Tycho and Kepler (28 page)

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 idea
¹⁴
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 ruin
¹⁷
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 then
¹⁸
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 right 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 fateful
¹⁹
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.

W
ITH MUCH OF
K
EPLER’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 fleece
²⁰
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 such
²²
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.”