A More Perfect Heaven: How Copernicus Revolutionized the Cosmos - Dava Sobel (2011)

Part III. Aftermath

Chapter 10. Epitome of Copernican Astronomy

I deem it my duty and task to advocate outwardly also, with all the powers of my intellect, the Copernican theory, which I in my innermost have recognized as true, and whose loveliness fills me with unbelievable rapture when I contemplate it.

—JOHANNES KEPLER, Epitome of Copernican Astronomy,
1617-21

Content with thePrutenic Tables, European astronomers took Copernicus at Osiander’s cautious word for the remainder of the sixteenth century—with two monumental exceptions. Between them, the flamboyant Tycho Brahe and the studious, passionately reverent Johannes Kepler carried Copernicus’s work to completion.

The Danish Tycho was literally star-struck in 1559, during his thirteenth summer, when a lunar eclipse illuminated the mathematics he was learning at a Lutheran university in Copenhagen. His noble birth gave him the means to purchase his own astronomy books, which he bought secretly, he said, and also read in secret, since his elders considered such pastimes beneath him. Soon he began logging his own observations of the planets and casting the horoscopes of famous men. At twenty-five, after losing most of his nose in a duel, he looked up one November night to see a nova’s explosion blaze suddenly to brilliance in the constellation Cassiopeia. He spoke of that 1572 event ever after as the moment when the heavens chose him to be their interlocutor.

“In truth, it was the greatest wonder that has ever shown itself in the whole of nature since the beginning of the world,” he announced in his hastily written book, De nova stella. Tycho’s new star indeed heralded a cataclysm. By its position in the heavens—too far from the zodiac to be a planet, too steadfast for a comet, and supralunar to boot—it boded the end of immutability in Aristotle’s celestial realms. Change could occur on high, Tycho’s careful observations showed, in the guise of a new star’s light. This claim competed for strangeness with Copernicus’s moving Earth—and perhaps Tycho winked at Copernicus when he compared the miracle of his Nova stella to Joshua’s stopping the Sun by prayer.

Tycho took his homeland’s far northern latitudes (worse than those bemoaned by Copernicus) as a proud birthright, and dedicated an early work to King Frederick of Denmark. While Tycho did allow that the extreme cold of the climate could disturb an astronomer’s serenity, it seems never to have deterred him. Five years after his nova discovery, in the early dark of another November night, Tycho stood fishing at a pond when a comet appeared to him. Its bright bluishwhite head and long ruddy tail—like a flame seen through smoke, he said—persisted through autumn into winter. That lengthy visitation gave Tycho time to prove that comets, though generally assumed to be quirks of the Earth’s atmosphere, actually traced paths among the planets. In contrast to contemporaries who feared the comet augured famine and pestilence, maybe even the death of a leader, Tycho confined its wrath to the heavens themselves. The Great Comet of 1577 condemned the ancient notion that solid celestial spheres carried the planets on their eternal rounds. Tycho saw plainly that no such structures impeded the comet’s free travel, and therefore concluded that no such structures existed. When he delivered this thunderbolt, one could almost hear the tinkle of shattering crystal.⁵

Tycho Brahe, Lord of Uraniborg.

Tycho’s admittedly nonacademic achievements soon gained him an adjunct faculty position at the University of Copenhagen, where he lectured briefly on Copernicus’s ideas and distributed the Prutenic Tables to his students. In addition to having read On the Revolutions, Tycho also acquired a handwritten copy of the Brief Sketch from a friend who had known Rheticus. Recognizing the mathematical importance of the document, Tycho made additional copies to distribute among other mathematicians, though he refused to accept the reality of the Earth’s motion. Bold as he was, and openly admiring of Copernicus, he stood firm on the stationary Earth. For, if the Earth truly pursued a great circle around the Sun, Tycho reasoned, then an Earthly observer would see the spaces between certain stars widen and narrow over the course of the year. He estimated the expected change, called parallax, at 7°, or about fifteen times the diameter of the full Moon. Tycho’s failure to perceive any parallax, even a tiny one, convinced him that no Earthly revolution took place. Copernicus’s explanation—that the stars’ tremendous distance precluded the perception of parallax—rang hollow to Tycho. Why, he asked, should the distance to the stars mushroom from Ptolemy’s ten thousand Earth diameters to the several million required by Copernicus? What purpose would all that emptiness serve? What’s more, stars visible across such immense gulfs would need to be absurdly large, perhaps bigger than the entire expanse of Copernicus’s great circle. Incredulous, Tycho sought alternative means to realize the best of Copernicus’s ideas without moving the Earth, and came up with the compromise that bears his name. In the Tychonic system, Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, while the Sun, in turn, carries them along as it orbits the central, immobile Earth.

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.