Johannes Kepler: The Celestial Harmonist
Johannes Kepler's life, work with Tycho Brahe, the Mysterium Cosmographicum, Astronomia Nova, the three laws, the Rudolphine Tables, and the Harmonices Mundi.
Johannes Kepler: The Celestial Harmonist
If Copernicus began the heliocentric revolution and Galileo clinched it observationally, it was Johannes Kepler who made the heliocentric theory mathematically precise. Kepler was the man who, by patient analysis of Tycho Brahe’s incomparable observations, discovered the elliptical shape of the planetary orbits, the equal-areas law of planetary motion, and the famous harmonic relationship between the orbital periods and the orbital sizes. These three laws, especially the third, were the empirical challenge that Newton’s gravitational theory would eventually meet. Without Kepler’s laws, Newton would have had nothing to derive from. Kepler was also a striking personality. He was a Protestant in a Catholic land, a man with bad eyes and bad luck, a mathematician of the first rank, and a thoroughgoing mystic who believed that the planetary system was a kind of cosmic music. He was the author of the first science-fiction story, a defense of the Copernican theory that has been read for four centuries, and the most brilliant astronomical theorist between Copernicus and Newton. This page follows Kepler’s life and work in some detail. The two articles treat the technical content in depth: What Are Kepler’s Three Laws of Planetary Motion? and How Did Kepler’s Laws Support Heliocentrism?. The biographical and contextual notes here should be read together with the Copernicus page, which sets the stage for Kepler’s work, and the Newton page, which shows how Newton’s theory closed the chain.
Early Life and the Mysterium Cosmographicum
Johannes Kepler was born on 27 December 1571 in Weil der Stadt, in the Duchy of Württemberg, in what is now southwestern Germany. His father was a mercenary soldier who was often away; his mother was the daughter of an innkeeper. The family was poor, and the young Johannes was a sickly child, with poor eyesight and a tendency to skin rashes. He was, however, precocious in mathematics, and he was educated at the monastic school at Adelberg and the seminary at Maulbronn, before being admitted to the University of Tübingen in 1589. At Tübingen, Kepler studied theology and mathematics. His astronomy teacher was Michael Maestlin, an astronomer of the first rank, who privately taught Kepler the Copernican theory. Maestlin was a careful teacher and a careful Copernican: he taught the official Ptolemaic astronomy in his lectures but explained Copernicus’s alternative in private sessions with his best students. Kepler was converted. He defended the Copernican theory in a student disputation, and he became, for the rest of his life, an open and enthusiastic Copernican. In 1594, Kepler accepted a position as a mathematics teacher at the Protestant seminary in Graz, in Austria. He was twenty-three. In 1595, while teaching a class on geometry, he had an inspiration: the five regular solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron) might be used to explain the structure of the solar system. The five solids were the only ones in which the faces were identical regular polygons; there were five of them, and there were five intervals between the six known planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn). If the orbits of the planets were spaced so that each one was inscribed in a regular solid, with the Sun at the center, then the sizes of the orbits would be determined by the geometry of the solids. Kepler wrote this up in his first book, the Mysterium Cosmographicum (1596), “The Sacred Mystery of the Cosmos.” The book was, on the whole, a youthful work. The geometry did not, in fact, fit the known planetary distances very well, and Kepler later acknowledged that the book’s central claim was wrong. But the Mysterium Cosmographicum had a deep idea that ran through all of Kepler’s later work: that the structure of the cosmos was the result of some simple, elegant, mathematical principle, and that the job of the astronomer was to find it. The book was widely read, and it was the founding document of the new astronomy.
Graz and the Move to Tycho
Kepler’s first years in Graz were productive, but the religious situation was precarious. Graz was a Protestant town in a Catholic duchy, and the Counter-Reformation was pressing hard. In 1598, the archduke of Austria ordered all Protestant teachers and preachers to leave Graz. Kepler, who had been a Lutheran since his student days, was briefly imprisoned and then expelled. He and his family wandered, jobless, for a year. In 1600, Kepler was invited to join Tycho Brahe at his observatory near Prague. Tycho, who had recently been driven from Denmark by his unfriendly new king, was the Imperial Mathematician to the Holy Roman Emperor Rudolf II. He had the best observations in Europe, and he was looking for a talented mathematician to help him analyze them. The partnership was uneasy — Tycho was secretive about his data, and Kepler was difficult to manage — but it was also the decisive encounter of Kepler’s life. Tycho died in October 1601, suddenly, of a urinary complaint (he had refused to leave a banquet to relieve himself, on the grounds that it would be impolite). Kepler succeeded him as Imperial Mathematician, and he inherited, after a long and complicated legal battle with Tycho’s heirs, Tycho’s incomparable data set.
The Astronomia Nova and the First Two Laws
The data Tycho had gathered was, above all, an exhaustive record of the position of Mars over many years. Mars was the planet of choice for testing astronomical theories, because its apparent motion is the most irregular of any planet known to the ancients, and because even small errors in theory produce large errors in prediction. Kepler was determined to use the data to find the true orbit of Mars, and through it the true shape of the planetary system. The work took him eight years. He tried, in succession, a series of models: circular orbits, eccentric circles, an oval orbit, a “vicarious” hypothesis, and finally an ellipse. In 1605, after a long struggle, he discovered that the orbit of Mars is an ellipse, with the Sun at one focus. The discovery was an accident: he had been trying to fit the data with a circle, and the small discrepancy of eight arcminutes — the size of a coin seen from a hundred meters — would not go away. The eight arcminutes forced him to abandon the circle. He tried an ellipse, and it fit. The result was published in 1609 as the Astronomia Nova — the “New Astronomy” — under the subtitle “A Physical Treatise on Celestial Mechanics.” The book contained the first two of Kepler’s three laws: the elliptical orbit of Mars (and, by extension, of all the planets), with the Sun at one focus; and the law that a line from a planet to the Sun sweeps out equal areas in equal times. The equal-areas law is, in a sense, the dynamical heart of the book. It is the first statement of a principle that be derived from Newton’s second law and the law of gravitation: that the rate at which a planet sweeps out area is constant because the force is directed toward the Sun. The detailed content of these laws is treated in What Are Kepler’s Three Laws of Planetary Motion?. The Astronomia Nova was not an easy book. It was written in Latin, in a sometimes tangled prose, and it assumed a great deal of background in astronomy. It was also, in the same year, overshadowed by the publication of Galileo’s Sidereus Nuncius, which was a much more accessible book about a much more dramatic subject. The two books together marked the high point of the heliocentric revolution: the mathematical and the observational cases were now both in.
The Third Law and the Harmonices Mundi
The third of Kepler’s three laws appeared in 1619, in a book titled Harmonices Mundi — “The Harmony of the World.” The book was an extension of the Mysterium Cosmographicum. Kepler was still searching for the simple, elegant, mathematical principle that would explain the structure of the solar system, and he was convinced that the principle would be a musical one: the planets, moving around the Sun, were singing a celestial music, inaudible but mathematically describable. The third law — that the square of a planet’s orbital period is proportional to the cube of its semi-major axis — is the simplest and most famous of the three. It is also, the most profound, because it relates the size of a planet’s orbit to its period, and it does so in a way that any gravitational theory would have to explain. Kepler’s derivation of the law was, by his own account, partly empirical and partly mystical. He had been collecting data on the periods and distances of the planets for years, and on 15 May 1618, he wrote, “the thing has come together in my head.” He was right. The third law was the most consequential of the three. It provided the empirical clue to the inverse-square law of gravitational attraction. The way it did so is told in How Did Kepler’s Laws Support Heliocentrism? and in What Is in Newton’s Principia Mathematica?.
The Rudolphine Tables
In 1627, Kepler published the Tabulae Rudolphinae — the Rudolphine Tables — dedicated to the memory of his late patron, Rudolf II. The tables were the most accurate planetary tables that had ever been produced, and they remained the standard for almost a century. They were based on Tycho’s observations and on Kepler’s elliptical orbits, and they predicted the positions of the Sun, Moon, and planets with a precision that no previous set of tables had achieved. They were the practical payoff of the heliocentric theory: they made the heliocentric system useful to astronomers, navigators, and astrologers alike. (Kepler himself cast horoscopes for a living, and he was not embarrassed by it; he described astrology as “the foolish daughter” of his wise mother astronomy, but he acknowledged that the daughter supported the mother financially.)
The Somnium
In 1634, four years after Kepler’s death, his son Ludwig published the Somnium — the “Dream” — a small book in which Kepler imagined a trip to the Moon. The work was the first significant work of science fiction in the European tradition. The narrator is visited by a daemon who explains how a trip to the Moon might be made (with the daemon’s help, and at some discomfort), and who describes what the Earth would look like from the Moon: a great globe, with the spots of the continents and the brightness of the oceans, going through phases like the Moon as seen from the Earth. The Somnium was, in addition, a defense of the Copernican theory. From the Moon, the Earth would appear to be just one body among many, and the heliocentric theory would be obvious to any lunar astronomer. The book was written as a dream, partly to deflect criticism: Kepler knew that it was dangerous to defend the Copernican theory openly, and he presented his argument in the form of a story. He was, in fact, tried by the Lutheran consistory in 1615, on a charge of “consorting with Catholics” and “introducing novelties,” and the Somnium was one of the issues.
Later Years and Death
The last decade of Kepler’s life was a long, painful struggle against poverty, religious persecution, and the chaos of the Thirty Years’ War. He had been a Lutheran, but his Lutheran colleagues in Württemberg had refused to accept him back after the affair of the Mysterium Cosmographicum, and he had been excommunicated by the Lutherans. He was also, increasingly, a defender of religious toleration, which made him suspect to both sides. In 1628, Kepler entered the service of Albrecht von Wallenstein, the famous military commander, who was a patron of astrology and a defender of Copernicus. Wallenstein was assassinated in 1634. Kepler spent his last months trying to collect a small sum of money owed to him by the Imperial treasury. He died in Regensburg on 15 November 1630, having traveled there in the hope of getting paid. He was fifty-eight years old. Kepler’s grave was destroyed in the Thirty Years’ War, and the location is no longer known. He left a small but extraordinary body of work: the Mysterium Cosmographicum, the Astronomia Nova, the Harmonices Mundi, the Dioptrice (a treatise on optics, including the first correct description of the workings of the telescope), the Rudolphine Tables, the Epitome Astronomiae Copernicanae (a textbook of Copernican astronomy), the Somnium, and many letters and minor works. The Kepler articles treat the technical content in detail: What Are Kepler’s Three Laws of Planetary Motion? and How Did Kepler’s Laws Support Heliocentrism?.
Kepler’s Place in the History of Science
Kepler’s place in this history is unique. He was the first astronomer to insist, against two thousand years of tradition, that the planetary orbits were not circles. He was the first to derive the orbits from data rather than from philosophical principle. He was the first to articulate a clear dynamical principle for planetary motion (the equal-areas law). He was the first to relate the periods and sizes of the orbits in a single mathematical formula (the harmonic law). And he was the first to construct planetary tables of the new precision that made the heliocentric theory practically useful. Kepler’s laws were the empirical foundation on which Newton built. The story of how Newton’s gravitational theory explained Kepler’s laws is told in What Is in Newton’s Principia Mathematica? and in the Laws of Motion and Gravity section. The way Kepler’s laws clinched the heliocentric case is treated in How Did Kepler’s Laws Support Heliocentrism?.