VIII. KEPLER: 1571–1630

It turned out well for science that Tycho moved to Prague, for there Kepler inherited his observations, and deduced from them the planetary laws that prepared for Newton’s theory of gravitation. From Brahe to Kepler to Newton and from Copernicus to Galileo to Newton are the basic and converging lines of modern astronomy.

Kepler was born at Weil, near Stuttgart, son of an army officer who repeatedly went off to war as preferable to domesticity. Returning at last, the father opened a tavern, in which Johann served as a waiter. The boy was sickly; smallpox crippled his hands and permanently impaired his vision. The Duke of Württemberg saw in him the possibility of a good preacher and paid for his education. At Tübingen Michael Maestlin, who as professor taught the Ptolemaic astronomy, privately converted Kepler to the Copernican theory, and the youth became so enthusiastic about the stars that he abandoned all thought of an ecclesiastical career.

After taking his degree he became a schoolmaster at Graz, in Styria, teaching Latin, rhetoric, and mathematics for 150 gulden a year, with free lodging, and adding twenty gulden by editing annually an astrological calendar. At twenty-five he married a woman of twenty-three who had buried one husband and divorced another; she brought him a dowry and a daughter; he added six children in due course. A year after his marriage he was forced as a Protestant to leave Graz (1597), for the new Archduke of Styria, Ferdinand, was a resolute Catholic who ordered all Protestant clergymen and teachers out of Styria. Kepler had given further offense by publishing Mysterium cosmographicum (1596), ardently advocating the Copernican system; hopefully he sent copies to Brahe and Galileo. After a year of despondent poverty he was saved by Tycho’s invitation to Prague. But Tycho was hard to get along with; there were difficulties with religion and bread; the wife developed epilepsy. Then Tycho died, and Kepler was appointed his successor, at five hundred florins a year.

Brahe had bequeathed his records to him, but not his instruments. Unable to buy the best, Kepler found himself driven to study Brahe’s observations rather than add to them. He could never have said with Newton, “I do not invent hypotheses”; on the contrary, his head hummed with them; “I have much store of fantasy.”71 His peculiar skill lay in testing hypotheses, and his wisdom lay in casting them aside when the consequences that he had mathematically deduced from them proved incompatible with the observed phenomena.72 In seeking to plot the orbit of Mars he tried seventy hypotheses through four years.

Finally (1604) he reached his basic and epochal discovery—that the orbit of Mars around the sun is an ellipse, not a circle as astronomers from Plato to and including Copernicus had supposed; only an elliptical orbit harmonized with the repeated observations of Brahe and others. Kepler’s agile mind leaped to the question, What if all the planetary orbits are elliptical? Rapidly he tested the idea with the recorded observations; it agreed with them almost completely. In a Latin treatise on the motions of Mars, Astronomia nova de motibus stellae Martis (1609), he published the first two of “Kepler’s laws”: first, each planet moves in an elliptical orbit, in which one focus is the sun; second, each planet moves more rapidly when near the sun than when farther from it, and a radius drawn from the sun to the planet covers, in its motion, equal areas in equal times. Kepler ascribed the differences in planetary speed to the greater emanation of solar energy felt by the planet as it neared the sun; in this connection he evolved from Gilbert an idea of magnetic attraction closely akin to Newton’s theory of gravitation.

When Emperor Rudolf died (1612) Kepler moved to Linz, and again he lived by teaching school. His wife having passed away, he married a poor orphan girl. In providing his new home with wine he was fascinated by the difficulty of measuring the contents of a cask with curved sides; the essay that he published on the problem helped to prepare the discovery of infinitesimal calculus.

After puzzling for ten years over the relation between the speed of a planet and the size of its orbit, Kepler published, in his book The Harmony of the World (1619), his third law: the square of the time of revolution of a planet around the sun is proportioned to the cube root of its mean distance from the sun. (For example: Mars’s time of revolution is demonstrably 1.88 times that of the earth; the square of this is 3.53; the cube root of this is 1.52; i.e., the mean distance of Mars from the sun will be 1.52 times that of the earth from the sun.) Kepler was so overjoyed by having reduced the behavior of the planets to such order and regularity that he likened each orbital speed to a note on a musical scale, and concluded that the combined motions make a “harmony of the spheres,” which, however, is audible only to the “soul” of the sun. Kepler mingled mysticism with his science, illustrating again Goethe’s generous saying that a man’s defects are the faults of his time, while his virtues are his own. We can forgive the pride that wrote, in the preface to The Harmony of the World:

What I promised my friends in the title of this book…. what, sixteen years ago, I urged as a thing to be sought—that for which I joined Tycho Brahe, … to which I have devoted the best part of my life—I have at length brought to light. … It is not eighteen months since the unveiled sun … burst upon me. Nothing holds me; I will indulge my sacred fury. … If you forgive me, I rejoice; if you are angry I can bear it. The die is cast, the book is written, to be read either now or by posterity, I care not which; it may well wait a century for a reader, as God has waited six thousand years for a discoverer!73

In an Epitome of the Copernican Astronomy (1618–21) Kepler showed how his laws supported, clarified, and amended the Copernican system. “I have attested it as true in my inmost soul,” he said, “and I contemplate its beauty with incredible and ravishing delight.”74 The treatise was placed on the Index of Prohibited Books because it argued that the Copernican theory had been proved. Kepler, a pious Protestant, was not disturbed. For a while he enjoyed prosperity and acclaim. His salary as Imperial astronomer was generally paid. From faraway Britain James I invited him (1620) to come and adorn the English court, but Kepler refused, saying that he would suffer from being cooped up in an island.75

He shared the prevailing belief in witchcraft. His mother was charged with practicing it; witnesses alleged that their cattle, or they themselves, had become ill because Frau Kepler had touched them; one witness swore that her eight-year-old daughter had been made ill by Mother Kepler’s witchery, and she threatened to kill the “witch” if she did not at once cure the girl. The accused woman denied all guilt, but she was arrested and chained in a cell. Kepler fought for her at every stage of the proceedings. The state’s attorney proposed that a confession be drawn from her by torture. She was taken to the torture chamber and was shown the instruments to be used upon her; she still asserted her innocence. After thirteen months’ imprisonment she was released, but she died soon afterward (1622).

This tragedy, and the impact of the spreading war, darkened Kepler’s final years. In 1620 Linz was occupied by Imperialist troops, and its inhabitants neared starvation. Through all the chaos he continued his labor of formulating the observations of Brahe, others, and himself, in the Rudolphine tables (1627), which catalogued and charted 1,005 stars and remained standard for a century. In 1626 he moved to Ulm. His Imperial salary fell far in arrears, and he was hard pressed to feed his family. He applied to Wallenstein for employment as astrologer; he was engaged, and for some years he followed the general, casting horoscopes for him and publishing astrological almanacs. In 1630 he went to Regensburg to appeal to the Diet for the arrears of his salary. The effort consumed his last physical resources; he was seized with fever and died within a few days (November 15, 1630), in the fifty-ninth year of his age. All traces of his grave were swept away by the war.

His function in the history of astronomy was to mediate between Copernicus and Newton. He advanced beyond Copernicus by replacing circular with elliptical orbits, by abandoning eccentrics and epicycles, and by placing the sun not at the center of a circle but at one focus of an ellipse. By these changes he freed the Copernican system from many of the difficulties that had almost justified Tycho Brahe in rejecting it; through him the heliocentric view now won a rapidly widening acceptance. He transformed what had been a brilliant guess into a hypothesis worked out in impressive mathematical detail. He provided Newton with the planetary laws that led to the theory of gravitation. While keeping his religious faith fervent and undiminished, he revealed the universe as a structure of law, as a cosmos of order in which the same laws ruled the earth and the stars. “My wish,” he said, “is that I may perceive the God whom I find everywhere in the external world in like manner within me.”76

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