by Dava Sobel
In order to prove the superiority of his system, published in 1588, over the Ptolemaic or the Copernican, Tycho needed reliable data—such data as had never before been available—regarding the planets’ motions. He single-handedly set new standards for accuracy and precision in observation, first by expanding the sizes of his custommade instruments to giant proportions. In place of a handheld cross-staff or pair of compasses, for example, Tycho substituted a mammoth quadrant that stood twenty feet high and required a crew of servants to operate. Later he fashioned other devices—still grand but not quite so unwieldy—that yielded good readings on large, legible scales, where each degree of arc divided into its full complement of sixty minutes (and in some cases further subdivided into multiples of arc-seconds). With the cooperation of his prestigious family, he built his country’s first astronomical observatory. King Frederick then provided the land and funding for a second one, equipped with more and still grander tools of Tycho’s design, which proved, by all accounts, the finest instruments in the world for pinpointing planetary positions. Both Tycho and his magnificent observatory, Uraniborg, on the island of Hven, drew income from canonries and other Church benefices assigned to them by the king. Here Tycho ruled a staff of talented assistants, a workforce of disgruntled peasants, and the whole of the night sky for more than twenty years.
THE TYCHONIC SYSTEM
Tycho set the planets in orbit around the Sun, but left the Earth immobile at the center of the universe. Although Tycho’s observations demonstrated the heavens’ solid spheres to be a fiction, Tycho could not bring himself to believe the Earth rotated and revolved.
After Frederick died, Tycho fell out of favor with Christian, the heir to the Danish throne, and felt forced to abandon Uraniborg. The search for a new patron led him to Prague in 1599, to the court of the Holy Roman Emperor, Rudolf II. Although Catholic, Rudolf acted liberally toward Lutherans in general, and smiled with special warmth on one so skilled in the art of astrology as Tycho Brahe. The emperor gave him his choice of castles and put him to work prognosticating affairs of state.
The move to Prague also put Tycho in proximity to Johannes Kepler, thereby facilitating their fateful collaboration. Kepler, not yet well known to most astronomers and living in modest circumstances, could never have afforded a visit to Tycho’s island. He welcomed Tycho’s presence in Bohemia as an act of God. By further provision of Providence, Kepler found Tycho’s chief assistant engaged in Mars studies when he joined the team at Benatky Castle in the spring of 1600. “I consider it a divine decree,” reflected Kepler, “that I came at exactly the time when he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy.”
Kepler had been an infant in arms in Weil der Stadt in southwest Germany the year of Tycho’s nova, but when he was five, his mother took his hand and led him up a hill outside town to see the Great Comet of 1577. By then, Kepler’s eyesight had already begun to fail him. Likewise the noble standing that once elevated the Kepler family name had eroded before his birth, so that the myopic young genius inherited little more than a coat of arms. By dint of his intellect, however, he won scholarships that carried him all the way through seminary and university. He focused his self-professed “burning eagerness” on studies of astronomy that convinced him of the correctness of the Copernican hypothesis.
Although Kepler prepared himself for a career as a Lutheran pastor, he accepted the first job offer he received—that of a secondary school teacher and district mathematician in a provincial outpost. One day in 1595 while at the blackboard, sketching the repetition pattern of Jupiter-Saturn conjunctions for his class, he experienced an epiphany. Geometry and divinity combined in his mind, helping him intuit the solution to three cosmic mysteries: why the planets assumed their specific distances from one another, why God had created only six of them, and why they revolved at different speeds around the Sun. In the first moments of excitement, Kepler envisioned the spheres of the planets as though each were inscribed inside a particular form of regular polygon—from triangle to square, pentagon, hexagon, and so on. But, since there were any number of regular polygons and only six planets, Kepler soon scrapped them for their rarer three-dimensional counterparts, called regular solids. The simplest of these, the tetrahedron, with four faces made by four identical equilateral triangles, fitted handily between the spheres of Mars and Jupiter. The cube (comprising six equal squares) accounted for the distance between Jupiter and Saturn, and the dodecahedron (consisting of twelve cloned pentagons) accommodated the Earth within the orbit of Mars. The glorious confluence of the five regular solids with the five interplanetary interstices flooded Kepler’s soul. It brought him to tears and redirected all his efforts.
“Days and nights I passed in calculating,” he reported in his 1596 book, Mysterium cosmographicum, “to see whether this idea would agree with the Copernican orbits, or if my happiness would be carried away by the wind.” At length he made everything fit. But he craved further confirmation, and that, Kepler knew, could come only from Tycho—from the trove of observational data collected over decades with scrupulous attention to detail.
Tycho had need of Kepler, too—of the German mathematician’s superlative ability to mine the data for its hidden wealth. If, as Tycho believed, his data verified his version of cosmic order, then his life work would surpass that of Ptolemy and reward his every sacrifice. But Tycho worried that Kepler, a confessed Copernican who had reprinted Rheticus’s First Account as an appendix to his own Mysterium, might uncover incontrovertible evidence for the rival theory—or that he might twist evidence that favored the Tychonic system to feign support for the Copernican. Thus the distrustful Tycho dallied, making Kepler pant for every bit of data he deigned to release. Only after Tycho’s sudden death, in October 1601, and the inevitable struggle with Tycho’s heirs over access to the data, did Kepler finally take possession of Tycho’s treasure and lay it at Copernicus’s feet.
Johannes Kepler, imperial mathematician to Rudolf II.
“I build my whole astronomy upon Copernicus’s hypotheses concerning the world,” Kepler proclaimed in his Epitome of Copernican Astronomy. He thanked Tycho for his observations, but dismissed the Tychonic system as inferior. The Earth, he averred, most assuredly moved among the planets, around the Sun, just as Copernicus maintained. But Copernicus had centered the planets’ revolutions on a point near the Sun, rather than on the Sun itself. Kepler found this notion physically implausible, so he corrected it. He relocated the center of all planetary motions in the body of the Sun, and imbued the Sun with a force that spread like light through the universe, pushing the planets now faster, now slower, depending on their distance. Not only did the planets nearest the Sun outpace the farther ones, as Copernicus had remarked, but each planet periodically altered its own distance from the Sun, and changed its speed accordingly. Kepler proved the path of a planet was not a perfect circle, or any combination of perfect circles, but the slightly flattened and double-centered circle known as an ellipse, with the Sun at one focus.
Kepler’s ever-so-slightly squashed Martian orbit barely deviated from perfect roundness, even though it proved more elliptical than that of any other planet. For this reason, Kepler considered Mars’s path—the one most closely trailed, most richly documented by Tycho—the “only possible” route to the truths of a “New Astronomy,” rooted in the laws of physics. Had he tackled Jupiter or Saturn, for example, the subtleties of the ellipse would have escaped his notice and caused insuperable problems.
“I was almost driven to madness in considering and calculating this matter,” wrote Kepler of the Mars situation. “I could not find out why the planet would rather go on an elliptical orbit. Oh, ridiculous me!”
Unlike Copernicus, who never divulged his thought processes in print, Kepler shared with his readers many details of his progress and setbacks. He gushed in reliving for them the “sacred frenzy” of his ecstatic insights, and begged their commiseration for all the
despair he endured. “If you are wearied by this tedious procedure,” he interjected in the description of his five-year “war” on Mars, “take pity on me who carried out at least seventy trials, with the loss of much time.” Sometimes he felt lost, “hesitating in doubt of how to proceed, like a man who does not know how to put together again the dismantled wheels of a machine.”
Kepler knew who had written the unsigned foreword “To the Reader” in the opening pages of On the Revolutions. His own secondhand copy of the first edition had the name Andreas Osiander penned in, right above the offending note, by the book’s original owner—a Nuremberg mathematician with ties to Rheticus and Schöner. Kepler took particular umbrage at Osiander’s assertions. In 1609, when he published his New Astronomy calling for a science based on physical forces, he named and attacked Osiander on theverso of the title page. Now everyone would know the identity of Copernicus’s anonymous apologist. “It is a most absurd fiction,” Kepler railed, “that the phenomena of nature can be demonstrated by false causes. But this fiction is not in Copernicus.”
By his own self-assessment, Kepler’s pioneering achievement lay in “the unexpected transfer of the whole of astronomy from fictitious circles to natural causes.”
Kepler demolished antiquity’s perfect circles while he was still wedded to the five regular solids as space-holders between the planetary orbits—a concept he nearly realized in silver, as a cosmic fountain for his patron the Duke of Württemberg. He never found cause to relinquish that fantastical vision of universal harmony. Nor did he ever abandon his Lutheran faith, though he felt compelled more than once to move house and change employment rather than convert to Catholicism at the insistence of local authorities. These beliefs sustained him through the difficulties of his chosen work, the deaths of his first wife and eight of his twelve children, his mother’s trial for witchcraft, and the outbreak of the Thirty Years’ War.
“Thee, O Lord Creator, who by the light of nature arouse in us a longing for the light of grace,” Kepler prayed in 1619 at the close of his book Harmonies of the World, “if I have been drawn into rashness by the admirable beauty of Thy works, or if I have pursued my own glory among men while engaged in a work intended for Thy glory, be merciful, be compassionate, and pardon me; and finally deign graciously to effect that these demonstrations give way to Thy glory and the salvation of souls and nowhere be an obstacle to that.”
Along with legal custody of Tycho’s data, Kepler assumed the title of imperial mathematician at the court of Rudolf II, and also the duty to compile new, improved astronomical tables in the emperor’s name. The Rudolfine Tables, published in 1627, indeed proved far superior to their Prutenic predecessors. Whereas predictions based on earlier tables might err by as much as five degrees, and sometimes misjudge an important event such as a conjunction by a day or two, the Rudolfine Tables honed positions to within two minutes of arc.
KEPLER’S VISION
While calculating conjunctions of Jupiter and Saturn, Kepler experienced a mystical vision that led him to suggest the orbits of the planets were numbered and spaced in accordance with the five regular (often called Platonic) solids. The cube that appears dominant in this image determines the interval between Jupiter and Saturn.
Although the Rudolfine Tables trumped the Prutenic, Copernicus’s original diagram of the Sun inside nested rings containing a planet apiece—the bull’s-eye icon that he drew in his manuscript and published with On the Revolutions—remained strangely apt. Copernicus no doubt intended the image as a mere approximation of planetary order, since he omitted more than a score of the thirty-odd circles described in his text. But now that Tycho had swept the cosmos clean of solid spheres and Kepler banished every last epicycle, the same streamlined schematic illustration rendered an actual map of the heavens.
Chapter 11
Dialogue Concerning the Two Chief
Systems of the World, Ptolemaic
and Copernican
The constitution of the universe, I believe, may be set in first place among all natural things that can be known, for coming before all others in grandeur by reason of its universal content, it must also stand above them all in nobility as their rule and standard. Therefore if any men might claim extreme distinction in intellect above all mankind, Ptolemy and Copernicus were such men, whose gaze was thus raised on high and who philosophized about the constitution of the world.
—GALILEO GALILEI, Dialogue Concerning the
Two Chief Systems of the World, 1632
In an exchange of letters in Latin between Galileo and Kepler in 1597, prompted by the publication of Kepler’s Mysterium, the Italian Catholic professor admitted to having long been “a secret Copernican” who could not openly espouse his belief in a moving Earth for fear of ridicule from colleagues. In reply, the German Lutheran exhorted him to join the pro-Copernican movement: “Would it not be better to pull the rolling wagon to its destination with united effort?”
Galileo answered Kepler with silence. Not until 1610, after refining the optical instrument he called a spyglass, and discovering through its lenses heavenly marvels such as the moons of Jupiter, did he outwardly avow his support for Copernicus.
Before Galileo’s innovations refined the rudimentary spyglass, instruments had aided astronomers in defining only the positions of bodies. Galileo’s telescopes enabled observers to glimpse composition as well. The lunar landscape, for example, erupted in rocky mountains and fell into deep valleys, mirroring the surface of the Earth. The Sun exhaled dark spots that gathered and glided across its face like windblown clouds. The telescope further upset the balance of the heavens by exposing unknown bodies—not “new” entities such as Tycho’s nova of 1572 (or Kepler’s of 1604) that suddenly caught the naked eye, but never-before-seen objects beyond the reach of human vision, including ear-like appendages flanking Saturn and hundreds of faint stars filling in the outlines of the constellations. Also the planet Venus revealed a cycle of phases, from crescent to full, demonstrating beyond doubt that it revolved around the Sun. Venus’s phases fit equally well into the Tychonic system or the Copernican, but Ptolemy’s universe could not embrace such a phenomenon. Galileo published his findings. The Starry Messenger, a slim volume expounding his “message from the stars,” sold out within one week of its printing in Padua in March of 1610. After that, he could not build telescopes fast enough to keep pace with the demand.
Galileo’s telescopic discovery of the four largest moons of Jupiter in January 1610, described and diagrammed here in his own hand, convinced him that the Earth was not the only center of motion in the universe, and he became an outspoken “Copernican.”
News of the new discoveries spread quickly to tremendous acclaim, but Galileo also became a lightning rod for all the criticism, ridicule, and outrage that Copernicus had dreaded. Thanks in part to Galileo’s loud praise of it, On the Revolutions came to the suspicious attention of the Sacred Congregation of the Index, a watchdog arm of the Church created late in the sixteenth century to proscribe books that threatened faith or morals.
Copernicus had predicted trouble from “babblers who claim to be judges of astronomy although completely ignorant of the subject,” who would distort passages of Scripture to censure him. Rheticus had also anticipated such calumny, and tried to ward it off by rectifying tenets of the Copernican system with chapter and verse, with Bishop Giese’s wholehearted approval. Even Osiander, whose anonymous note “To the Reader” had so offended Giese and Kepler, probably intended to protect the book by dismissing Copernicus’s bold assertions as clever calculation devices. And, as expected, On the Revolutions provoked the ire of religious authorities almost from the moment it appeared.
Pope Paul III, the dedicatee, had established the Roman Holy Office of the Inquisition in 1542, a year before the book’s publication, as part of his campaign to quash the Lutheran heresy. Whether through the efforts of Rheticus or Giese, His Holiness duly received a gift copy of On the Revolutions. He turned it over to his p
ersonal theologian, Bartolomeo Spina of Pisa, Master of the Sacred and Apostolic Palace. Spina took sick, however, and died before he could review the book, leaving that task to his friend and fellow Dominican friar Giovanni Maria Tolosani. In an appendix to the treatise On the Truth of Holy Scripture, published in 1544, Tolosani denounced the deceased Copernicus as a braggart and a fool who risked straying from the faith.
“Summon men educated in all the sciences, and let them read Copernicus, Book I, on the moving Earth and the motionless starry heaven,” Tolosani challenged. “Surely they will find that his arguments have no solidity and can be very easily refuted. For it is stupid to contradict a belief accepted by everyone over a very long time for extremely strong reasons, unless the naysayer uses more powerful and incontrovertible proofs, and completely rebuts the opposed reasoning. Copernicus does not do this at all.”
