Tycho and Kepler

by Kitty Ferguson

  By the same token, in a stroke of insight, ancient astronomers realized that if the planets moved continually in smaller circles centered on the rim of a larger circle centered on Earth, the result would be the regularly occurring retrograde motion they were observing.

  The technical term in Ptolemaic astronomy for the small circle in which a planet moved was epicycle. The larger circle on which the epicycles turned (in figure 1.2, the inner circle—the radius at which the minicarousels are bolted to the floor) was the deferent. By adjusting the size, direction, and speed of the epicycles, astronomers could explain many irregularities they observed in the way the planets, Sun, and Moon move. A planet traveling in its epicycle would sometimes be closer to Earth and sometimes farther away, which explained apparent variations in its brightness. In Ptolemaic astronomy a planet’s sphere was just large enough for the planet to cartwheel along on its epicycles.

  Tycho, Kepler, and their peers at university also learned the use of the eccentric. With an eccentric, the planet (perhaps simultaneously traveling in an epicycle) orbited Earth, but the orbit wasn’t centered precisely on Earth. Its center was a point a small distance away from Earth.

  Figure 1.3: Devices of Ptolemaic astronomy: eccentric orbit, deferent, epicycle, and equant.

  Epicycles, deferents, and eccentrics were devices Ptolemy refined from earlier astronomy, but another, the equant, was probably his own invention. Many astronomers were uncomfortable with it, for it was not only complicated to use but also seemed to cheat a bit on the requirement of uniform motion. The equant was an imaginary point that Ptolemy used to rationalize a planet’s apparently slowing down and speeding up as it wheeled in its epicycles around the deferent. It was possible to establish mathematically that if one were able to view the heavens from the equant, the velocity of a planet would appear to be uniform, though from Earth or the eccentric center of the orbit it would appear to vary.

  Ptolemy combined these devices in a complex and highly successful model of heavenly motion. Without removing Earth from its position as unmoving center, his astronomy could, with a surprising degree of accuracy, predict and account for the changing positions of the Sun, the Moon, and the five planets that were known at that time. Fulfilling the hopes of centuries of scholars before him, Ptolemy was able to accomplish this feat entirely in terms of circles, spheres, and uniform motion.

  Students and scholars of Tycho Brahe’s and Johannes Kepler’s generations were also steeped from childhood in a worldview that far pre-dated Ptolemy: Nineteen centuries removed from its origin in ancient Greece, Aristotelian philosophy and cosmology still had an enormously strong hold on the thinking of scholarly and religious Europe. This worldview held that everything below the orbit of the Moon was subject to change, degradation, and decay, while the heavenly spheres beyond the Moon were a realm of unvarying, eternal perfection. Both experience and observation gave weight to these ideas. Before the telescope, there was little evidence to challenge the perfect immutability of the heavenly spheres. Nor was it possible to deny that things were different on Earth.

  This dichotomy had entered the thinking of European Latin-speaking scholars when the first Latin translation of Aristotle appeared in the twelfth century. These men knew nothing of Ptolemy, though the heritage from his astronomy was still flourishing in Islamic parts of the world. They came to revere Aristotle, instead, as the final authority on science and cosmology, and Aristotle’s cosmology, filtered through the understanding of these scholars, merged with medieval Judeo-Christian thought. Somewhat later, when Ptolemaic astronomy arrived in Latin Europe, there was a second merger. Scholars, who in both instances were all clergymen, put prodigious effort and much debate into reconciling the Bible first with Aristotle and later with Ptolemaic astronomy. To do so, they began to give the Scriptures a less literal, more metaphorical interpretation. What emerged over time was a coherent body of philosophical, scientific, and religious thought, with astronomy giving a visual, geometric structure to abstract medieval Judaism and Christianity. Aristotle’s picture of the degraded, changing, decaying nature of Earth and the pristine perfection of everything beyond the Moon was consistent with the Judeo-Christian view of fallen, lost humanity on Earth and the eternal, holy realms above.

  From the thirteenth century until the sixteenth, most educated Europeans accepted this worldview as reality. For them, astronomy seemed capable not only of describing and predicting planetary movement and providing a map of the cosmos but also of accurately describing the human condition, with men and women pitifully torn between the passions of the squalid, death-ruled Earth and the lure of the deathless, sacred heavens. In the fourteenth century, Dante gave this worldview eloquent poetic expression in his Divine Comedy, describing a journey downward through nine circles of hell toward the center of Earth, the most debased point in the universe, and a journey upward through the celestial spheres of the planets to reach the throne of God. It is no wonder that Melanchthon believed that the study of astronomy was essential to the clergy.

  Both young Tyge and the young Kepler found this picture compatible with all they knew of Earth and heaven. However, though both men remained devoutly religious all their lives and found no contradiction between their science and their belief, they would leave this primitive worldview in tatters.

  fn1 Information about Tycho’s childhood and youth is found in Tycho’s own later accounts and in Victor E. Thoren’s splendid scholarly treatment, The Lord of Uraniborg: A Biography of Tycho Brahe. Thoren was the leading Tycho Brahe scholar of the twentieth century.

  fn2 The significance of this event for Tycho was recorded by his first biographer, the early-seventeenth-century astronomer Pierre Gassendi.

  2

  ARISTOCRAT BY BIRTH, ASTRONOMER BY NATURE

  1562–1571

  TYCHO CELEBRATED HIS fifteenth birthday in December 1561. He had been at university for three years, and it was time to begin a new phase of his education. As the scion of a noble family, presumably destined for public life, he needed to become familiar with the history, music, art, literature, and architecture not only of Denmark but of the whole of Europe. He also needed to be able to speak other languages besides Danish and the Latin, Greek, and Hebrew he had already studied, and to experience the idiosyncrasies of foreign courts and their rulers and learn something of military science and political theory.

  Traditionally, a young Danish aristocrat began to acquire this sophistication by serving as a page in the household of a kinsman and then as squire to a foreign nobleman. At the age of twenty-one, he would move up to the level of a courtier or a knight and finally come back to Copenhagen to serve the king and his court, the last stage of training that equipped him and gave him the credentials to take on the governance and defense of a royal fief. Tycho’s four younger brothers followed that path. Two of them eventually became members of the Rigsraad. Had Tycho grown up in his father’s castle, or had his aunt not been from the intellectually inclined Oxe family, he probably would have done the same.

  The paths of the young men in Inger Oxe’s family, like those of the Brahe family, had led them abroad, but not to foreign courts and wars. They had gone to foreign universities. Inger’s older brother Peder Oxe had traveled for five years with a tutor from university to university, and this alternate form of education had not prevented his succeeding in public life. Indeed, though by the time Tycho left Copenhagen Peder had suffered a severe downturn of political fortune, there had for a while been no man in Denmark whose career had been more spectacularly successful. In 1548, when Tycho was still a child, Peder led the entourage of Princess Anne of Denmark when she wed the duke of Saxony, and that was the start of a meteoric rise to power that brought Peder, at the age of thirty-two, to a position in the Rigsraad.

  Jørgen and Inger chose the University of Leipzig,1 in Saxony, as the place for young Tycho to begin his foreign experience. They had traveled to Saxony themselves for Princess Anne’s wedding, and Inger still corresponded regularly wi
th Anne, who was now Electress Anne of Saxony. The language there was that spoken at the Danish court, a “pure” form of High German. Furthermore, Saxony was the birthplace of Lutheranism.

  A fifteen-year-old wasn’t sent abroad alone. Jørgen and Inger carefully chose Tycho’s “preceptor,” Anders Sørensen Vedel. Four years older than Tycho, he came from a respectable middle-class background and had excelled at the University of Copenhagen. As a preceptor, Vedel’s duties combined those of companion, chaperon, and tutor. In return for the payment of his expenses, and supposedly adhering to instructions in letters sent from home, he was to supervise Tycho’s university studies, act as his spiritual and moral guide, see that he received language instruction and lessons in fencing, riding, and dancing, and manage the purse. All of these responsibilities added up to a formidable assignment, but being a preceptor was nevertheless a good way for a young man of modest means to support his own education abroad and make invaluable contacts.

  Tycho and Vedel left Denmark on February 14, 1562, traveling, for safety and companionship, as part of a caravan. The journey took five weeks, first by ship across the icy Baltic and then on horseback along the roads beside the Elbe and Saale Rivers (see map, Tycho and Kepler’s Europe, here). Many Danish students attended the University of Wittenberg, but Tycho and Vedel’s travels took them two days beyond that, to Leipzig.

  Germany, then, was still three centuries from unification, and Saxony was not nearly so significant or wealthy a power as Denmark. Leipzig was, however, the site of one of Europe’s largest and most important universities. Though there were few Danes in residence, one of Vedel’s classmates back home had a brother there, and there were similarities to the University of Copenhagen that made it less alien to Tycho and Vedel. Instruction was in Latin, as it was in all European universities, and education went according to the pattern and philosophy of the Philippists, with many Philippists among the faculty. At Leipzig, Tycho studied classical languages and classical culture. He also continued, at first clandestinely, with astronomy.

  Tycho later wrote that he had “bought astronomical books2 secretly and read them in secret.” He studied the constellations from maps drawn by Albrecht Dürer. He began to keep track of the planets by a rough method of lining up a planet and two stars, holding up a “taut piece of string,” and then figuring the positions of the planet from the locations of the two stars on a little globe that he owned, “no bigger than a fist.” Flawed as this method inevitably was, Tycho was nevertheless able to come to a conclusion that impressed him deeply. Neither the Alfonsine Tables, which had been calculated in the thirteenth century using Ptolemy’s Earth-centered model, nor the Prutenic Tables, based on Copernicus’s Sun-centered astronomy and drawn up much more recently, were dependable in their predictions of planetary positions.fn1

  When sixteen-year-old Tycho began to keep a logbook of his own astronomical observations, in August 1563, during the second summer of his stay in Leipzig, the first record he made in it was of an observation of Mars, and the second was of a conjunction of the planets Jupiter and Saturn. A conjunction is the coincidence of two or more heavenly bodies at the same celestial longitude. To an earthly observer, one appears to pass the other. This happens with Jupiter and Saturn once every twenty years. Tycho found that neither the predictions of the conjunction based on Ptolemy nor those based on Copernicus were correct. The discrepancies were great enough to show up clearly even with his amateur efforts. The Copernican tables weathered the test slightly better than the Ptolemaic ones, which were off by an entire month. The cocky sixteen-year-old concluded that someone ought to produce better tables, and he began to think of himself as the person destined to “rectify this sorry state of affairs.”3

  In Tycho’s day a conjunction of the planets was considered to have more than astronomical interest. It was of great astrological significance. For practice, Tycho was casting predictions and horoscopes of famous men (without their knowledge) and recording the results in a notebook.

  Despite the best efforts of Vedel to keep his charge on track with his studies of other subjects, Tycho was soon practicing his astronomy more openly. Bartholomew Schultz, a more advanced student at Leipzig, gave him some instruction and introduced him to the more technical side of the subject. Tycho needed a better instrument. He managed to acquire one—his first real astronomical instrument—a cross staff, or radius. On May 1, 1564, when he was seventeen, he entered his first observation from it in his log. After that, he often “stayed awake the whole night5 through, while my governor [Vedel] slept and knew nothing about it; for I observed the stars through the skylight.”

  Though Schultz showed him a trick, using “transversal points” that would allow him to obtain more refined measurements (see figure 7.8c), Tycho soon became dissatisfied with the imprecision of his radius. He began to discover errors in his data, which he traced to faulty logic in its construction. The only recourse was to rectify them with a table of corrections, for he “had no opportunity6 of having a new [instrument] made, since my governor, who held the purse strings, would not allow things of this kind to be made for me.” Tycho had already begun to be more seriously concerned about the precision of observations than anyone before him, or any of his contemporaries.

  The next December, 1564, on Tycho’s eighteenth birthday, one of the professors at dinner described an illiterate craftsman he had met as “an astronomer by nature.” Tycho recorded that phrase in his notebook. The same month he set himself a research project to test a popular notion that the day-to-day positions of the heavens during the twelve days of Christmas, beginning on December 25, presaged the month-by-month pattern of the weather for the next twelve months. During those twelve days Tycho recorded every feature he could of the heavens, planning to check the weather throughout the coming year to see whether the data agreed.

  Figure 2.1: The cross staff, or radius:4 To find the apparent or “angular” distance (see appendix 1) between two stars, an observer sighted from where the “eye” appears in the drawing and slid the crossbar up and down the staff until the distance between the two stars was exactly covered by the length of the crossbar. Tycho’s cross staff was more sophisticated. Like the one shown here, it had two sights on the crossbar, and one of them was movable. He adjusted the movable sight so that he could see one star through it and the other through the sight fixed at the center of the crossbar. He then found the angular distance between the two stars by reading the scales etched on the crossbar and the staff and using a table of tangents.

  The following May, 1565, Tycho and Vedel returned home on a vessel that threaded its way among warring ships. Denmark was once again engaged in combat with its perennial rival, Sweden. Disembarking at Copenhagen, Tycho continued his journey to Knutstorps Borg, taking observations and recording the latitude at each stop on the way.

  Knutstorps Borg in May 1565 was much larger and more impressive than it had been when Tycho was born there. In 1551 Otte and Beate had rebuilt the ancient manor house. From a causeway and drawbridge over the lake, a gate now led into a square central court surrounded by four ranges of buildings. Those on the north and south side had tall, steep roofs with scalloped end gables. The walls were three to four feet thick, with arrow-slit windows, for the castle was intended to be a fortress as well as a stately home.

  Though Otte and Beate’s manor was never directly threatened, the war with Sweden came close to Knutstorp in the form of border raids. Beate’s mother and father, Tycho’s grandparents, died defending their castle, Baahus. Even more drastic for Tycho was the death of his uncle Jørgen in June 1565. Jørgen was vice admiral of the Danish fleet, which was in Copenhagen for repairs and reprovisioning. King Frederick and Jørgen had been drinking, and the king fell into the water under Amager Bridge. Jørgen dived in to rescue him. The king recovered, but Jørgen either drowned there or died almost immediately thereafter from injuries or illness attributable to his rescue effort.

  His foster father’s death should have left Tych
o a wealthy man. Jørgen had no children of his own, and he had been in the process of making Tycho his legal heir. Unfortunately that process had not been completed. Inger held life tenancy of the manor at Tostrup as her “widow’s jointure,” but eventually, at her death, the castle and the income from its hundreds of tenants would not come to Tycho but revert to general distribution among the Brahe family. Meanwhile, responsibility for Tycho, who at eighteen had not yet reached his majority, fell to his natural mother and father.

  Tycho left Denmark again a year later, in the spring of 1566. Somehow he had convinced his father to allow him to continue his education abroad rather than take advantage of the excellent opportunity the war provided to begin a career of civil service to the king. This time Tycho’s destination was Wittenberg, where Anders Vedel was already working toward his master of arts degree. Five months after Tycho arrived in Wittenberg, an epidemic struck the town, and most of the students fled. Tycho moved to the more northern university town of Rostock and began studies there in September. This move, though not particularly significant for Tycho’s future as an astronomer, was extremely significant for his future physical appearance.

  On December 10, Tycho was a guest at a betrothal celebration. During the dancing, he fell to quarreling with another aristocratic Danish student, his third cousin, Manderup Parsberg. The quarrel may have erupted as the result of some levity, at Tycho’s expense, about an unfortunate astrological prediction he had made that autumn. There had been an eclipse of the Moon on October 28 that Tycho concluded presaged the death of Suleiman the Great, the Turkish sultan. With a flair for the dramatic and poetic, Tycho composed a Latin poem announcing this prediction. Then the news arrived that the sultan had already been dead for six months.

  Whether or not it was an insult having to do with that embarrassment that precipitated Tycho’s and Parsberg’s dispute, it did not end at the betrothal celebration. The two young men resumed their argument at another party on December 27.