Tycho and Kepler

by Kitty Ferguson

  Figure 12.3: A drawing of the arrangement of the planetary orbits and the five Platonic solids, according to Kepler’s polyhedral theory, from Kepler’s Mysterium.

  Likewise these five perfect solids seemed to dictate the distances apart these planets must orbit. In other words, just as, in the drawing Kepler had made for his class, the triangle dictated the size of one circle in relation to the other, he was now thinking that the requirement of fitting a cube between the sphere of Saturn and the sphere of Jupiter dictated how far apart those spheres must be. A tetrahedron must in turn dictate how the size of the sphere of Jupiter compares with the size of the sphere of Mars—and so forth.

  Kepler proceeded to test this idea about God’s geometric logic against Copernican theory and the available observational records “to see whether this idea14 would agree with the Copernican orbits, or if my happiness would be carried away by the wind.” To his joy and awe, “within a few days everything worked, and I watched as one body after another fit precisely into its place among the planets.” If only he had access to better observations, to be certain! Indeed, if only he could study the best observations in the world and could test his theory against them. The best observations in the world were those of Tycho Brahe.

  The months that followed marked a change in the focus of Kepler’s thinking. He had considered himself mainly interested in the big questions regarding the deep, underlying truths. Now, to find out whether his answers to some of those questions were correct, he had to turn his attention to mathematical minutiae. His earlier mathematical and astronomical training seemed sorely inadequate to the task—after all, he had judged it inadequate even for teaching school—and he realized that stupendous mathematical obstacles lay ahead of him if he was to put to rest the disturbing doubts that followed almost immediately on his elation about what he had found. In August 1595 he wrote to Mästlin for advice and help. In that letter he first called his new idea his “polyhedral theory.”15 Mästlin’s replies were cautious but full of approval and excitement.

  In October Kepler reported to Mästlin that he had decided to write a book. It was clear now why God had interrupted his theological studies and sent him into what seemed such a meaningless exile in Graz. “Just as I pledged myself to God,”16 he told Mästlin, “so my intention remains. I wished to be a theologian, and for a while I was anguished. But now, behold, God is glorified also in astronomy through my work.” God, he also wrote, “wants to be known from the Book of Nature.”

  Kepler hoped that by the time he finished writing his book, he would be able to answer another of the questions he had been pondering: Why each of the planets took the particular length of time it did to complete an orbit of the Sun. This length of time is called a planet’s period. Kepler had learned as a student that the planets nearer the Sun have shorter periods than those farther away.

  The first part of the explanation for this was obvious. A planet farther from the Sun has to travel a greater distance to get all the way around its orbit, just as a runner in the outside lane of a racetrack has to run farther to complete a lap than a runner in an inner lane. If all the runners in this celestial race were moving at the same speed, those farther out would take longer to complete a lap. But Kepler thought that the amount by which planets farther from the Sun lagged behind was greater than could be accounted for in this simple way. It seemed the runners in the outside lanes really were slower runners, not merely handicapped by their lane position. Pondering why this should be so, Kepler began to speculate about a possible force, resident in the Sun, that caused the planets to whirl around it. A planet closer to the Sun would feel more of the force than one farther away.

  Kepler worked this idea into a formula: The increase in the length of period from planet to planet will be twice the difference of their distances from the Sun. This formula showed planetary distances that were not far off from those he had derived from his theory of the polyhedrons, but it was not correct, as Kepler himself later realized.

  In every spare moment he had that autumn and in the beginning of the bitter winter of 1596, while still teaching and fulfilling the duties of district mathematician, Kepler continued to work on his book. He thought of still more questions: Was there any meaning to the particular arrangements of the polyhedrons? Was there a reason, for instance, that the cube must be the outermost, followed by the tetrahedron? Kepler was sure there had to be a reason, and he tried to discover it, while at the same time continuing to think about the force in the Sun that might be whirling the planets.

  When he was putting the final polish on his manuscript, Kepler’s thoughts focused more on the way a single planet moves in its orbit. Both Ptolemy’s and Copernicus’s models took note of the way a planet speeds up as its orbit brings it nearer the Sun and slows down as it moves farther away. It occurred to Kepler that this could be easily explained in the Copernican system by the idea that the closer the planet comes to the Sun, the more it feels the Sun’s whirling force. The speeding up and slowing down were much more difficult to explain in Ptolemaic theory, with the planets orbiting the Earth. This seemed another good reason to think that Copernicus had been right about what is in the center.

  Mästlin was not pleased when he heard about this idea of the force that moves the planets. He suggested it might “lead to the ruin17 of astronomy,” as in his view Kepler was failing to respect that delicate dividing line between “physics” (which concerned itself with “causes,” physical reasons why the universe operates as it does, and the nature and structure of the universe) and the use of mathematics to produce theories of planetary motion. Kepler was mixing the two areas of study by suggesting that physics (i.e., the whirling-force explanation) could explain the mathematics of a planetary system. Interestingly, Mästlin and Kepler were two of the very few scholars in Europe who should have recognized that Copernicus himself had trampled on that dividing line, from both directions, by suggesting that his mathematical theories revealed a fundamental truth about the structure of the universe—that it is Sun-centered—and that this fundamental truth made sense of his mathematical theories.

  In January 1596 Kepler’s studies were interrupted by the news that both his grandfathers were seriously ill, and in February he took a leave of absence from his school and traveled home to the duchy of Württemberg. Old Sebald, his father’s father, in whose house Kepler had been born, died during Kepler’s visit.

  Kepler welcomed the opportunity to visit Tübingen to discuss his book with Mästlin in person. Such a publication, he pointed out to his mentor, would improve his stature as a scholar and make his position in Graz more secure. It seemed ironic to him that a year earlier he had been eager to leave that position as soon as possible.

  Kepler also opened negotiations with a printer in Tübingen who, on the enthusiastic recommendation of Mästlin, agreed to publish Kepler’s book. The only stipulation was that it be approved by the university senate. The senate, though unperturbed about approving the publication of a flagrantly pro-Copernican book, wanted two changes. First, Kepler should explain Copernicus’s hypotheses and his (Kepler’s) own discovery in a more understandable, popular style. Second, Kepler should remove a chapter in which he reconciled the idea of a Sun-centered universe with biblical passages that could be interpreted as supporting either Copernicus or Ptolemy. Kepler felt strongly about this chapter. He had settled in his own mind that Copernican astronomy was not incompatible with Scripture, which, he had concluded, was intended to speak to people living on Earth who had no knowledge of the true working of the cosmos. Furthermore, it was not the purpose of the Scriptures to teach them about these matters. So the Scriptures deliberately spoke in words that would make sense to such people. As he would put it later, in the introduction to another book, Astronomia Nova, “What wonder then18 if the Scripture speaks according to man’s apprehension, at such time when the truth of things doth dissent from the conception of all men?” It seemed essential to Kepler that a book showing that Copernicus had been ri
ght should bring its readers along on this point. Without that, the book fell short of the glorification of God that he intended it to be. Nevertheless, he bowed to the senate’s judgment that, though he might be right, interpreting Scripture was not in his bailiwick.

  Kepler also visited Stuttgart during his leave, to pay his respects to the duke of Württemberg, who had earlier supported his education and then so graciously allowed him to move to Graz. This was Kepler’s first experience of castle life. He had the temerity to ask for and was given a seat at the Trippeltisch, the dining table for ducal officials who were not of the highest echelon. For Kepler it was a major achievement. Gripped by (as he put it) “a childish or fateful19 desire to please princes” (a state of mind Tycho Brahe would have been wise to emulate at this time), Kepler presented to the duke a plan to create an elaborate model of the solar system incorporating the five solids. Whether it would be built was not settled on this occasion. Negotiations and trial runs dragged on for several years after Kepler had gone back to Graz, with him diverting much of his scarce time to providing detailed proposals, drawings, and even a paper model. At one stage, the plan was to create an enormous punch bowl. Each space between the different planetary spheres would contain a different beverage, and guests could fill their glasses from small faucets spaced around the rim, connected by means of hidden pipes and valves with the appropriate spheres. The duke finally decided to advance money to have the model fashioned in silver, but the project got bogged down in problems with the silversmith, and it was never completed.

  WITH MUCH OF KEPLER’S TIME during his visit in Germany spent “pleasing princes” in Stuttgart, and with Tübingen proving even more hospitable—for not only Mästlin but others in the university had heard of Kepler’s new idea—Kepler’s absence from Graz stretched far beyond the two months he had requested. He stayed away for seven months, which almost proved disastrous to another project in which he was currently engaged and which he had left in the hands of representatives back in Graz—arranging for his marriage. The December before he had gone away, he had met Barbara Müller, the eldest daughter of a prosperous mill owner named Jobst Müller, whose estate, Mühleck, was about two hours’ journey south of Graz.

  It was not wise for a prospective suitor to disappear for so long. Much as Kepler’s scholarly accomplishments may have impressed his former professors at Tübingen and stood him in good stead at the duke’s castle in Stuttgart, they did not make him a prime candidate for husband or son-in-law in the eyes of Jobst Müller. In spite of Müller’s misgivings, however, the intermediaries negotiating on Kepler’s behalf had some success. In June 1596, five months after Kepler left for Germany, they urged him to return to Graz and pause only long enough in Ulm to have his and his fiancée’s wedding wardrobes made “with very good silk fleece20 or at least the best double taffeta.”

  Kepler dawdled three months longer and then came back, expecting a warm welcome and congratulations all round. Instead, he learned there was to be no wedding. His prolonged absence had given Herr Müller time and cause to reconsider once again, and he was now convinced that his daughter could do better. Kepler was sorely disappointed, but he could not much blame Müller and mentioned frankly that one Stephan Speidel, who may have been working against the match for his own selfish reasons, probably only wanted to see Barbara better provided for. Though Kepler had exclaimed that when he met Barbara she had “set [his] heart on fire,”21 theirs does not seem to have been a heated romance.

  Nevertheless, that autumn, Kepler doggedly continued his suit for Barbara’s hand. He may not have been ardent, but he was stubborn. The rector of his school spoke in his favor, and when, in a moment of discouragement, Kepler asked the church government either to free him from his promise to Barbara or to act on his behalf, that body also chose to influence the bride and her family to accept his proposal. Herr Müller, impressed by the authority of the church and skittish about public mockery, agreed to the union again in January 1597, and plans were set in motion for an April wedding.

  As Kepler had recognized, Müller’s concern for his daughter was not unreasonable. It was far from obvious that Kepler had accomplished anything of value. He had no prospect of ever being other than a poorly paid teacher, and he could promise Barbara and her young daughter by a former marriage little by way of financial support. Barbara was twice a widow. Her first husband had been a wealthy cabinetmaker and her second a district paymaster or clerk, a respected man until disreputable dealings came to light at his death. Though Kepler requested and received a pay increase on the grounds that he would no longer require lodging in the school, he wrote to Mästlin rather pitifully as the wedding date approached, “My assets are such22 that if I were to die before a year is up, hardly anyone could leave worse conditions behind at his death. I must make great outlays from my own pocket, for it is the custom here to celebrate a marriage in a showy fashion.”

  Kepler continued his letter to Mästlin in a vein that indicates how ambivalent he was about the marriage plans. Barbara’s father and Barbara herself were wealthy. The alliance gave Kepler financial security and brighter prospects. It also chained him to Graz. He wrote,

  It is certain23 that I am tied and fettered to this place no matter what becomes of our school. For my bride has properties, friends, and a wealthy father here. It seems that I would not, after a few years, need any salary, if that would suit me. However, I could not leave the land unless a public or private misfortune befell. A public one if the land were no longer safe for a Lutheran or if it were further pressed by the Turk . . . a personal misfortune if my wife were to die. Thus a shadow hovers over me. Yet I dare not ask more of God than He in these days allots to me.

  Kepler reported that the wedding would take place under ominous constellations. The best that could be said was that the stars predicted “a more agreeable than happy marriage, in which, however, there was love and dignity.”

  13

  DIVINE RIGHT AND EARTHLY MACHINATION

  August 1596–June 1597

  THE PREVIOUS AUGUST, while Johannes Kepler stretched his stay in Germany into its sixth month, Tycho Brahe went to Roskilde Cathedral, location of the belatedly repaired chapel, for the coronation of Christian IV of Denmark. The child whose wishes Tycho had taken too lightly had come of age and was now king. Tycho had suffered recent social embarrassment over Magdalene’s ill-fated betrothal, but he nevertheless made a splendid showing at the festivities. He wore the golden chains of the Order of the Elephant (a symbol that was prominent in the Chapel of the Magi) and medallions with portraits of two kings. The Brahe family was much in evidence. Tycho’s brother Steen bore the royal orb. All the members of the Rigsraad held the crown to place it on Christian’s head, symbolizing that the highest power lay not with the king but with the aristocratic oligarchy.

  In truth, the old symbolism had almost run its course. A new age was dawning, and it would not benefit Tycho’s relatives or other great noble families. The coronation oration, delivered by Bishop Peter Winstrup, celebrated a philosophy of government favored by the new king and his closest advisers, that kings rule not by the election or consent of any oligarchy but by divine right. So far that could be dismissed as only coronation rhetoric. In the days following the coronation Uraniborg seemed like its old magnificent self again and likely to endure forever, as numerous foreign guests who had come for the festivities visited Tycho. He played the magnanimous noble host and showed off the splendors of his home. Nevertheless, he and his relatives were watching the new regime with trepidation, braced for possible trouble ahead.

  Scarcely a month after the coronation, the ax began to fall. Christian, conflicting philosophies of government notwithstanding, did not have complete power that could be exercised without consulting the Rigsraad, but one thing that was in his power was the transfer of fiefs from one noble to another. As part of a general reorganization, he took the Norwegian fief of Nordfjord from Tycho and gave it to the lord-lieutenant of Bergen.

 
Several times in the past that same fief had passed out of Tycho’s hands and then been restored to him when he petitioned the crown. He did so now, using the opportunity to send along a summary of his accomplishments at Uraniborg, a copy of his published astronomical correspondence, and a pamphlet with woodcuts of his instruments. Tycho’s petition spoke of the unfailing support King Frederick II had given this work and mentioned that the old king had intended to endow Uraniborg as a permanent research institute but was prevented by his death from doing so. Tycho even enclosed a copy of the declaration signed by the Rigsraad promising to advise Christian when he came of age to carry out his father’s will, placing Uraniborg eventually under the leadership of Tycho’s descendants.

  In spite of the unsettled political climate, Tycho had good reason to hope that Christian would honor the old king’s wishes and endow Uraniborg permanently. The chancellor to whom Tycho wrote had paid a pleasant visit to Hven, and his wife was a distant relative. Christian had clearly fallen in love with Uraniborg during his childhood visit. Tycho had, finally, repaired the chapel roof.

  However, the nineteen-year-old king was strong-willed, eager to exercise his own divine right, and in no mood to respect an expensive promise made so long ago by a father he had hardly known. He chose to regard Uraniborg as a relic of the past, run by an aging aristocrat who had become too proud and powerful to respond promptly to royal commands, who had too long treated regents and rulers as his equals, who had forgotten how to be adequately deferential.

  Christian’s shattering reply came to Tycho through the chancellor in January 1597: Tycho had to surrender the fief of Nordfjord, and that surrender could not be postponed. The king also did not choose to endow Uraniborg permanently. Though the letter ended politely with the promise that future requests would be received with pleasure, its message was clear. All Tycho’s efforts over many years to secure the future of Uraniborg and his children had come to naught. The documents and assurances he had collected were as worthless as his peasants’ old claim to own their land on Hven. It counted for nothing with Christian that Tycho had fulfilled his promise to Frederick to bring glory to Denmark, so that people of other nations would come there to “see and learn1 that which they could hardly acquire knowledge of in any other place.” Christian’s father had treated Tycho like a well-loved younger brother. The son regarded him as a wearisome elderly petitioner.