Tycho and Kepler

by Kitty Ferguson

  Kepler was not the colorless, drab individual that some authors and historians have made him out to be. He had enthusiasms in abundance. By his own report he, as a boy, “devoted [himself] wholeheartedly and energetically to games.” In his teens he “had a high opinion of sense of duty, self-control, and industriousness,” but “a man who is really useful has to have not only the power of good judgment but also ardor and passion.” Perhaps following that last maxim, “I didn’t obey reason until my twenty-sixth year” (the year he wrote these words).

  Earnestly but exuberantly religious, Kepler had a vivid and adventurous life of the mind. In his spare time, which was scarce, the teenage Kepler took pleasure in attempting to write original poetry in a variety of meters, imitating the ancient forms. He reveled in jokes and puzzles, loved allegories and riddles, liked to play with anagrams, was pleased with paradoxes. Purely for enjoyment, he tried to improve his memory by learning the longest psalms by heart and attempting to memorize all the examples in one of his grammar books. The way his mind flew quickly among various subjects was a joy to him, rarely a problem. In fact, all his life his writing continued to be full of peculiar and interesting leaps from one train of thought to another, leaving readers attempting to follow him puzzled by his mental track.

  Though Kepler may not have chosen to “obey reason,” he was a serious student, and he thought and prayed a great deal about the religious controversies and his private reactions to them. At Adelberg some of Kepler’s young teachers, fresh from Lutheran university at Tübingen and afire with their newly acquired learning, were particularly eager to refute the doctrine of the Holy Communion espoused by the Calvinists. Kepler stubbornly followed his usual practice of accepting little except what he had worked out for himself after listening carefully to the sermons or arguments, praying, and studying his Bible. He was approaching the awkward conclusion that the correct interpretation of the Bible was exactly the one he was hearing condemned by his instructors and from the pulpit.

  Kepler was particularly disturbed about the idea held by some that God damns the heathen who do not believe in Christ. That doctrine he could not accept, nor did he keep quiet about it. He also was so bold as to recommend peace between Lutherans and Calvinists, and claimed also to be “just to the Catholics,” setting a course that would have tragic consequences for him later, and that would, in fact, eventually leave him no choice but to appeal to Tycho Brahe for a job.

  In October 1587 Kepler became a registered student at the University of Tübingen, but the “Stift,” where he was to lodge as a scholarship student supported by the duchy of Württemberg, had no room available for that year. He remained for a third year at Maulbronn, as a “veteran,” and ended up taking his examination and completing his B.A. degree by examination the following September, though he had not yet attended a class at the university.

  WHILE KEPLER WAS a schoolboy, mastering subjects that he and others thought essential for his future, Tycho, with trial and error and his own superior inventive intellect as his teachers, continued to explore the frontiers of astronomy with a rigor that no one else considered essential. One splendid result of this effort were the great instruments of Hven, unique and unsurpassed among the astronomical instruments that predated the telescope.

  The first masterpiece Tycho produced in his own instrument shop was a giant globe2 that became the centerpiece of Uraniborg’s library. The instrument maker Schissler in Augsburg had begun to construct it under Tycho’s guidance in 1570, but Tycho had left Augsburg to join his dying father in Denmark before it was completed, and he did not see it until he returned five years later. By that time the wood had warped, and there were splits between the pieces.

  Nevertheless, Tycho had not forgotten the globe languishing in Augsburg, and in August 1576 he had the poor relic brought to Hven, where his artisans filled in the cracks and restored its shape “by inserting3 many hundred pieces of parchment.” Tycho allowed the globe to sit two years longer while he watched for seasonal changes in its wooden structure. Finally in 1578, satisfied that “it stayed completely spherical at every point,” he had it surfaced with brass sheets “with such great care and accuracy that one might believe the globe to be of solid brass.” After waiting another year to find out whether the globe would still stay completely spherical, he had the equator and the zodiac etched onto the brass “and divided each degree of these circles accurately into sixty minutes of arc by means of transversal points according to our custom.” By the time he had finished, his remark that he had the globe made “at no small cost” was an understatement.

  All this effort and expense were not merely to produce a decorative piece. The globe represented the celestial sphere and allowed one to view that sphere from the “outside.” Transforming trigonometrical coordinates, which was necessary if an astronomer knew the altitude and azimuth of a celestial object and wanted to calculate from them its declination and right ascension (see appendix 2), was a tedious undertaking in Tycho’s day. The globe made this process considerably easier.

  Tycho later included a drawing of this remarkable instrument (see color plate section) in his book Astronomiae Instauratae Mechanica, which shows the globe girdled by a platformlike ring resembling a ring of Saturn. The ring represented the horizon for an observer at Uraniborg. The circle seen outlining the perimeter of the globe was the meridian (see appendix 2). The globe rotated on an axis running from the north celestial pole (I) to the south celestial pole (K). There was another rulerlike strip (somewhat right of center in the drawing) running from the zenith (B) to the horizon, which was the equivalent of the curved edge of a quadrant. It allowed Tycho to measure altitude on the globe. Fixed at the zenith, it could be moved around the horizon at its other end to measure azimuth. Two other lines on the globe that are visible in the drawing were the equator (farthest to the left as it reaches near the top of the globe) and the ecliptic. The support for the globe, from the ground to the horizon ring, was about five feet high, and the globe itself measured almost six feet in diameter.

  Tycho proudly referred to his great globe as “a huge and splendid piece of work” and wrote that “a globe of this size, so solidly and finely worked, and correct in every respect, has never I think been constructed up to now . . . anywhere in the world. (May I be forgiven if I boast.)” It became the chief conversation piece of Uraniborg and the envy of visitors. He entered on it the positions of all the stars he had observed and cataloged—as they would appear in the year 1600. His goal was a thousand stars, “so that all the stars that are just visible to the eye were entered on the globe.” Defending the length of time it took him and his artisans to finish the globe and for him to catalog the stars and enter them on it—the task would eventually require about twenty-five years—Tycho used words that many have taken as a motto for all his work: “If it has been done well enough, it has been done quickly enough.”

  In the next two and a half years after the completion of the globe in 1580, Tycho and his artisans on Hven produced more large instruments, most notably two quadrants, inaugurated in 1581 and 1582. Tycho named the first his “large quadrant” and henceforth referred to the old quadrans mediocris orichalcicus azimuthalis as his “small quadrant.” The second was his “great mural quadrant,” an artistic as well as scientific masterpiece that more than any of his other instruments has come to symbolize Tycho Brahe.

  Tycho built the great mural quadrant4 into the structure of his house, using a section of wall constructed along an astronomically precise north-south line. The instrument, a solid brass arc six and a half feet in radius, five inches wide, and two inches thick, was mounted on the wall. On this quadrant the curved edge of the pie slice was nearer the observer. Movable sights were clamped onto the arc. The engraving Tycho later included in Astronomiae Instauratae Mechanica (see color plate section) shows them set near twenty and seventy-five, with one of Tycho’s assistants peering through the one near twenty. There was no physical connection (such as the alidade was in earli
er quadrants) between these near sights and the farther sight—the cylinder in the opening in the wall visible in the upper left of the engraving.

  Before 1587, the wall on which the quadrant was mounted probably remained blank. Then Tycho commissioned Steenwinkel, who had helped design and build Uraniborg, to paint scenes symbolizing Tycho’s palace and his work, framed by six arches. Steenwinkel’s painting showed the basement with its alchemical laboratory and furnaces, the library on the floor above it with the great globe, and the observatory above that. Hans Knieper, the finest landscape artist in Denmark, was working at Elsinore, and Tycho brought him to Hven to paint a distant landscape for the background, visible through the arches of the observatory level and above them. For the life-size portrait of himself, seated in the foreground within the arc with a dog at his feet, raising his arm to point at the front sight of the quadrant, Tycho commissioned Tobias Gemperle, a painter he had met during his 1575 European sojourn and brought to the attention of King Frederick. Frederick had named him court artist, and Tycho had previously commissioned him to paint the altar of St. Ibb’s Church. Tycho was extremely pleased with the portrait in the mural quadrant. “The likeness5 could hardly be more striking,” he wrote, “and the height and stature of the body is rendered very realistically.” He regarded the background mural as the artistic masterpiece of Uraniborg.fn1

  Tycho was also experimenting with armillaries, instruments consisting of arrangements of rings showing the relative positions of the various circles on the celestial sphere such as the meridian, the celestial equator, and the ecliptic. Tycho planned to do extensive work on the planets, and armillaries were particularly useful for calculating the coordinates involved in planetary observations. He had begun work in 1577 on a small model with only three inner rings.

  Figure 8.1: Tycho’s first armillary. Drawing from Astronomiae Instauratae Mechanica. The outermost ring represented the meridian (see appendix 2). The devices marked C and D represented the north and south celestial poles and are the points on the meridian ring on which the next smaller ring is attached. C and D could be raised or lowered along the meridian ring until they corresponded with the latitude of the place at which the observer was located, with B (from which hangs a plumb line) representing the zenith. The next smaller ring served to carry a slightly smaller ring representing the ecliptic, which carried a fourth ring for measuring latitude.

  IN THE EARLY 1580s, having spent considerable money, time, and ingenuity on producing by far the best instruments in existence, Tycho still knew he lacked the tools necessary for what he hoped to accomplish. As a case in point, his armillary tended to bend and flex unpredictably as the rings were adjusted to different positions. A smaller, lighter armillary would not give him fine enough readings, while a larger one would bend and flex even more. Tycho set his mind to solving these particular problems, and this time, as he had done when he designed his mural quadrant, he thought big and, at the same time, simple. He came rapidly to the conclusion that in order to accommodate a successful design he would need a ground-level observatory beyond Uraniborg’s perimeter wall.

  By 1583, Uraniborg was too crowded. Tycho and his assistants were stumbling over one another. Instruments already in use or in various stages of construction threatened to overflow the space available, and Tycho had not by any means stopped planning new instruments. The large ones he now had in mind would work much better with access to all 360 degrees of the sky, which neither Uraniborg’s large observatories nor the smaller satellites provided. Outside the perimeter wall, with some excavation, he could have the advantage of being able to build an amphitheaterlike structure around each instrument, allowing an observer to position himself on a level high above the base of the instrument. The shelter of the amphitheater would prevent gusts of winter winds from affecting sensitive readings, not to mention chilling the observer. Tycho also saw the auxiliary observatory as a way of separating his assistants and establishing better control over the accuracy of their findings. Some would continue to make observations from the castle, others from these new “cellars.” They would not get in one another’s way and would also not compare results and make adjustments to them before he had a chance to study findings that disagreed and think about the implications.

  There was a small rise in the landscape not far beyond the south corner of Uraniborg’s outer wall. Tycho decided that a structure there would not spoil the symmetry of the house or the gardens, and the wall and the house would block only an insignificant low portion of the northern heavens, the least interesting direction. He set the islanders digging again, and he constructed “with no small difficulty6 and expenditure, a subterranean observatory.” He christened it Stjerneborg, “Star Castle.”

  Figure 8.2: Tycho’s drawings of Stjerneborg, the partially subterranean observatory that he built outside the perimeter wall of Uraniborg, from Astronomiae Instauratae Mechanica.

  Stjerneborg (see color plate section) was designed with five great cellars or amphitheaters to house a giant armillary that figured largely in Tycho’s observational plans, a revolving quadrant, a zodiacal armillary, a large steel quadrant, and a four-cubit sextant. Each cellar had a roof that could be removed or swung aside. There was ample storage for other instruments as well, and space to use them. Tycho’s design also did not neglect his own comfort or that of his assistants. There was a “heating installation,” a bed for Tycho “when accidentally there were clouds and we could not enjoy a constant clearness of the sky,” and a second larger bed to be shared by others.

  Despite being purpose-built as an observatory that pushed the boundaries of what such a building should be and what it should allow its users to achieve, Stjerneborg was far from strictly functional7 in design and decor. Tycho and Steenwinkel drew plans with the same attention to symmetry, harmony, and detail that characterized Uraniborg itself. A significant difference was that Tycho was by this time much more preoccupied with his self-image as a man of stature and wealth, with classical roots, the equal of kings, the greatest of all living astronomers, occupying a preeminent place in history. Stjerneborg was laden with symbolism to convey this image. Above the entrance stood three elaborately carved lions with crowns on their heads. On the back of the portal an inscription in gold letters sang the praises of Tycho and his instruments. Beyond the entrance and several steps down from it was the warming room that gave access to the five round cellars, and this and other subterranean rooms were embellished with poems inscribed in gold letters. The warming room walls displayed seven portraits of astronomers from the ancients to Tycho, with an eighth portrait of a future astronomer named “Tychonides.” The message was clear: Tycho was the equal of the greatest astronomers in history, and he anticipated that Tychonides would come from his own lineage.

  Tycho was diverting some of the attention previously reserved for astronomy to promoting that image. He was eager for the stream of scholars, intellectuals, and highborn curiosity seekers, who regularly detoured in their travels to visit Hven, to recognize his greatness and also realize that, though his descendants could never be noble Brahes, the mantle of their father could fall onto their shoulders in a far more significant way.

  Tycho’s “great equatorial armillary” (figure 8.3) was destined to become the most famous of Stjerneborg’s instruments. Like the great mural quadrant inside the house, it was built into the building’s structure. The foundation for its axis was put in place in December 1584, but it was not until the following summer solstice that the massive instrument was ready for use.

  Figure 8.3: The great equatorial armillary8 as illustrated in Astronomiae Instauratae Mechanica. To find the position of a star, an observer stood on a tier of the amphitheater, behind the half circle (O) representing the celestial equator. Through the movable sight (R), which could be positioned anywhere along this half circle, he peered toward the axis pole (B) and moved the sight along the half circle until, looking through the slits of the sight, he saw the star on both sides of the axis pole. Rulerli
ke markings on the half circle indicated, from the new position of the sight, the right ascension of the star (distance in degrees east of the prescribed meridian established by the position of the Sun at the vernal equinox). In order to compare this finding with the right ascension of another star whose position was already known, two observers sighted from the half circle, one for each star. They learned the difference between the stars’ right ascensions by noting the distance on the arc between the new positions of the sights.

  To find a star’s declination (distance above the celestial equator), assistants pivoted the armillary on its axis until the large complete ring had one edge toward the observer and the other toward the star. There were two alidades—the “fan blades” that met in the center at a cylinder (E) with their other ends on the large ring. The drawing shows those ends at two positions on the ring, (F). Like hands on a clock, the alidades were fixed at the center and moved along the ring. Assistants moved one until, sighting along the alidade, the observer saw the star on both sides of the central cylinder (E). The new position of the sight indicated the declination of the star.

  To double-check an observation, Tycho gave the entire apparatus a half turn on its axis and used the other alidade for the same measurement. As he informed his readers, “the two values found9 should agree with each other.”

  It was difficult to see that the instrument was an armillary, for most of the familiar rings (compare with figure 8.1) seemed to be missing. Except for brass alidades (the two “fan blades” that ran from the center at E on Tycho’s drawing to the outer edge, marked F) and graduation strips to act as rulers on the rings, the great equatorial armillary was made of wood for easier handling and to minimize the distortions caused by the weight of metal. It pivoted on a hollow steel axle (the pole marked B in the drawing). At first glance, the entire apparatus looks to be strangely skewed from plumb, but take a globe of the world and tilt it so that Denmark is on “top” and the skew makes sense.