fit for his position in society. He went to the University of Leipzig, where he arrived on 24 March, accompanied by a respectable young man called Anders Vedel, who was only four years older than Tycho but was appointed by Joergen as his tutor, to act as a companion and (it was clearly understood) to keep the younger man out of mischief. Vedel was partly successful. Tycho was supposed to study law in Leipzig, and he did this work with reasonable diligence. But his great academic love was still astronomy. He spent all his spare money on astronomical instruments and books, and stayed up late making his own observations of the heavens (conveniently, when Vedel was asleep). Even though Vedel held the purse strings, and Tycho had to account to him for all his expenditure, there was little the elder man could do to curb this enthusiasm, and Tycho’s skill as an observer and knowledge of astronomy increased more rapidly than his knowledge of law.

When Tycho became more knowledgeable about astronomy, though, he realized that the accuracy with which men seemed to ‘know the positions of the stars’ was much less impressive than he had thought at first. In August 1563, for example, a conjunction of Saturn and Jupiter took place – a rare astronomical event in which the two planets are so close together on the sky that they seem to merge. This had great significance for astrologers,² had been widely predicted and was eagerly anticipated. But while the actual event occurred on 24 August, one set of tables was a whole month late in its prediction and even the best was several days in error. At the very start of his career in astronomy, Tycho took on board the point which his immediate predecessors and contemporaries seemed unwilling to accept (either out of laziness or too great a respect for the Ancients) – that a proper understanding of the movement of the planets and their nature would be impossible without a long series of painstaking observations of their motions relative to the fixed stars, carried out to a better accuracy than any such study had been carried out before. At the age of 16, Tycho’s mission in life was already clear to him. The only way to produce correct tables of the motions of the planets was by a prolonged series of observations, not (as Copernicus had) by taking the odd observation now and then and adding them more or less willy-nilly to the observations of the Ancients.

Remember that the instruments used to make observations in those days, before the development of the astronomical telescope, required great skill in their construction and even greater skill in their use (with modern telescopes and their computers, it is the other way around). One of the simplest techniques used by Tycho in 1563 was to hold a pair of compasses close to his eye, with the point of one leg of the pair on a star and the other point on a planet of interest – say, Jupiter. By using the compasses set with this separation to step off distances marked on paper, he could estimate the angular separation of the two objects on the sky at that time.³ But he needed much better accuracy than this could provide. Although the details of the instruments he used are not crucial to my story, it is worth mentioning one, called a cross-staff or radius, which Tycho had made for him early in 1564. This was a standard kind of instrument used in navigation and astronomy in those days, consisting basically of two rods forming a cross, sliding at right angles to one another, graduated and subdivided into intervals so that by lining up stars or planets with the ends of the cross pieces it was possible to read off their angular separation from the scale. It turned out that Tycho’s cross-staff had not been marked up correctly, and he had no money to get it recalibrated (Vedel was still trying to do his duty by Joergen Brahe and keep Tycho from spending all of his time and money on astronomy). So Tycho worked out a table of corrections for the instrument from which he could read off the correct measurement corresponding to the incorrect reading obtained by the cross-staff for any observation he made. This was an example that would be followed by astronomers trying to cope with imperfect instruments right down the centuries, including the famous ‘repair’ made to the Hubble Space Telescope by using an extra set of mirrors to correct for flaws in the main mirror of the telescope.

As an aristocrat with a (seemingly) secure future, there was no need for Tycho to complete the formality of taking a degree, and he left Leipzig in May 1565 (still accompanied by Vedel) because war had broken out between Sweden and Denmark, and his uncle felt he should return home. Their reunion was brief. Tycho was back in Copenhagen by the end of the month, where he found that Joergen had also just returned from fighting a sea battle in the Baltic. But a couple of weeks later, while the King, Frederick II, and a party that included the admiral were crossing the bridge from Copenhagen castle into the town, the King fell into the water. Joergen was among those who immediately went to his rescue, and although the King suffered no long-term ill effects, as a result of his immersion, Joergen Brahe contracted a chill, complications developed and he died on 21 June. Although the rest of the family (with the exception of one of his maternal uncles) frowned upon Tycho’s interest in the stars and would have preferred him to follow a career fitting his station in society, he had an inheritance from his uncle and there was nothing they could do (short of another kidnap) to tie him down. Early in 1566, soon after his nineteenth birthday, Tycho set off on his travels, visiting the University of Wittenberg and then settling for a time and studying at the University of Rostock, where he did eventually graduate.

These studies included astrology, chemistry (strictly speaking alchemy) and medicine, and for a time Tycho made few observations of the stars. The breadth of his interests is not surprising, since so little was known about any of these subjects that there wasn’t much point in trying to be a specialist, while the astrological influence meant that there was thought to be, for example, a strong connection between what went on in the heavens and the workings of the human body.

Tycho was, like his peers, a believer in astrology and became adept at casting horoscopes. Not long after his arrival in Rostock, there was an eclipse of the Moon, on 28 October 1566. On the basis of a horoscope he had cast, Tycho declared that this event foretold the death of the Ottoman Sultan, Sulaiman, known as the Magnificent. In truth, this wasn’t a very profound prediction, because Sulaiman was 80 years old. It was also a popular one in Christian Europe, since he had earned his sobriquet the Magnificent partly by conquering Belgrade, Budapest, Rhodes, Tsabriz, Baghdad, Aden and Algiers, and had been responsible in 1565 for a massive attack on Malta, successfully defended by the Knights of St John. The Ottoman Empire was at its peak under Sulaiman and a serious threat to the eastern parts of Christian Europe. When news reached Rostock that the Sultan had indeed died, Tycho’s prestige soared – although the shine was taken off his achievement when it turned out that the death had occurred a few weeks before the eclipse.

Later the same year, one of the most famous incidents in Tycho’s life occurred. At a dance held on 10 December, Tycho quarrelled with another Danish aristocrat, Manderup Parsbjerg. The two ran into one another again at a Christmas party on 27 December, and the row (we don’t know for sure what it was about, but one version of the story is that Parsbjerg mocked Tycho’s prediction of the death of a Sultan who was already dead) reached such a pitch that it could only be settled by a duel. They met again at 7 pm on 29 December in pitch darkness (such an odd time to choose that it may have been an accidental encounter) and lashed out at each other with swords. The fight was inconclusive, but Tycho received a blow which cut away part of his nose, and he concealed this disfigurement for the rest of his life using a specially made piece manufactured out of gold and silver. Contrary to most popular accounts, it wasn’t the tip of the nose that Tycho lost, but a chunk out of the upper part; he also used to carry a box of ointment about with him and could often be seen rubbing it on to the afflicted region to ease the irritation.

Apart from its curiosity value, the story is important because it correctly portrays Tycho, now just past his twentieth birthday, as a bit of a firebrand, arrogantly aware of his own abilities and not always willing to follow the path of caution. These traits would surface in later life to bring him a lot more grief than a damaged nose.

During his time in Rostock, Tycho made several visits to his homeland. Although he was unable to convince his family that he was doing the right thing by following his interests in things like astronomy, in other quarters, his increasing stature as a man of learning did not go unnoticed. On 14 May 1568, Tycho received a formal promise from the King, still Frederick II, that he could have the next canonry to become vacant at the Cathedral of Roskilde, in Seeland. Although the Reformation of the church had taken place more than thirty years before, back in 1536, and Denmark was staunchly Protestant, the income that had formerly gone to the canons of the cathedral was now spent on providing support for men of learning. They were still called canons and they still lived in a community associated with the cathedral, but they had no religious duties and the posts were entirely in the gift of the King. Frederick’s offer certainly reflected Tycho’s potential as a ‘man of learning’, but it is also worth remembering, if the promise seems rather generous to one so young, that Tycho’s uncle had died, all too literally, in the service of the King.

Having completed his studies in Rostock, and with his future secured by the promise of a canonry, in the middle of 1568 Tycho set off on his travels again. He visited Wittenberg once more, then Basle, before settling for a spell in Augsburg, early in 1569, and beginning a series of observations there. To assist in this work, he had a huge version of the instrument called a quadrant made for him. It had a radius of about 6 metres, big enough so that the circular rim could be calibrated in minutes of arc for accurate observations, and it stood on a hill in the garden of one of his friends for five years, before being destroyed by a storm in December 1574. But Tycho had left Augsburg in 1570, returning to Denmark when news came that his father was seriously ill. In spite of this, Tycho was not to be distracted from his life’s work, and was making observations from Helsingborg Castle by the end of December that year.

Otto Brahe died on 9 May 1571, just 58 years old, and left his main property at Knudstrup jointly to his two eldest sons, Tycho and Steen. Tycho went to live with his mother’s brother, also called Steen, the only person in the family who had ever encouraged his interest in astronomy, and who, according to Tycho himself, had been the first person to introduce papermaking and glass manufacture on a large scale to Denmark. Until late in 1572, perhaps under the influence of the elder Steen, Tycho devoted himself mainly to chemical experiments, although he never abandoned his interest in astronomy. But in the evening of 11 November 1572 his life was changed again by one of the most dramatic events that the Universe can provide.

That evening Tycho was returning to the house from his laboratory, and taking in the panorama of the stars along the way, when he realized that there was something odd about the constellation Cassiopeia – the W-shaped constellation that is one of the most distinctive features of the northern sky. There was an extra star in the constellation. Not only that, but it was particularly bright. To appreciate the full impact of this on Tycho and his contemporaries, you have to remember that at that time stars were regarded as fixed, eternal and unchanging lights attached to a crystal sphere. It was part of the concept of the perfection of the heavens that the constellations had been the same for all eternity. If this really were a new star, it would shatter that perfection – and once you accepted that the heavens were imperfect, who could say what might follow?

One observation, though, did not prove that what Tycho had seen was a new star. It might be a lesser object, such as a comet. At that time, comets were thought to be atmospheric phenomena occurring only a little way above the surface of the Earth, not even as far away as the Moon (although for all anyone knew, the atmosphere itself extended at least as far as the Moon). The way to tell would be to measure the position of the object relative to the adjacent stars of Cassiopeia, and see if it changed its position, like a comet or meteor, or was always in the same place, like a star. Fortunately, Tycho had just completed the construction of another very large sextant, and whenever the clouds cleared in the nights that followed, he concentrated his attention on the new star. It stayed visible for eighteen months, and in all that time it never moved relative to the other stars. It was, indeed, a new star, so bright at first (as bright as Venus) that it could be seen in daylight, although it gradually faded from December 1572 onwards. Of course, many other people saw the star as well, and many fanciful accounts of its significance were circulated in 1573. Tycho had written his own account of the phenomenon. Although he was at first reluctant to publish it (possibly because he was concerned at how others might react to the shattering of heavenly perfection, but also because the star was still visible so his account was necessarily incomplete and not least because it might be regarded as unseemly for a nobleman to be seen to be involved in such studies), he was persuaded by friends in Copenhagen that he ought to do so to set the record straight. The result was a little book De Nova Stella (The New Star), which appeared in 1573 and gave us a new astronomical word, nova.⁴ In the book, Tycho showed that the object was not a comet or meteor and must belong to the ‘sphere’ of the fixed stars, discussed the astrological significance of the nova (in vague and general terms) and made a comparison with an object reported to have been seen in the heavens by Hipparchus around 125 BC.

It was quite easy to read astrological significance into anything visible in the heavens at that time, since much of Europe was in turmoil. Following the initial success of the Reformation movement, the Catholic Church was fighting back, notably through the activities of the Jesuits in Austria and the southern German states. In France, the Protestant Huguenots were suffering severe setbacks in the middle part of what became known as the French Wars of Religion, and there were bloody battles in The Netherlands between the independence fighters and the Spanish. Tycho could hardly write a book about a new star appearing in the midst of all that turmoil without at least nodding in the direction of astrology. But the key facts were clear from De Nova Stella – that the object was fixed among the fixed stars and met every criterion to be regarded as a genuinely new star. Many other astronomers studied the object (including Thomas Digges, whose position closely matched Tycho’s own), but Tycho’s measurements were clearly the most accurate and reliable.

There is one irony in all this. Tycho in particular made an intensive study of the star to see if there was any trace of the parallax shift that could be expected if the Earth really did move around the Sun. Because Tycho was such a superb observer and had built such accurate instruments, this was the most sensitive search for parallax yet undertaken. He could find no evidence of parallax, and this was an important factor in convincing him that the Earth is fixed, with the stars rotating about it on their crystal sphere.

Tycho’s life was not immediately transformed by his work on the new star (now sometimes referred to as Tycho’s star or Tycho’s supernova), but in 1573 it did change significantly for personal reasons. He formed a permanent liaison and settled down with a girl called Christine (or Kirstine). Very little is known about Christine except that she was a commoner – some accounts say she was the daughter of a farmer, others the daughter of a clergyman and others that she was a servant at Knudstrup. Probably because of the difference in status, the couple never went through a formal marriage ceremony. In sixteenth-century Denmark, however, such a wedding was regarded as something of an optional extra, and the law said that if a woman openly lived with a man, kept his keys and ate at his table, after three years she was his wife. Just in case there might be any doubt, some time after Tycho’s death several of his relatives signed a legal declaration that his children were legitimate and that their mother had been his wife. Whatever the formal status, the marriage was a successful and seemingly happy one, producing four daughters and two sons who survived childhood, and two more babies who died in infancy.

In 1574, Tycho spent part of his time in observing, but most of the year in Copenhagen, where, at the behest of the King, he gave a series of lectures at the university. But although, as this request shows, his reputation was on the increase, he was not happy with the conditions in Denmark and felt that he could get more support for his work if he went abroad. After extensive travels during 1575 he seems to have decided to settle in Basle, and returned to Denmark at the end of the year to put his affairs in order for the move. By now, though, there was an awareness at court that Tycho’s presence in Denmark added to the prestige of the whole country, and the King, already sympathetic, was urged to do something to keep the now-famous astronomer at home. Tycho turned down the offer of a royal castle for his base – perhaps wisely, given the administrative duties and responsibilities that would have been involved, but not the kind of offer that most people would refuse. Undaunted, King Frederick hit on the idea of giving Tycho a small island, Hveen, located in the sound between Copenhagen and Elsinore. The proposal included an offer to pay for the construction of a suitable house on the island out of the royal purse, plus an income. This really was an offer Tycho couldn’t refuse, and on 22 February 1576 he made his first visit to the island where he would make most of his observations, fittingly carrying out an observation of a conjunction of Mars and the Moon on the island that evening.⁵ The formal document assigning the island to Tycho was signed by the King on 23 May. At the age of 29, Tycho’s future seemed secure.

As long as Frederick remained on the throne, Tycho was able to enjoy an unprecedented amount of freedom to run his observatory just as he liked. The island was small – roughly oblong in shape and just three miles from shore to shore along its longest diagonal – and the highest point on it, chosen as the site for Tycho’s new residence and observatory, was only 160 feet above sea level. But at first money was no object, as in addition to his other income, Tycho was granted more lands on the mainland. He neglected his duties as Lord of the Manor in connection with these lands abominably, and this would eventually lead to problems, but at first he seemed to have all the benefits with none of the responsibilities. Even the long-promised canonry finally fell into his lap in 1579. The observatory was christened Uraniborg, after Urania, the Muse of astronomy, and over the years developed into a major scientific institution with observing galleries, library and studies. The instruments were the best that money could provide, and as the work of observing developed and more assistants came to the island to work with Tycho, a second observatory was built near by. Tycho established a printing press in Uraniborg to ensure the publication of his books and astronomical data (and his rather good poetry), and when he had difficulty obtaining paper he built a papermaking works as well. But don’t run away with the idea that Uraniborg was entirely the forerunner of a modern observatory and technological complex. Even here, Tycho’s mysticism was reflected in the layout of the buildings, itself intended to reflect the structure of the heavens.

Most of Tycho’s work on the island over the next twenty years can be glossed over, because it consisted of the dull but essential task of measuring the positions of the planets relative to the fixed stars, night after night, and analysing the results. To put the task in perspective, it takes four years of observing to track the Sun’s movements ‘through’ the constellations accurately, twelve years for each of Mars and Jupiter, and thirty years to pin down the orbit of Saturn. Even though Tycho had started observing at the age of 16, his earlier measurements were incomplete, and less accurate than those he could now make; even twenty years on, Hveen was barely enough for the job in hand. This work would not come to fruition until Johannes Kepler drew upon Tycho’s tables to explain the orbits of the planets, years after Tycho had died. But in 1577, alongside his routine work Tycho observed a bright comet, and his careful analysis of how the comet moved showed once and for all that it could not be a local phenomenon, closer to the Earth than the Moon is, but must travel among the planets themselves, actually crossing their orbits. Like the observations of the supernova of 1572, this was a shattering blow to the old ideas about the heavens, this time destroying the notion of crystal spheres, since the comet moved right through the places where these spheres were supposed to be.

Tycho first saw the comet on 13 November 1577, although it had already been noticed in Paris and London earlier that month. Other European observers also calculated that the comet must be moving among the planets, but it was universally acknowledged that Tycho’s observations were more accurate than those of anyone else, and it was his work that clinched the matter in the minds of most of his contemporaries. Several other, fainter, comets were studied in the same way over the next few years, confirming his conclusions.

The comet studies and his earlier observations of the supernova encouraged Tycho to write a major book, Astronomiae Instauratae Progymnasmata (Introduction to the New Astronomy), which appeared in two volumes in 1587 and 1588.⁶ It was in this book that he laid out his own model of the Universe, which looks to modern eyes like something of a backward step, because it is a kind of halfway house between the Ptolemaic system and the Copernican system. But there were elements of the Tychonic model that broke new ground, and it deserves more credit than it is usually given.

Tycho’s idea was that the Earth is fixed at the centre of the Universe and that the Sun, the Moon and the fixed stars orbit around the Earth. The Sun itself was seen as being at the centre of the orbits of the five planets, with Mercury and Venus moving in orbits smaller than the orbit of the Sun around the Earth, and with Mars, Jupiter and Saturn moving in orbits which are centred on the Sun, but which include both the Sun and the Earth within those orbits. The system did away with epicycles and deferents, and it explained why the motion of the Sun was mixed up with the motion of the planets. In addition, by displacing the centre of the planetary orbits from the Earth, Tycho filled up most of the space out to the assumed position of the fixed stars – which, in Tycho’s model, was just 14,000 Earth radii away from us (there was no problem with parallax, of course, because in this model the Earth did not move). But the really significant, modern-looking idea in all this is that Tycho did not regard the orbits as being associated with anything physical like crystal spheres, but saw them merely as geometrical relationships which describe the movement of the planets. Although he did not state it this way, he was the first astronomer to imagine the planets hanging unsupported in empty space.

But in other ways Tycho was less modern. He could not accept what he called the ‘physical absurdity’ of letting the Earth move, and he was convinced that if the Earth were rotating on its axis then a stone dropped from a tall tower would fall far to one side of the tower as the Earth moved underneath it while it was falling. It is also relevant to note that at this time the most virulent opposition to the Copernican system still came from the Protestant churches of northern Europe, while it was largely ignored by the Catholic Church (Bruno had yet to stir up their opposition to these ideas). Religious tolerance was not a feature of Denmark in the late sixteenth century, and anyone whose position depended utterly on the patronage of the King would have been mad to promote Copernican ideas, even if he did believe in them (which, it is clear, Tycho did not).

While the routine observations (so important to science, but utterly boring to describe) continued, Tycho’s position at Hveen came under threat, just at the time his book was being printed, with the death of Frederick II in 1588. Frederick’s successor, his son Christian, was only 11 when the King died, and the Danish nobles elected four of their number to serve as Protectors until he reached the age of 20. At first, there was little change in the government’s attitude to Tycho – indeed, more money was provided later that year to cover debts that he had incurred building up the observatory. During his last years at Hveen, Tycho was clearly regarded as a great national institution, and he received many distinguished visitors, including James VI of Scotland (later, on the death of Elizabeth, to become James I of England), who had come to Scandinavia to marry Anne, one of King Christian’s sisters. The two hit it off, and James granted Tycho a thirty-year copyright for all his writings published in Scotland. Other visitors were not so congenial, and Tycho clearly did not always relish his role as a kind of performing poodle. He managed to offend several members of the nobility with his offhand manner towards visitors he did not like, and by his flouting of protocol by allowing his low-born common-law wife a place of honour at table. Although we don’t know all the reasons, it is clear that Tycho was becoming dissatisfied with the arrangements for his work at Hveen as early as 1591, when he wrote in a letter to a friend that there were certain unpleasant obstacles to his work which he hoped to resolve, and commented that ‘any soil is a country to the brave, and the heavens are everywhere overhead’.⁷ Tycho also quarrelled with some of his tenants on the mainland and got into trouble with the ruling Council for neglecting the maintenance of a chapel that formed part of his estates. But none of these distractions seems to have affected his observations, which included a major catalogue of the positions of the fixed stars, which he said reached a thousand in 1595, although just 777 of the best positions were eventually published in the first volume of Kepler’s edition of Tycho’s Progymnasmata.

A year later, King Christian IV was crowned and soon began to make his presence felt. Christian saw a need to make economies in just about every area of state activity, and among many other things immediately withdrew the mainland estates granted to Tycho by Frederick II from his stewardship. Most of Tycho’s friends at court had died by now (Tycho himself was nearing 50), and the King was probably right in thinking that with Uraniborg long since built and running smoothly, it ought to be possible to keep things ticking over there on a greatly reduced budget. But Tycho was used to being given considerable indulgence and saw any reduction in his income as an insult, as well as a threat to his work. If he couldn’t maintain Uraniborg at the level he wanted, with many assistants, printers, papermakers and all the rest, he wouldn’t maintain it at all.

Things came to a head in March 1597, when the King cut off Tycho’s annual pension. Although he was still a wealthy man in his own right, Tycho felt this to be the last straw, and made immediate plans to move on. He left the island in April 1597 and spent a few months in Copenhagen before setting off on his travels, initially to Rostock, accompanied by an entourage of about twenty people (students, assistants and so on), his most important portable instruments and his printing press.

There, Tycho seems to have had second thoughts, and wrote what he probably regarded as a conciliatory letter to King Christian, in which he said (among many other things) that if he had a chance to continue his work in Denmark he ‘would not refuse to do so’. But this only made the situation worse. Christian was offended at Tycho’s high tone and the way he treated the King as an equal, and not least by this haughty phrase, which implied that Tycho might refuse a royal request. In his reply, he said that ‘it is very displeasing to us to learn that you seek help from other princes, as if we or the kingdom were so poor that we could not afford it unless you went out with woman and children to beg from others. But whereas it is now done, we have to leave it so, and not trouble ourselves whether you leave the country or stay in it’. I must admit to having rather more sympathy for Christian than he is usually given, and a less arrogant individual than Tycho might well have been able to reach an accommodation with the King without leaving Hveen. But then a less arrogant individual than Tycho would still have had his nose intact and might never have become such a great astronomer in the first place.

His boats home well and truly burned, Tycho moved on to Wandsbeck, near Hamburg, where he resumed his observing programme (the heavens were, indeed, everywhere overhead) while he sought a new permanent base for his work. This led to an invitation from the Holy Roman Emperor, Rudolph II, a man much more interested in science and art than he was in politics. This was good for Tycho but bad for most of middle Europe, with Rudolph’s reign leading, partly through his poor qualities as a politician (some historians think he was actually mad), to the Thirty Years War. Tycho arrived in Prague, the capital of the Empire, in June 1599 (having left his family in Dresden). After an audience with the Emperor, he was appointed Imperial Mathematician, granted a good income and offered a choice of three castles in which to set up his observatory. Tycho chose Benatky, 35 kilometres to the northeast of Prague, and left the city itself with some relief – a contemporary account describes the walls of the city as:

Less than strong, and except the stench of the streetes drive backe the Turks…there is small hope in the fortifications thereof. The streets are filthy, there be divers large market places, the building of some houses is of free stone, but the most part are of timber and clay, and are built with little beauty or art, the walles being all of whole trees as they come out of the wood, the which the barke are laid so rudely as they may on both sides be seen.

A far cry from the peace and comfort of Uraniborg. It is no surprise that towards the end of 1599 Tycho spent several weeks at a secluded Imperial residence in the countryside to avoid an outbreak of plague. But with the threat gone and his family arrived from Dresden, Tycho began to settle in at the castle, sending his eldest son back to Denmark to fetch four large observing instruments from Hveen. It took a long time to get the instruments to Benatky, and the castle had to be adapted to make a suitable observatory. It is hardly surprising that Tycho, now in his fifties, didn’t make any significant observations here in the short time that remained before his death. But even before arriving in Prague, he had entered into a correspondence that would ensure that his life’s work would be put to the best possible use by the ablest member of the next generation of astronomers, Johannes Kepler.

Kepler had none of the advantages of birth which had given Tycho a head start in life. Although he came from a family that had once ranked among the nobility and had its own coat of arms, Johannes’s grandfather, Sebald Kepler, was a furrier, who moved from his home town of Nuremberg to Weil der Stadt, not far from Stuttgart in the southern part of Germany, some time around 1520. Sebald was a successful craftsman who rose high in the community, serving for a time as mayor (burgomeister). This was no mean achievement, since he was a Lutheran in a town dominated by Catholics; Sebald was clearly a hard worker and a pillar of the community. The same could hardly be said of his eldest son, Heinrich Kepler, who was a wastrel and drinker whose only steady employment was as a mercenary soldier in the service of whichever prince needed hired hands. He married young, a woman called Katherine, and the couple shared a house with several of Heinrich’s younger brothers. The marriage was not a success. Apart from Heinrich’s faults, Katherine herself was argumentative and difficult to live with, and she also had great faith in the healing powers of folk remedies involving herbs and such like – scarcely an uncommon belief at the time, but one which was to contribute to her eventual imprisonment as a suspected witch, and cause much grief to Johannes.

Johannes had a distinctly disturbed and rather lonely childhood (his only brother, Christoph, was much younger than him). He was born on 27 December 1571, but when he was only 2 his father went off to fight in the Netherlands, and Katherine followed, leaving the infant in the care of his grandfather. Heinrich and Katherine returned in 1576 and moved the family to Leonberg, in the Duchy of Württemberg. But in 1577 Heinrich was off to war again. On his return, he tried his hand at various businesses, including, in 1580, the favourite of the drunkard, running a tavern, this time in the town of Ellmendingen. Not surprisingly, he lost all his money. Eventually, Heinrich set off to try his luck as a mercenary again and disappeared from his family altogether. His fate is not known for sure, although he may have taken part in a naval campaign in Italy; whatever, his family never saw him again.

In all this turmoil, Johannes was tossed about from household to household and school to school (but at least his family was still far enough up the social ladder that he did go to school, with the aid of scholarships from a fund established by the Dukes of Württemberg). As if this weren’t bad enough, while staying with his grandfather he caught smallpox, which left him with bad eyesight for the rest of his life, so that he could never have become an observer of the heavens like Tycho. But his brain was unaffected, and although he was often set back by having to change schools when his family moved, by the age of 7 he was allowed to enter one of the new Latin schools in Leonberg. These schools had been introduced after the Reformation, primarily to prepare men for service in the Church or the state administration; only Latin was spoken in the schools, in order to inculcate the pupils with the language of all educated men at the time. With all the interruptions, it took Johannes five years to complete what should have been three years’ worth of courses – but as a graduate of a Latin school, he was entitled to take an examination to be admitted to a seminary and train for the priesthood, the obvious and traditional route out of poverty and a life of toil for an intelligent young man. Although Kepler’s interest in astronomy had already been stirred as a child when he saw (on two separate occasions) a bright comet (the same one studied by Tycho in 1577) and an eclipse of the Moon, his future in the Church seemed clearly mapped out when he passed the examination in 1584 and was admitted to a school in Adelberg at the age of 12. Once again, the language of the school was Latin, in which Kepler became fluent.

Although the discipline at the school was harsh and Kepler was a sickly youth who was often ill, he showed such promise academically that he was soon moved to a more advanced school at Maulbronn and prepared by his tutors for entry to the University of Tübingen to complete his theological studies. He passed the entrance examination for the university in 1588, then had to complete a final year at Maulbronn before he could take up his place at the university, at the age of 17. Although training to become a priest, the courses Kepler was required to attend in his first two years at Tübingen included mathematics, physics and astronomy, in all of which he was an outstanding pupil. He graduated from this part of the course in 1591, second out of a class of fourteen, and moved on to his theological studies described by his tutors as an exceptional student.

Along the way, he had also learned something that was not in the official curriculum. The university’s professor of mathematics was Michael Maestlin, who dutifully taught his students in public the Ptolemaic system approved by the Reformed Church. In private, though, Maestlin also explained the Copernican system to a select group of promising pupils, including Kepler. This made a deep impression on the young man, who immediately saw the power and simplicity of the Sun-centred model of the Universe. But it wasn’t just in his willingness to accept the Copernican model that Kepler deviated from the strict Lutheran teaching of his time. He had grave doubts about the religious significance of some of the Church rituals, and although he believed firmly in the existence of God, he never found a formally established Church whose teachings and rituals made sense to him, and he persisted in worshipping in his own way – a distinctly dangerous attitude in those troubled times.

Just how Kepler would have reconciled his own beliefs with a role as a Lutheran clergyman we will never know, because in 1594, the year he should have completed his theological studies, his life was changed by a death in the distant town of Graz, in Austria. In spite of its distance, there was a seminary in Graz that had always had close academic connections with the University of Tübingen, and when the mathematics professor there died, it was natural for the authorities to ask Tübingen to suggest a replacement. The Tübingen authorities recommended Kepler, who was rather startled to be offered the post just when he was thinking about starting life as a clergyman. Although initially reluctant, he allowed himself to be persuaded that he really was the best man for the job, and left on the understanding that if he wanted, he could come back to the university in a couple of years, finish his training and become a Lutheran minister.

The 22-year-old professor of mathematics arrived in Graz on 11 April 1594. Although still within the Holy Roman Empire, he had crossed a significant invisible border, from the northern states where the Reformed Churches held sway to the southern region where the Catholic influence was dominant. But this invisible border was constantly changing, since under the treaty known as the Peace of Augsburg, settled in 1555, each prince (or duke, or whatever) was free to decide the appropriate religion in his domain. There were dozens of princes ruling individual statelets within the ‘empire’, and the state religion sometimes changed literally overnight when one prince died, or was overthrown, and was replaced by one of a different religious persuasion. Some princes were tolerant and allowed freedom of worship; others insisted that all their subjects convert to the new flavour of the month or forfeit their property at once. Graz was the capital of a statelet called Styria, ruled by Archduke Charles, who was determined to crack down on the Protestant movement, although at the time Kepler arrived exceptions such as the Lutheran seminary in Graz were still being tolerated.

Kepler was a poor man with no financial resources from his family – his university studies had been paid for by a scholarship and he had to borrow money for the journey to Graz. His situation wasn’t improved when the authorities at the seminary decided to put him on a three-quarter salary until he proved his worth. But there was one way in which he could both make some money and endear himself to the top people in the Graz community – by casting horoscopes. Throughout his life, Kepler used astrology as a means to supplement his always inadequate income. But he was well aware that the entire business was utter tosh, and while he became skilful at the art of talking in vague generalities and telling people what they wanted to hear, in private letters he referred to his clients as ‘fatheads’ and described the astrology business as ‘silly and empty’. A good example of Kepler’s skill in this despised art came when he was commissioned to produce a calendar for 1595 predicting important events for the year ahead. His successful predictions included rebellious activity by the peasants in Styria, incursions into Austria by the Turks in the east and a cold winter. His skill in dressing these common-sense predictions up in astrological mumbo jumbo not only established his reputation in Graz, but got his salary increased to the full level appropriate for his post.

But although Kepler may have been less superstitious than many of his peers, he was still too mystically inclined to be called the first scientist. This is clearly highlighted by his first important contribution to the cosmological debate, which spread his reputation far beyond the confines of Styria.

Kepler was never able to be an effective observer of the heavens because of his bad eyesight, and in Graz he had no access to observational data. So he was left to follow in the mental footsteps of the Ancients, using pure reason and imagination to try to come up with an explanation for the nature of the cosmos. The question that particularly intrigued him at that time was why there should be six, and only six, planets in the Universe, accepting that Copernicus was right and the Earth itself is a planet. After puzzling over this for some time, Kepler hit on the idea that the number of planets might be related to the number of regular solid figures that can be constructed using Euclidean geometry. We are all familiar with the cube, which has six identical square faces. The other four regular solids are: the tetrahedron, made up of four identical triangular sides; the dodecahedron, made of twelve identical pentagons; the icosahedron (a more complicated twenty-sided figure made of identical triangular faces); and the octahedron (made from eight triangles).

The bright idea that Kepler came up with was to nest these (imaginary) figures one inside the other, so that in each case the corners of the inner figure just touched the surface of a sphere surrounding the solid, and that sphere in turn just touched the inner sides of the surfaces of the next solid figure out in the nest. With five Euclidean solids to play with, and one sphere inside the innermost solid as well as one outside the outermost solid, this defined six spheres – one for each of the orbits of the planets. By putting the octahedron in the middle, surrounding the Sun and just enclosing a sphere with the orbit of Mercury, followed by an icosahedron, a dodecahedron, a tetrahedron and a cube, he got a spacing between the corresponding spheres that more or less corresponded to the spacing of the orbits of the planets around the Sun.

The agreement was never more than approximate, and it was based on a mystical belief that the heavens must be governed by geometry, not on anything that we would now call science. The model fell apart as soon as Kepler himself showed that the orbits of the planets are elliptical, like an elongated circle, not circular; and, in any case, we now know that there are more than six planets, so the geometry cannot be made to work even on its own terms. But when Kepler came up with the idea late in 1595 it seemed to him like a Divine revelation – which is ironic, since by espousing the Copernican model with the Sun at the centre of the Universe, Kepler’s idea flew in the face of Lutheran teaching, and he was still a Lutheran, of sorts, himself.

Kepler spent the winter of 1595/6 working out his idea in detail, and corresponded with his old teacher Michael Maestlin about it. Early in 1596, he was granted leave of absence from his teaching duties to visit his ailing grandparents, and took the opportunity to call in on Maestlin in Tübingen. Maestlin encouraged Kepler to develop his ideas in a book and oversaw the printing of the book, which appeared in 1597, not long after Kepler returned (rather late, but trailing clouds of glory from his now widely discussed model) to his duties in Graz. The book is usually known as Mysterium Cosmographicum (The Mystery of the Universe), and it contained an idea which, with hindsight, is even more significant than the model of nested solids it described. Kepler picked up on the observation by Copernicus that the planets move slower in their orbits the further they are from the Sun, and suggested that they were kept moving in those orbits by a force (he called it ‘vigour’) reaching out from the Sun and pushing them along. He argued that the vigour would be less vigorous (so to speak) further from the Sun, and would only be able to push more distant planets more slowly. This idea, which was partly stimulated by the work of William Gilbert on magnetism (more of this in the next chapter) was an important step forward because it suggested a physical cause for the motion of the planets, where previously the best idea anyone had come up with was that the planets were pushed around by angels. Kepler specifically said that ‘my aim…is to show that the machine of the universe is not similar to a divine animated being, but similar to a clock’.⁸

Kepler sent copies of his book to the most eminent thinkers of his day, including Galileo (who didn’t bother to reply, but mentioned the new model in his lectures) and, most significantly, Tycho, at that time based in Germany. Tycho replied to Kepler with a detailed critique of the work, and was impressed by the mathematical skill of the author of the book, even though the idea of a Sun-centred Universe was still anathema to him. Indeed, Tycho was sufficiently impressed that he suggested that Kepler might care to join the team of assistants surrounding the older man. The offer soon proved extremely opportune.

In April 1597, Kepler married Barbara Müller, a young widow and daughter of a wealthy merchant. Although his need for financial security may have been a factor in the marriage, everything went well at first, with Kepler now on full salary and enjoying a happy home life. But two children died in infancy (although three others later survived), Barbara’s family, feeling that she had married beneath her status, withheld money she was entitled to, and life with Kepler on a teacher’s salary (even a full one) proved to be much tougher than life as the daughter of a successful merchant. Another problem blew up out of Kepler’s eagerness to consolidate his new reputation by associating with other mathematicians and discussing his ideas with them. He wrote a letter to the then Imperial Mathematician, Reimarus Ursus, seeking his opinion on his own work, and sycophantically praising Ursus as the greatest mathematician of all time. Ursus didn’t bother to reply, but took Kepler’s praise out of context and published it as a kind of endorsement of some of his own work – which, as it happens, was critical of Tycho. It took a lot of tactful correspondence before Kepler was able to soothe Tycho’s offended feelings and restore friendly relations with the great astronomer. Increasingly, Kepler longed for an opportunity to get his hands on Tycho’s by now legendary wealth of observational data and test his ideas about planetary orbits using these accurate figures for the movement of the planets.

While all this was going on, the political situation in Styria deteriorated. In December 1596, Archduke Ferdinand, a devout Catholic, became the ruler of Styria. At first, he moved slowly to reform (or counter-reform) the state more to his liking, but after a few months the Protestant community, upset by changes in taxation which favoured the Catholics at their expense, and by other ‘reforms’, submitted an official list of complaints about their treatment under the new regime. This was a big mistake – probably the very response that Ferdinand had been trying to provoke, so that he could represent the Protestants as unruly troublemakers. After a visit to Italy in the spring of 1598, when he had an audience with the Pope and visited holy shrines, Ferdinand came back determined to wipe out the Protestant influence in Styria. In September, an edict was published telling all Protestant teachers and theologians to leave the state within two weeks or convert to Catholicism. There was no choice but to obey, and Kepler was among the many ejected Lutherans who took refuge in neighbouring states – although most left wives and families behind in the hope that they would be allowed to return. Out of the entire contingent of refugees from Graz, however, Kepler alone, for reasons that are not entirely clear but may have owed much to his increasing stature as a mathematician, was allowed back within a month. After all, in addition to his teaching post he was the district mathematician, a post which required its holder to live in Graz (the Archduke could, though, have simply sacked him and appointed another district mathematician). But the severity of the conditions Kepler now had to live under is highlighted by the fact that when his baby daughter died and he evaded the ceremony of last rites, he was not allowed to bury the infant until he had paid a fine for this omission.

In 1599, when the situation in Graz was becoming intolerable for Kepler, Tycho was establishing himself some 320 kilometres away near Prague, where people were free to worship in their own manner. In January 1600, an offer that was to transform Kepler’s life came along. A Styrian nobleman called Baron Hoffman, who was impressed by Kepler’s work and liked the mathematician, was also a Counsellor of the Emperor, Rudolph II, and had met Tycho. He had to go to Prague on court business, and offered to take Kepler with him and introduce him to Tycho. As a result, the first meeting of the two men who were between them to lay the foundations of scientific astronomy took place at Benatky Castle on 4 February 1600. Tycho was now 53, Kepler 28. Tycho had the greatest body of accurate astronomical data yet assembled, but was tired and in need of help to analyse the material. Kepler had nothing but his mathematical ability and a burning zeal to unlock the mysteries of the Universe. It might seem a marriage made in heaven, but there were still hurdles to be overcome before Kepler could achieve the breakthrough that made him a key figure in the history of science.

Although Kepler had intended paying a fairly brief visit to Tycho at this time (he had left his wife and stepdaughter behind in Graz and had not resigned his posts there), it became an extended sojourn. The impoverished Kepler desperately needed an official post with an income so that he could work with Tycho, and he equally desperately needed to get his hands on the data, which Tycho doled out only in driblets, cautious about giving a relative stranger a free hand with his life’s work. Tycho’s extensive entourage and the construction work going on at the castle to turn it into an observatory made it difficult for Kepler to settle down to work anyway, and he inadvertently offended one of Tycho’s key assistants, who had been struggling with the problem of calculating the orbit of Mars, by offering to take over the task (an offer interpreted as an arrogant gesture by Kepler, setting himself up as a superior mathematician). Realizing that Tycho would never part with a copy of his data that he could take away to work on at home, and that the only way to get to grips with the puzzle was to stay for a year or more, Kepler (who was also well aware that his mathematical skills were second to none) drew up a list of his requirements if he were to be able to stay at the castle. Kepler gave the list to a friend, asking him to mediate with Tycho – but Tycho got hold of the list itself and took exception to what he saw as Kepler’s high-handed demands, even though he had, in fact, been negotiating with Rudolph to obtain an official post for Kepler. Eventually, things were smoothed out to the point where Tycho offered to pay Kepler’s moving expenses from Graz and assured him that the Emperor would come through with a paid position soon.

In June 1600, Kepler returned to Graz to try to sort out his affairs there – only to be confronted with an ultimatum from the city officials, tired of his long absences, who wanted him to go to Italy and study to be a physician, so that he would be more useful to the community. Before Kepler had time to make any decision, a deterioration in the religious situation made the decision for him. In the summer of 1600, all citizens of Graz who were not already Catholics were required to change their faith at once. Kepler was among sixty-one prominent citizens who refused to do so, and on 2 August he was dismissed from both his posts and, like the other sixty, given six weeks and three days to leave the state, forfeiting virtually all of what little property he had. Kepler wrote to the only two good contacts he had, Maestlin and Tycho, asking for help. Tycho’s reply came almost by return, assuring him that negotiations with the Emperor were going well and urging that Kepler should head for Prague at once, with his family and what goods he was allowed to take.

The family arrived in the stinking, unhealthy city of Prague in mid-October, and were housed by Baron Hoffman through a winter which saw both Johannes and Barbara severely ill with fever, while their limited supply of money diminished rapidly. Still with no appointment from the Emperor, in February 1601 the Keplers moved in with Tycho’s household at a new residence provided by Rudolph for the astronomer. Their relationship remained uneasy – Kepler unhappy at being dependent on Tycho, Tycho unhappy with what he saw as Kepler’s ingratitude. But eventually Kepler was formally introduced to the Emperor, who appointed him as Tycho’s official (and paid!) assistant in compiling a new set of tables of planetary positions which was to be called, in the Emperor’s honour, the Rudolphine Tables.

At last Kepler’s position had been regularized, although Tycho continued to dole out his wealth of data in penny packets, as and when he thought Kepler needed it, rather than giving him free access. It was hardly a close and friendly relationship. But then, on 13 October, Tycho was taken ill. After ten days when he was frequently delirious and close to death, and heard to cry out on more than one occasion that he hoped he should not seem to have lived in vain, on the morning of 24 October his mind cleared. With his younger son and his pupils, as well as a visiting Swedish nobleman in the service of the King of Poland, gathered around what was obviously going to be his deathbed, Tycho handed over the task of completing the Rudolphine Tables, and with it the responsibility for the vast treasury of planetary data, to Kepler – although he urged him to use the data to demonstrate the truth of the Tychonic model of the world, not the Copernican model.

Tycho’s mind was certainly clear at that point, as he realized that for all their disagreements, Kepler was the most able mathematician in his entourage, the person most likely to make best use of Tycho’s data and to ensure that, indeed, he had not lived in vain. He died soon after making this bequest of his life’s work to the stunned younger man, who only weeks before had been a penniless refugee. Kepler must have been even more stunned a couple of weeks later to be appointed as Tycho’s successor as Imperial Mathematician to the Court of Rudolph II, with responsibility for all of Tycho’s instruments and unpublished work. It was a far cry from his early life in Germany. Although his life would still not be easy, and he would often have trouble getting his full salary out of the Emperor, at least Kepler would be able, at long last, to get to grips with the puzzle of planetary motion.

Kepler’s work during his years in Prague was hampered by many factors. There were the continuing financial difficulties; there was interference from Tycho’s heirs who were both eager to see the Rudolphine Tables and Tycho’s other posthumous publications in print (not least in the hope of getting money from the books) and concerned that Kepler might distort (in their view) Tycho’s data to lend credence to Copernican ideas; and there were his duties as Imperial Mathematician (meaning Imperial Astrologer), requiring him to spend much of his time in what he knew to be the fatuous task of advising Rudolph on the significance of heavenly portents for the prospects of war with the Turks, bad harvests, the progress of the religious troubles and so on. In addition, the calculations themselves were laborious and had to be checked and rechecked for arithmetical slips – surviving pages of Kepler’s interminable calculations show sheet after sheet packed with arithmetical calculations of planetary orbits, a labour almost unimaginable in these days of pocket calculators and portable computers.

Not surprisingly, it took years to solve the riddle of the orbit of Mars, with Kepler moving in stages away from the idea of a perfectly circular orbit centred on the Sun. First, he tried an offset (but still circular) orbit, so that Mars was closer to the Sun in one half of the circle than the other – this matched up to some degree with the discovery that Mars moved faster in one half of its orbit (the half nearer the Sun). Along the way, Kepler made the now seemingly obvious, but then highly significant, step of carrying out some of his calculations from the perspective of an observer on Mars, looking at the Earth’s orbit – a huge conceptual leap which presages the idea that all motion is relative. It was actually while still working with his ‘eccentric’ circular orbit, in 1602, that Kepler came up with what is now known as his second law – that an imaginary line joining the Sun to a planet moving in its orbit around the Sun sweeps out equal areas in equal times. This is a precise way of expressing just how much faster the planet moves when it is closer to the Sun, since a shorter radius line has to sweep across a bigger angle to cover the same area that a longer radius line sweeps out when moving across a smaller angle. It was only after this discovery that Kepler realized (after trying out other possibilities) that the shape of the orbit is actually elliptical, and in 1605, having been distracted from the task by other work, he came up with what is now known as his first law, that each planet moves in its own elliptical orbit around the Sun, with the Sun at one of the two foci (the same focus for each of the planets) of the ellipse. With those two laws, Kepler had done away with the need for epicycles, equants and all the complicating baggage of earlier models of the Universe, including his own mystical idea of nested solids (although he never accepted this).

Although news of Kepler’s discoveries spread, the full discussion of his ideas didn’t appear in print until his book Astronomia Nova was published in 1609 – publication was delayed by printing problems and lack of finance. But even the publication of the book did not bring the kind of instant acclaim from his peers that you might expect. People didn’t like the idea of elliptical orbits (many people still had not accepted that the Earth was not at the centre of the Universe), and only a skilled mathematician could appreciate that Kepler’s model was not just another piece of mystical thinking (like his nested solids or Tycho’s model) but was securely founded on observational fact. It’s no surprise, really, that Kepler only achieved the stature he deserves in the eyes of historians after just such a mathematician, Isaac Newton, used Kepler’s laws in combination with his own theory of gravity to explain how the planets moved in elliptical orbits. Indeed, in his own time, Kepler was more famous as an astrologer than as an astronomer, although the distinction between the two was rather blurred. This is highlighted by one of the distractions from his planetary work, which occurred in 1604, when another ‘new’ star, as bright as the planet Jupiter, appeared in the sky during the summer and remained visible to the naked eye until well into 1606. To most people, this was an event of dramatic astrological importance, and Kepler had to interpret its significance as part of his duties as Imperial Mathematician. Although judiciously noncommittal about the implications of the event in his report to the Emperor, Kepler stuck his neck out sufficiently to suggest that in spite of its brightness the star must be at the same distance as the other stars, and was not a phenomenon in the region of the Universe occupied by the planets. Like Tycho before him, he saw the supernova as undermining the Aristotelian notion of literally fixed and eternal stars.

Not all of Kepler’s ‘distractions’ from his planetary work lacked scientific significance. Also in 1604, he published a book about optics, analysing the way the eye works by refracting light rays that enter the pupil to focus them on the retina, so that all the rays coming from a single point on an illuminated object are focused at a single point on the retina. He then used this idea to explain that some people have bad eyesight (clearly a subject close to his heart) because imperfections in the eye cause the rays to be focused at a point either in front of or behind the retina – and he went on to describe how eyeglasses worked to correct these defects, something nobody had previously understood, even though glasses had been used for more than 300 years on an empirical basis. After Galileo applied the telescope to astronomy and news of his discoveries spread, Kepler developed his ideas about optics to explain how the telescope works. His scientific interests could be thoroughly down-to-earth, not just concerned with the heavenly spheres.

The years following the supernova saw a deterioration in the political and religious situation in central Europe, as the rival religious groups formed the political alliances which were to become involved in the Thirty Years War. Apart from the impact it had on the rest of Kepler’s life, this struggle is significant in the history of science since the turmoil in central Europe, combined with the suppression of Galileo’s ideas by the Catholic Church, were at least contributory factors in stunting the growth of scientific ideas in the region and ensuring that the full flowering of the seed that Kepler planted took place in England, where (in spite of the Civil War) there was a more settled academic environment in which people like Newton could work.

In 1608, several Protestant states joined together as the Protestant Union, while their rivals formed the Catholic League the following year. Rudolph was by now a semi-recluse, obsessed by his art treasures, and distinctly odd, if not completely mad. Even in peacetime, he was in no condition to rule the Holy Roman Empire effectively (in so far as any Emperor actually did rule this disparate collection of states), he had run out of money and power gradually passed into the hands of his brother, Matthias, who became Emperor when Rudolph died in 1612. Kepler had long seen which way the wind was blowing and sought an appointment at his old University, Tübingen, but was rejected out of hand because of his unorthodox religious beliefs. At the same time, there were troubles at home. In 1611, Barbara became ill with epilepsy and one of their three children died of smallpox. Anxious to get out of Prague before everything fell apart politically, Kepler travelled to Linz, where he applied for a job as district mathematician and was accepted in June. But on hurrying back to Prague to make arrangements for the move, he found his wife seriously ill once again. She died of typhus a few days after his return. Depressed and uncertain about his future, Kepler lingered in Prague until Rudolph died, when, to his surprise, Matthias confirmed him in the post of Imperial Mathematician, offered him an annual salary (not that Kepler would ever see much of it), but gave him leave to go to Linz and take up the post there as well. Leaving his remaining children with friends for the time being, Kepler, still only 40 years old, set off on his travels again.

Even in Linz, though, his troubles continued. That part of Styria was firmly in the grip of the extreme orthodox Lutheran Church; the chief priest was a Tübingen man who knew of Kepler’s nonmainstream views and refused to allow him to receive Holy Communion, a source of deep distress to Kepler, who was profoundly religious, albeit in his own way. Repeated appeals to the church authorities failed to resolve the situation, but took up time that Kepler might have spent on his planetary work. He also had his duties as district mathematician, and he soon remarried, a young woman of 24 who bore him six children, three of whom died in infancy. Kepler was also involved in religious work of another kind, using an eclipse of the Moon recorded in Herod’s time to show that Jesus had actually been born in 5 BC, and he was involved in calendar reform (it was only in 1582 that Pope Gregory XIII had introduced the modern calendar, and many states in Protestant Europe were reluctant to make the change). The greatest distraction, though, came in the years after 1615, when Kepler’s mother was accused of witchcraft. To put the seriousness of this in perspective, that year six so-called witches were burned in the town where she was now living, Leonberg. This was not a situation that Kepler could ignore,⁹ and over the next few years he made repeated visits to Leonberg and was involved in lengthy petitions to the authorities on her behalf while the threat of a trial hung over her. It was only in August 1620 that the old woman was finally arrested and imprisoned. Although she was tried later that year, the judges found that there was insufficient evidence to convict her, but enough to cast doubt. She was held in prison until October 1621, when it was decided that she had suffered enough and was released. She died six months later.

In view of these particular troubles, and his troubled personal life in general, it is ironic that one of Kepler’s last great works carried the title Harmonice Mundi (Harmony of the World), although, of course, it referred to the world of the planets, not to the troubled Earth. It was in that book (mostly a mystical volume of no scientific significance) that he described how, on 8 March 1618, the idea that has become known as Kepler’s third law came to him, and how it was completed later that year. The law relates the time it takes a planet to go around the Sun once (its period, or year) to its distance from the Sun in a very precise way, quantifying the general pattern that Copernicus had discovered. It says that the squares of the periods of any two planets are proportional to the cubes of their distances from the Sun. For example (using modern measurements), Mars is 1.52 times as far from the Sun as the Earth is, and 1.52³ is 3.51. But the length of the ‘year’ on Mars is 1.88 times the length of the year on Earth, and 1.88² is 3.53 (the numbers don’t quite match because I rounded them off to two decimal places).

Harmonice Mundi was published in 1619, by which time the Thirty Years War was in full swing. Because of difficulties caused by the war, and his mother’s trial for witchcraft, the other great work published by Kepler around this time, his Epitome of Copernican Astronomy, appeared in three volumes, produced in 1618, 1620 and 1621. As well as boldly making the case for the Sun-centred Universe of Copernicus, this more accessible book brought Kepler’s ideas to a wider readership, and in some ways signalled the end of his great contributions to astronomy. But there was still one outstanding commitment to be resolved. Thanks in no small measure to the invention of logarithms by John Napier (1550–1617) in England, which had recently been published and greatly eased the burden of arithmetical calculation for Kepler, the Rudolphine Tables were at last published in 1627 (delayed by war, riots and even a siege of Linz), ending Kepler’s obligations to the Holy Roman Empire. The tables made it possible to calculate the positions of the planets to an accuracy thirty times better than the tables Copernicus had compiled, and remained the standard used for generations. Their value was highlighted in 1631, when the French astronomer Pierre Gassendi observed a transit of Mercury (when Mercury passes in front of the Sun), which had been predicted by Kepler using the new tables. This was the first transit of Mercury ever observed.

Printing wasn’t the only part of Kepler’s life disrupted by the war. In 1619, Ferdinand II had become Emperor after Matthias died, and this was the same fervently Catholic Ferdinand who had caused Kepler so much grief in Styria earlier in his career. Having already been persecuted in Linz by his own Lutheran Church for not being sufficiently orthodox, after 1625 the changing political situation under Ferdinand brought Catholic dominance across all of Austria, and now he was persecuted for being too Lutheran. There was no longer any prospect of him retaining his court position unless he converted to Catholicism, and this he still would not contemplate (although it seems that Ferdinand was well disposed towards Kepler personally and would have been happy to have him back in Prague if he would even pay lip service to such a conversion). In 1628, Kepler managed to secure a position with the Duke of Wallenstein, a man who tolerated all forms of religious worship (provided they were Christian) and who never made a move without consulting his astrologers. He knew Kepler from his time in Prague, when he had cast a horoscope which, in the eyes of the Duke, was remarkably accurate in its prophecies. Wallenstein seemed an ideal benefactor and protector, a powerful man whose positions included commander of the army for Ferdinand.

The Kepler family arrived in the Silesian town of Sagan to start their new lives in July 1628. The best thing about the new job was that Kepler was paid regularly. The most curious is that he had time to complete one of the first science-fiction stories, Dream of the Moon. The most unfortunate is that soon after he arrived, Duke Wallenstein decided to go along with the Counter Reformation in order to curry favour with the Emperor, and although Kepler, as an employee of the Duke, was exempt from the new laws that were promulgated, once again he saw his Protestant neighbours ruined and living in fear. In spite of his efforts to please the Emperor, in the summer of 1630 Wallenstein fell from favour and was dismissed from his key post as commander of the army. Once again, Kepler’s future looked uncertain, and he needed to draw on every resource he had in anticipation of another move. For some time he had been trying to get his hands on some money that was owed to him in Linz, and he was summoned to a meeting with the authorities there to settle the matter. In October, he set out from Sagan to keep this appointment (for 11 November), travelling slowly via Leipzig and Nuremberg as far as Regensburg, where he arrived on 2 November. There, he was struck down by a fever and took to his bed. On 15 November 1630, a few weeks short of his fifty-ninth birthday, Kepler died. He was a man of his time, poised between the mysticism of the past (which even coloured his own thinking about the Universe) and the logical science of the future, but whose stature as a voice for reason stands even higher in the context of a world where princes and emperor’s still depended on the prognostications of astrologers, and where his own mother was tried for witchcraft. At the same time as Kepler was carrying out his great work, an even more powerful voice of scientific reason was being heard further south in Italy, where although there was just as much superstition and religious persecution as in central Europe, at least there was some measure of stability and the persecution always came from the same Church.

^1.Quoted by Dreyer, from Gassendi’s biography of Tycho, first published in 1654, which drew on Tycho’s personal papers.

^2.Some astronomers now think that a series of similar conjunctions at the time of the birth of Jesus may have been the phenomenon known as the ‘star of Bethlehem’.

^3.Telling the time accurately was, of course, another big problem in the 1560s, long before the development of accurate clocks – one of the many examples of the interdependence of science and technology.

^4.We now know that there are two kinds of ‘new star’, one bright and relatively common, one very much brighter still and much rarer. The super-bright novae are called, logically enough, supernovae. The new star of 1572 was actually one of the super-bright objects, and is now regarded as a supernova. But what mattered most in Tycho’s day was not its brightness but its newness.

^5.A conjunction is when one astronomical object moves in front of (or behind) another; a solar eclipse is a conjunction in which the Moon passes in front of the Sun.

^6.‘Appeared’ in so far as printing of at least a large part of the book took place on Hveen. But only a few copies were circulated to Tycho’s contacts at that time. Full publication did not take place until 1603, under the editorship of Johannes Kepler.

^7.Quoted by Dreyer. Other quotes in this chapter from the same source, unless otherwise specified.

^8.Quoted by Shapin.

^9.Apart from his natural feelings for his mother, if she were convicted of witchcraft he would be unlikely to be able to hold on to his Imperial appointment.