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Kepler, Johannes (1571–1630)

KEPLER, JOHANNES
(15711630)

Johannes Kepler, the founder of modern astronomy, was born in Weil der Stadt, near Stuttgart. During his life he was a student of theology, teacher of mathematics and astronomy, assistant to Tycho Brahe, imperial mathematicus to the emperors Rudolf II and Matthias, and astrologer to the duke of Wallenstein. His principal scientific discoveries were the three planetary laws named after him, the principle of continuity in geometry, and the Keplerian telescope. He was also responsible for decisive advances in the theory of optics and in work that led to the development of the infinitesimal calculus, and incidentally he coined a number of terms whose paternity has been forgotten, including satellite (for the moons of Jupiter), dioptrics, focus (of a conic section), and camera obscura.

Significance of Kepler's Laws

Kepler's three laws of planetary motion postulate that the planets travel in elliptical orbits, one focus of each ellipse being occupied by the sun; that the radius vector connecting sun and planet sweeps over equal areas in equal times; and that the squares of the periods of revolution of any two planets are in the same ratio as the cubes of their mean distances from the sun.

The promulgation of the three laws was in several respects a turning point in the history of thought. They were the first "laws of nature" in the modern sense: precise, verifiable statements, expressed in mathematical terms, about universal relations governing particular phenomena. They put an end to the Aristotelian dogma of uniform motion in perfect circles, which had bedeviled cosmology for two millennia, and substituted for the Ptolemaic universea fictitious clockwork of wheels turning on wheelsa vision of material bodies not unlike Earth freely floating in space, moved by physical forces acting on them. Kepler's laws severed the ties between astronomy and theology and replaced the moving spirits of medieval cosmology by physical causation.

What has come to be called the Copernican revolution was in fact mainly the work of Kepler and Galileo Galilei. Kepler's laws and Galileo's studies on the motion of projectiles were the basic ingredients of the Newtonian synthesis. Nicolas Copernicus's De Revolutionibus was published in 1543, nearly thirty years before Kepler was born. Its first edition of a thousand copies never sold out, and it had altogether four reprintings in 400 years. By way of comparison, Christopher Clavius's textbook The Treatise on the Sphere had nineteen reprintings within fifty years; Copernicus's book had one. This curiosity is mentioned because it illustrates the fact that the Copernican theory attracted very little attention on the continent of Europe for more than fifty yearsthat is, for the next two generations. De Revolutionibus was an unreadable book describing an unworkable system. It revived the Pythagorean idea of a heliocentric universe, first proposed by Aristarchus of Samos in the third century BCE, but it adhered to the dogma of circular motion. As a result, Copernicus was forced to let the planets run on no less than forty-eight epicycles and eccentrics. He was in fact, as Kepler remarked, "interpreting Ptolemy rather than nature."

Kepler was the first astronomer to raise his voice in public in favor of the Copernican system. His Mysterium Cosmographicum, published in 1597, fifty-four years after Copernicus's death, initiated the controversy; Galileo only entered the scene fifteen years later. At that time Kepleraged twenty-sixknew little of astronomy. He had started as a theologian, but a chance opportunity made him accept the post of teacher of mathematics and astronomy at the provincial school of Gratz in Styria. Three years later, however, he became assistant to Tycho Brahe, whose observational data, of a hitherto unparalleled richness and precision, provided the empirical foundation for Kepler's efforts to determine the orbit of Mars. It took Kepler eight years of nerve-racking labor to succeed. The result was his magnum opus, published in 1609, which contains the first and second laws (the third came nine years later). It bears a provocative title:

a new astronomy Based on Causation
or a physics of the sky
derived from Investigations of the
motions of the star mars
Founded on Observations of
the noble tycho brahe.

The title is indeed symbolic of the work's revolutionary intent and achievement. Astronomy before Kepler had been a purely descriptive geometry of the skies, divorced from physical reality. Since the observed motions of the planets did not conform to the demands of circularity and uniformity, an increasing number of auxiliary wheels had to be added to the fictitious clockwork to save the phenomena. These wheels were thought to be somehow connected with the eight crystal spheres of medieval cosmology, which were kept in motion by a hierarchy of angels, but any pretense to regard them as a physically workable model had to be abandoned. The situation was summed up in a famous remark by Alfonso X of Castile, called the Wise, when he was initiated into the Ptolemaic system: "If the Lord Almighty had consulted me before embarking on the Creation, I should have recommended something simpler."

Copernicus upset the cosmic hierarchy by placing the sun in its center, but his universe was still cluttered (in John Milton's words) "with centric and eccentric scribbled o'er, Cycle and epicycle, orb in orb." It was Kepler who, by banishing epicycles and eccentrics "to the lumber-room" (as he wrote), finally demolished the very scaffolding, as it were, on which the medieval universe rested and replaced its hierarchy of spirit forces with the interplay of physical forces. The tortuous way in which he achieved this may serve as a cautionary tale to scientists and philosophers and represents a significant episode in the history of thought.

Mysticism and Empiricism

In Kepler all the contradictions of his age seem to have become incarnatethe age of transition from the medieval to the "new philosophy," as the scientific revolution was called by its founders. One half of his divided personality belonged to the past; he was a mystic, given to theological speculation, astrology, and number lore. However, he was also an empiricist with a scrupulous respect for observational data, who unhesitatingly threw out his earlier theory of planetary motions, the product of five years of dogged labor, because certain observed positions of Mars deviated from those that the theory demanded by a paltry eight-minute arc. He later wrote that Ptolemy and Copernicus had been able to shrug away such minor blemishes in their theories because their observations were accurate only within a margin of ten minutes, anyway, but those who, "by divine kindness," were in possession of the accurate observations of Brahe could no longer do so. "If I had believed that we could ignore those eight minutes," he wrote in the Astronomia Nova (II, Ch. 19), "I would have patched up my hypothesis accordingly. But since it was not permissible to ignore them, those eight minutes point the road to a complete reformation of astronomy."

This newfound respect for hard, obstinate facts was to transform what used to be called "natural philosophy" into the "exact" (or "experimental") sciences and to determine, to a large extent, the climate of European thought during the next three centuries. It provided Kepler with the necessary discipline and put a restraint on his exuberant fantasy, but the primary motivation of his researches was mysticism of a Pythagorean brand. Throughout his life he was obsessed by certain mystic convictions, each of which had the power of an idée fixe. The first was the belief that the solar system was patterned on the perfect, or "Pythagorean," solids (Saturn's orbit circumscribed a cube into which was inscribed the orbit of Jupiter; into this was inscribed the tetrahedron that circumscribed the orbit of Mars; and so on down to the octahedron inscribed into the orbit of Mercury). The second was the equally Pythagorean belief that the planetary motions were governed by musical harmonies (the book containing the third law is called Harmonice Mundi ). Fortunately, both lent themselves to mathematical juggling almost ad lib, until they fitted the data. Far from interfering with his reasoning powers, these irrational obsessions were harnessed to his rational pursuits and provided the drive for his tireless labors. From a subjective point of view, Kepler's fundamental discoveries were in fact merely by-products of his chimerical quest. Toward the end of his life he proudly mentioned in retrospect some of his minor achievements, but there is no mention whatsoever of his epoch-making first and second laws.

Emergence of the Concept of Force

The apparent paradox of a mystically inspired prejudice acting as a spur to scientific achievement is most clearly exemplified in the circumstances that led Kepler to introduce into astronomy the concept of physical forces. As has already been stated, he started his career as a student of theology (at the Lutheran University of Tübingen). The reason the concept of a heliocentric universe attracted the young theologian was later stated by him repeatedly. Thus, in the "Preface to the Reader" of his Mysterium Cosmographicum he explained that he had often defended the opinions of Copernicus in the discussions of the candidates at the seminary and had also written "a careful disputation on the first motion which consists in the rotation of the earth around the sun for physical, or if you prefer, metaphysical reasons." (The last phrase is emphasized because it is repeated verbatim in various passages in Kepler's works.)

He then proceeded to explain the nature of these "metaphysical reasons." They were originally based on a supposed analogy between the stationary sun, the stars, and interstellar space, on the one hand, and God the Father, the Son, and the Holy Ghost, on the other. In his first book the young Kepler promised the reader to pursue this analogy in his future cosmographical work; twenty-five years later, when he was over fifty, he reaffirmed his belief in it. "It is by no means permissible to treat this analogy as an empty comparison; it must be considered by its Platonic form and archetypal quality as one of the primary causes" (Mysterium Cosmographicum, note to 2nd ed.).

He stuck to this belief to the end of his life, as he stuck to the Pythagorean solids and the harmony of the spheres. But gradually his cherished analogy underwent a significant change. The fixed stars were replaced by the moving starsthe planets. The sun in the center of the planets, "himself at rest and yet the source of motion," continued to represent God the Father, and "even as the Father creates through the Holy Ghost" so the sun "distributes his motive force through a medium which contains the moving bodies" (letter to Maestlin, March 10, 1595).

Thus, the Holy Ghost no longer merely fills the space between the motionless sun and the fixed stars. It has become an active agent, a vis motrix that drives the planets. Nobody before had suspected the existence of such a force emanating from the sun. Astronomy had been concerned not with the causes of the heavenly motions but with their description. The passages just quoted are the first intimation of the forthcoming synthesis of cosmology and physics. Once he conceived the idea, derived from his analogy, that the sun was the source of the power that makes the planets go round, Kepler hit upon a question no one else had asked before him: Why do the planets closer to the sun go round faster than those farther away? His first answer to it, in the Mysterium Cosmographicum, was that there exists only one "moving soul" in the center of all the orbitsthat is, the sunwhich drives the planets "the more vigorously" the closer they are, but by the time it reaches the outer planets the force is quasi exhausted "because of the long distance and the weakening of the force which it entails."

Twenty-five years later, in the notes to the second edition, he commented that if we substitute for the word soul the word force, "then we get just the principle which underlies my physics of the skies." He continued to explain that he had once firmly believed the motive force was a soul; yet as he reflected that the force diminishes in proportion to distance, just as light diminishes in proportion to distance, he came to the conclusion "that this force must be something substantial'substantial' not in the literal sense but in the same manner as we say that light is something substantial, meaning by this an unsubstantial entity emanating from a substantial body."

The twenty-five years that separate these two quotations mark the transition from anima motrix to vis motrix, from a universe animated by purposeful intelligences to one moved by inanimate, "blind" forces devoid of purpose. For the rest of his life Kepler struggled with this new concept emerging from the womb of animism (its very name, virtus, or vis, betrays its origin) without ever coming to terms with it. At first he was not aware of the difficulties inherent in it. In a letter to a friend, which he wrote when the Astronomia Nova was nearing completion, he outlined his program:

My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork (and he who believes that a clock has a soul, attributes the maker's glory to the work), insofar as nearly all the manifold motions are caused by a most simple, magnetic, and material force, just as all motions of the clock are caused by a simple weight. And I also show how these physical causes are to be given numerical and geometrical expression. (Letter to Herwart, February 10, 1605)

Kepler had defined the essence of the scientific revolution. But it turned out to be easier to talk about a "most simple, magnetic, material force" than to form a concrete idea of its working. Kepler's efforts to visualize the nature of the "moving force" emanating from the sun are not only of exceptional interest from the historian's point of view; they also illuminate the philosophical difficulties that were inherent in the concept of "force" from its very beginning. Since no English translation of the Astronomia Nova was published by the time this article was written, a few quotations may be found in order. First, Kepler compared the "moving force" of the sun with the light emitted by it:

Though the light of the sun cannot itself be the moving force it may perhaps represent a kind of vehicle, or tool, that the moving force uses. But the following considerations seem to contradict this. First, the light is arrested in regions that lie in shade. If, then, the moving force were to use light as a vehicle, darkness would bring the planets to a standstill.

This kind of force, just like the kind of force that is light, can be regarded not as something that expands into the space between its source and the movable body but as something that the movable body receives out of the space it occupies. It is propagated through the universe but it is nowhere received except where there is a movable body, such as a planet. The answer to this is: although the moving force has no substance, it is aimed at substance, i.e., at the planet-body to be moved.

Who, I ask, will pretend that light has substance? Yet nevertheless it acts and is acted upon in space, it is refracted and reflected, and it has quality, so that it may be dense or sparse and can be regarded as a plane where it is received by something capable of being lit up. For, as I said in my Optics, the same thing applies to light as to our moving force: it has no present existence in the space between the source and the object it lights up, although it has passed through that space in the past; it "is" not, it "was," so to speak. (Astronomia Nova, III, Ch. 33)

Thus, Kepler's gropings brought him closer to the modern concept of the field than to the Newtonian concept of force, and the modern scientist grappling with the paradoxes of quantum theory will find here an echo of his own perplexities. This may be the reason Kepler, having hit on the concept of universal gravity, subsequently discarded itas Galileo and René Descartes were to discard it.

Gravity and Animism

The most precise pre-Newtonian formulations of gravity are to be found in the preface to the Astronomia Nova. Kepler started by refuting the Aristotelian doctrine according to which all "earthy" matter is heavy because it is its nature to strive toward the center of the worldthat is, Earth. But all "fiery" matter strives by its nature toward the periphery of the universe and is therefore light. Kepler explained that there is no such thing as lightness, but, rather, the

matter that is less dense, either by nature or through heat, is relatively lighter and therefore less attracted [to the earth] than heavier matter. Supposing the earth were in the center of the world, heavy bodies would be attracted to it, not because it is in the center, but because it is a material body. It follows that regardless of where we place the earth, heavenly bodies will always seek it.

Gravity is the mutual bodily tendency between cognate [i.e., material] bodies toward unity or contact (of which kind the magnetic force also is), so that the earth draws a stone much more than the stone draws the earth.

If the earth and the moon were not kept in their respective orbits by a spiritual or some equivalent force, the earth would ascend toward the moon 1/54 of the distance, and the moon would descend the remaining 53 parts of the interval, and thus they would unite. But this calculation presupposes that both bodies are of the same density.

If the earth ceased to attract the waters of the sea, the seas would rise and flow into the moon.

If the attractive force of the moon reaches down to the earth, it follows that the attractive force of the earth, all the more, extends to the moon and even farther.

If two stones were placed anywhere in space near to each other, and outside the reach of force of a third cognate body, then they would come together, after the manner of magnetic bodies, at an intermediate point, each approaching the other in proportion to the other's mass.

In the same passage is to be found the first approximation to a correct theory of the tides, which Kepler explained as "a motion of the waters toward the regions where the moon stands in the zenith." In a work written at the same time"SomniumA Dream of the Moon" (an early exercise in science fiction)he furthermore postulated that the sun's attraction, too, influences the tidesthat is, that the gravitational force of the sun reaches as far as Earth.

But here we are faced with another paradox. In the preface to the Astronomia Nova, Kepler, as we have seen, had grasped the essence of gravity and even the idea that its force is proportionate to its mass; yet in the text of Somnium, and all subsequent works, he seems to have completely forgotten it. The force that emanates from the sun in the Keplerian universe is not a force of attraction but a tangential force, a kind of vortex or "raging current which tears all the planets, and perhaps all the celestial ether, from West to East."

To the question of what made Kepler drop gravity no answer is found anywhere in his profuse writings. Everything points to some unconscious psychological blockage, and we may gather hints about its nature in the writings of the other pioneers of the scientific revolution. Kepler's suggestion that the tides were caused by the moon's attraction Galileo indignantly rejected as an "occult fancy" (Dialogue concerning the Two Chief World Systems ). Descartes was equally repelled by the idea of a nonmechanical force acting at a distance and, like Kepler, substituted for it vortices in the ether. As for Isaac Newton, his attitude is summed up in his famous third letter to Richard Bentley, in which he said it is inconceivable that "inanimate brute matter" should, without some mediating material substance, act upon other bodies.

That gravity should be innate, inherent, and essential to matter, so that one body may act upon another, at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.

Kepler, Galileo, and Descartes did not fall into the philosophical abyss; their thinking was much too "modern"that is, mechanisticfor that. The notion of a "force" that acts without an intermediary agent and pulls at immense stellar objects with ubiquitous ghost fingers appeared to them mystical and unscientific, a lapse into that Aristotelian animism from which they had just broken loose. Universal gravity, gravitatio mundi, smacked of the anima mundi of the ancients. Newton overcame the obstacle and made the concept of gravity respectable by invoking a ubiquitous ether, whose attributes were equally paradoxical, and by refusing to speculate on the manner in which gravity worked (his hypothesis non fingo refers to this problem, and to this problem only, though it is often quoted out of context). But above all, he provided a precise mathematical formula for the mysterious agency to which gravity referred. That formula Newton deduced from the laws of Kepler, who had intuitively glimpsed universal gravity and shied away from it. In such crooked ways does the tree of science grow.

Synthesis of Astronomy and Physics

In the Aristotelian cosmos, physical forces operated only among the four elements in the sublunary sphere; the motions of the celestial bodies, made of a fifth element, were due to spiritual agencies and governed by the demands of geometrical perfection. Kepler and Galileo broke down this dualism by postulating that physical causality permeates the entire universe. Kepler's "physics of the sky" we know to have been all wrong. He had no notion of inertial momentum, and he had dropped gravity. In Kepler's universe the sun exerted a tangential force (diminishing in direct ratio with increasing distance), which the "lazy" planets resisted, and the eccentricity of the orbits was accounted for by magnetic forces. (Since the planets' magnetic poles always pointed in the same direction, they would be drawn closer to the sun in the aphelion and repelled in the perihelion.)

But though the model was wrong in every detail, his basic assumption, that there were several antagonistic forces acting on the planets, guided him in the right direction. A single force, as previously assumedthe Prime Mover and the allied hierarchy of angelswould never produce elliptical orbits and periodic changes of velocity. These could only be the result of some tug of war going on in the sky, and this dynamic concept, supported by a series of wild ad hoc hypotheses, led him in the end, after countless detours, to his three laws.

Kepler's determination of the orbit of Mars became the unifying link between two hitherto separate universes of discourse, celestial geometry and earthly physics. His was the first serious attempt to explain the mechanism of the solar system in terms of physical forces. Once the example was set, astronomy and physics could never again be divorced.

See also Aristotelianism; Copernicus, Nicolas; Descartes, René; Force; Galileo Galilei; Geometry; Laws of Nature; Mass; Matter; Milton, John; Nature, Philosophical Ideas of; Newton, Isaac; Philosophy of Physics; Pythagoras and Pythagoreanism; Scientific Revolutions.

Bibliography

works by kepler

Joannis Kepleri Astronomi Opera Omnia. 8 vols., edited by C. Frisch. Frankfurt and Erlangen: Heyder and Zimmer, 18581871.

Johannes Kepler, Gesammelte Werke, edited by W. van Dyck, Max Caspar, and Franz Hammer. Munich: C.H. Beck, 1938.

"Somnium, Sive Astronomia Lunaris" (SomniumA Dream of the Moon). Translated by Patricia Frueh Kirkwood, in John Lear, Kepler's Dream. Berkeley: University of California Press, 1965.

works on kepler

Barker, Peter. "Constructing Copernicus." Perspectives on Science 10(2) (2002): 208227.

Caspar, Max. Johannes Kepler. Stuttgart: Kohlhammer, 1948. Translated by C. D. Hellman. New York, 1962 (paperbound).

Chen Morris, Raz D. "Optics, Imagination, and the Construction of Scientific Observation in Kepler's New Science." Monist 84(4) (2001): 453486.

Dear, Peter. Revolutionizing the Sciences: European Knowledge and its Ambitions, 15001700. Princeton, NJ: Princeton University Press, 2001.

Diederich, Werner. "The Structure of the Copernican Revolution." Dialogos 36(77) (2001): 724.

Franklin, Allan, and Colin Howson. "Newton and Kepler, a Bayesian Approach." Studies in History and Philosophy of Science 16 (1985): 379385.

Holton, Gerald. Thematic Origins of Scientific Thought: Kepler to Einstein, Revised Edition. Cambridge, MA: Harvard University Press, 1988.

Jarine, N. The Birth of History and Philosophy of Science: Kepler's 'A Defence of Tycho Against Ursus', with Essays on Its Provenance and Significance. New York: Cambridge University Press, 1984.

Kiikeri, Mika. "Interrogative Reasoning and Discovery: A New Perspective on Kepler's Inquiry." Philosophica 63(1) (1999): 5187.

Kleiner, Scott A. "A New Look at Kepler and Abductive Argument." Studies in History and Philosophy of Science 14 (1983): 279314.

Koestler, A. "Kepler and the Psychology of Discovery." In The Logic of Personal Knowledge, Essays Presented to Michael Polanyi, edited by Marjorie Grene. London: Routledge and Paul, 1961.

Koestler, A. The Sleepwalkers. London: Hutchinson, 1959.

Kozhamthadam, Job. The Discovery of Kepler's Laws: The Interaction of Science, Philosophy, and Religion. Notre Dame: University of Notre Dame Press, 1994.

Kozhamthadam, Job. "Kepler and the Sacredness of Natural Science." Philosophy in Science 7 (1997): 936.

Martens, Rhonda. "Kepler's Solution to the Problem of a Realist Celestial Mechanics." Studies in History and Philosophy of Science 30a(3) (1999): 377394.

Phalet, A. "On the Logic of Kepler's Evolving Models" In Logic of Discovery and Logic of Discourse, edited by Jaakko Hintikka. New York: Plenum Press, 1985.

A. Koestler (1967)

Bibliography updated by Tamra Frei (2005)

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