# JOHANNES KEPLER.

Born: 1571, Weil-der-Stadt, GermanyDied: 1630, Regensburg, Germany

Major Works: Mysterium Cosmographicum (1596), Astronomia Nova (1609), Harmonice Mundi (1618). Epitome Astronomiae Copernicanae (1617-21), Tabulae Rudolphinae (1627)

Major Ideas

God did not create the universe haphazardly: A rational architecture underlies the structure of the solar System.

Three laws govern the motion of the planets:

1. The planets move in elliptical, not circular, orbits.

2. The velocities of the planets are not uniform but vary at different points in their orbits; the areas swept by the radius vectors in equal times are equal.

3. The velocities of the planets relative to each other can be expressed mathematically: The squares of the periods of revolution are proportional to the cubes of the distances from the sun.

A force emanating from the sun governs the motion of the celestial bodies.

Weight arises from the mutual attraction between two bodies.

Aristotelian physics, which postulates four terrestrial elements (earth, air, fire, water) with weight and one celestial element (the ether,) without, is false; celestial matter is not fundamentally different from terrestrial matter, and the physics of celestial motion is no different from that of terrestrial motion.

The work of Johannes Kepler marks a fundamental advance 6V& the Aristotelian physics and Pto1emaic astronomy inherited from antiquity. His immediate predecessor Copernicus, who wrote the first systematic exposition of heliocentric astronomy (De Revolutionibus, 1543), had maintained the earlier postulates: Celestial bodies move with uniform circular motions the visible motions can be modeled by supplying a sufficient number of deferents and epicycles; no motive force is needed, because the planets move of their own nature. Kepler's deep-seated belief that the sun emits a force that pervades the cosmos and drives all the celestial bodies on their courses, a belief which meshed well with his Christian faith led him to investigate the causes of celestial motions and to postulate the existence of a force, now called gravity, which links the cosmos into one organism. His willingness to treat the planets as objects having the same nature as terrestrial bodies enabled him to discard the necessity for circular motions and to adopt elliptical orbits. His mathematical curiosity drove him to make correlations between what had been considered unrelated phenomena and from these phenomena to deduce laws.

Johannes Kepler was born to a respectable family of Weil-der-Stadt, in Wurttemberg, southern Germany. His grandfather was the mayor of Weil, his father a professional soldier who campaigned in the low countries. After preparatory schooling, Kepler entered the university at Tubingen in 1588. There he was influenced by the astronomy professor Michael Maestlin, a thoroughgoing Copernican. In 1594, Kepler, although he had almost completed his graduate program in theology, was assigned to teach mathematics at the Lutheran school in Graz, Austria. This fortuitous appointment, made over Kepler's protests, must count as one of the turning points in scientific history He had hardly any pupils. and his additional duties, which included preparing almanacs and astrological forecasts for the Province of Styria, left him the leisure to meditate on the structure of the universe. The results of these meditations appeared in his first book, the Mysterium Cosmographicum.

This text is characteristic of all Kepler's works. Its style, a combination of wild fancy and detailed, sober mathematical investigation, strikes the modern reader as bizarre, and its goal, an attempt to explain the principles by which God created the universe in its existing configuration, recalls traditional philosophical teleology.

In the prefatory chapter of the Mysterium Cosmographicum, Kepler outlines the Copernican hypothesis and defends it, not on the basis that it simplifies computation--its usual defense--but on the basis that it describes reality and explains phenomena that hitherto had simply been accepted as "natural": Planets at apogee (farthest from the earth) are at the same time in conjunction with the sun because they are on the other side of the sun from the earth; at perigee (closest to the earth) they are in opposition to the sun because the earth is between them and the sun; Mercury and Venus never appear in opposition to the sun because their orbits are between the earth and the sun; and a number of other points.

It must be remembered that in the fifty years after Copernicus's De Revolutionibus appeared, his system had not been widely accepted, largely because it represented celestial motions no better than did Ptolemy's system and was based not on recent data but on Ptolemy's observations of 1400 years earlier. Like most of his contemporaries, Copernicus had treated his heliocentric model as a computational convenience, not as an accurate description of reality. Kepler was not satisfied with this: He wanted to discover the structure of reality.

He recounts in detail how this discovery was made "by a gift of divine Providence." Since God did not create haphazardly, perhaps the mathematician could divine the architecture behind the creation. Therefore Kepler tried to correlate planetary orbits with numbers, ratios, and plane figures, but nothing worked. He then tried to nest the five regular solids between the planetary orbits: Between the earth and Mars he circumscribed a dodecahedron (twelve sides); between Mars and Jupiter he placed a tetrahedron; between Jupiter and Saturn he placed a cube. Then the inner planets: Between earth and Venus was an icosahedron (twenty sides), and between Venus and Mercury an octahedron. The editions of the Mysterium Cosmographicum have beautiful engravings of these nested solids. Kepler then calculated the relative distances of the planetary orbits assuming the intervening solids, and the correspondence with the truth was astonishing: After a little adjustment, everything fit within 5 percent. Thus he seemed to have discovered the geometrical structure that governed the solar system.

The final sections of the Mysterium Cosmographicum explain the orbital motion of the planets. These bodies do not move with the same velocities: For example, Saturn traverses its orbit at a slower rate than Jupiter traverses its orbit. Why is this? Kepler accepted Aristotle's theory of motion (an object moves only so long as there is a force acting on the object), and he speculated that the sun emits the necessary motive force, and that this force naturally weakens with distance. The sun is the Father, the motive force is the Holy Ghost, as he metaphorically expressed it. He tried to calculate the ratio between the planet's velocity and its distance from the sun, but failed. In his later Harmonice Mundi, he succeeded when he formulated his third law.

The concepts outlined in the Mysterium Cosmographicum remained at the heart of Kepler's work: the rationality of the created universe, the mathematical relationships between planetary orbits, the ratio between orbital period and distance from the sun, the force emanating from the sun. This work was still dear to him when he published a second edition with notes twenty-five years later (1621).

Most important for later astrophysics was the importance attributed to the sun. In Copernican astronomy, the sun acted simply as an illuminator; all motion was referred to the center of the earth's orbit, near which the sun happens to be located. It was Kepler who made the sun the dynamically active center of the cosmos.

The Mysterium Cosmographicum established Kepler as a leading theoretician. Most important for later astronomy, Tycho Brahe received a copy and responded in a letter that was as gracious as the acerbic Danish astronomer could manage. For twenty years at his observatory on Hveen, an island near Copenhagen Brahe had been regularly observing and recording planetary positions and had a .mass of data of unparalleled accuracy at his disposal. Leaving Hveen in 1597, Brahe had moved to Prague as the "Imperial Mathematician" of Rudolph II. Meanwhile, in 1599, Kepler was forced to leave Graz because of anti-Lutheran agitation. After learning of Brahe's move, he set out for Prague to visit with the Dane. Brahe welcomed the younger astronomer and invited him to join his staff. Brahe was in the process of drawing up a new and more accurate set of astronomical tables, and Kepler was assigned the task of working out the theory of the motion of Mars. Despite the personality conflicts between the two astronomers, Kepler later considered this assignment as an act of Providence, for through his studies of this difficult planet. he came to the theories described in his most important work, the Astronomia Nova.

In this work, Kepler describes his struggles to correlate Brahe's observations of Mars's orbit with various motions, first circular, then oval, finally elliptical. Continuing the speculations of the Mysterium Cosmographicum, Kepler rethought his views on the mechanism by which the sun governed the planets. He knew that the planets' velocities varied inversely with their distances from the sun, and under the influence of William Gilbert's De Magnete (1660), he decided that a rotating sun drove the planets by means of magnetic vortices whose energy would be less for the more distant planets. (He makes the analogy with light, whose illuminating power decreases with distance.) First assuming that the orbits are eccentric circles (as did Ptolemy), he formulated his second law (chronologically the first) The radius vector of the orbit sweeps out equal areas in equal times. This law in its original form, applied to circular orbits, did not work for Mars, but left an 8' discrepancy: Mars was 8' closer to the earth a t the orbital points 90[degrees] from aphelion (point farthest from the sun) and from perihelion '(point closest to the sun). Now, such a small amount would have been ignored by earlier astronomers, but Kepler knew that Brahe's observations were accurate to 8'. The discrepancy had to be resolved.

Kepler finally concluded that the planetary orbits are elliptical, not circular and eccentric, and that the sun is at one focus of the ellipse. This is his first law. With the ellipse, he could reconcile Brahe's observations with theory and supply a satisfactory dynamic for the sun--planet interaction. In adopting elliptical orbits, Kepler finally broke with the Aristotelian physics that had governed all earlier cosmological speculation. Aristotle had stated that the sublunary world consisted of earth, air, fire, and water, while the celestial world consisted of the fifth element, ether, whose primary inherent characteristic is its eternal circular motion--hence no further explanation of celestial motion was necessary. Kepler rejected this theory and laid the groundwork for modern astrophysics: the investigation of celestial motion on mechanical principles. The completion of these investigations in modern astrophysics became possible only with Newton's calculus and Einstein's relativity theory.

While finishing the Astronomia Nova, Kepler began investigating optics, as had Ptolemy before him. His results were published as Astronomiae Pars Optica (1604). Its chapters discuss parallax and refraction, and show for the first time that vision proceeds by images formed on the retina of the eye. In this work no mention is made of lenses or telescopes. Not until 1610 did Kepler even have access to a telescope; in that year he observed Jupiter, duplicating the observations of Galileo's Sidereus Nuncius.

The years from 1611 to the end of his life were restless and troubled. His wife and several children died of disease in the troubles of the Counter-Reformation; his aged mother in Wurttemberg was accused of witchcraft (several months of the period from 1617-21 were devoted to her defense); and his protector, Rudolph II, abdicated in the face of riots in Prague. As a result of this last misfortune, Kepler moved to Linz, Austria, where he resided for fourteen years. During this period he prepared three major works, Harmonice Mundi, Epitome Astronomiae Copernicanae, and the Tabulae Rudolphinae. Among the minor works of this period are the Stereometria doliorum vinariorum (The Measurement of Wine Casks), in which he developed a precursor of the calculus to measure the volume of irregular solids; the Somnium, the first science-fiction adventure, a trip to the moon; and a number of astrological almanacs, which he regularly produced to supplement his irregular income as imperial mathematician.

In the Harmonice Mundi, Kepler elaborated concepts first outlined in the Mysterium Cosmographicum. The basic principles of the cosmos are based on geometry: Specifically, the regular polygons are archetypal forms in the human soul as well as in the celestial world; when the planets in their orbits form angles corresponding to the angles of these polygons (for example, 90[degrees] square, 60[degrees] trine), they inspire and excite the soul. Kepler pursued this line of thought in his astrological writings. Musical harmony is also based on these angles: The ratios of the musical scale (octave, fifth, and so forth) can be derived from the polygons by suitable construction. Furthermore, the planets' orbital velocities create a harmony: (1) There is a simple ratio between the planet's velocity at aphelion and its velocity at perihelion; (2) the squares of the periods of revolution of any two planets (the time in which they complete one orbit) are proportional to the cubes of their mean distances from the sun. Thi s latter is Kepler's third, or harmonic, law, and his joy at its discovery was unbounded. In the final chapters of Harmonice Mundi he assigns musical "notes" to the planets at aphelion and perihelion and demonstrates by the variations in the "tunes" thus played by each planet the eccentricity of the orbit of each: Venus, with an almost circular orbit, plays a monotonous tune; the very eccentric Mercury runs up and down the scale.

Much of Harmonice Mundi has been termed mystic fantasy, but this fantasy, as always, was founded on carefully observed fact and aimed at explicating the dynamics and structure of the solar system. Kepler's imaginative mind structured and explained data in terms strange to us, but this exuberant imagination did succeed in discovering his three laws of planetary motion.

In the Epitome Astronomiae Copernicanae, Kepler summarized his own--not Copernicus's--work on astronomy: The nested polygons of the Mysterium, the elliptical orbits, and the sun's propulsive force all appear. New in this book was his long theoretical justification of his third law. He establishes that a planet's velocity on its orbit depends on four factors: (1) the length of the orbit; (2) the density of the planet; (3) the volume of the planet; and (4) the emanation from the sun, by which the sun sends into space a magnetic whirlwind that both carries the planets along and makes them rotate. The greater (1) and (2) are, the slower the planet; the greater (3) and (4) are, the faster the planet. One consequence is that the large, slower planets farther from the sun (Jupiter, Saturn) must be less dense, while those closer to the sun, particularly Mercury, must be very dense. Not knowing of the existence of Neptune or Pluto, Kepler could defend this law with telescopic observations showing the great size of th e known outer planets. For him this third law simply stated a fact about the six known planets. In this work Kepler also developed an accurate theory of lunar motion: He was the first to calculate for the moon an elliptical orbit that is modified by the influence of the earth and the sun.

The Tabulae Rudolphinae (Rudolphine Astronomical Tables), Kepler's last major work, appeared three years before his death. These tables, whose remote ancestors were Ptolemy's Handy Tables, enabled astronomers to determine the position of any celestial body at any date, past or future, with unparalleled accuracy, and they quickly superseded all other tables. Their accuracy served as proof of the truth of Kepler's astronomical theories. The use of the tables was explained in a preface, but the reader was referred to the Epitome for an explanation of their theoretical basis.

Kepler's work is an example of the deduction of general laws from a mass of observations--the essence of science. But it was primarily his attempt to apply physical principles to astronomical data that marks his break with ancient astronomy. His work was completed by Isaac Newton, who reworked his ideas about the sun's emanations and his three laws into a theory of universal gravitation and thus made Kepler's speculations into principles of astrodynamics.

Further Reading

Caspar, Max. Johannes Kepler. Stuttgart, 1948. 2d ed., 1950, English translation by C. Doris Hellman. New York, Abelard-Schuman, 1959. The definitive biography. Much of this biography has been reworked in Koestler's Sleepwalkers.

Duncan, A. M. Johannes Kepler: Mysterium Cosmographicum/The Secret of the Universe. New York: Abaris Books, 1981. This facsimile of the second (1621) edition with a facing English translation is an excellent introduction to the guiding themes of Kepler's thought.

Koestler, Authur. The Sleepwalkers. New York: Macmillan, 1959. The best part of this history of man's changing view of the universe is the long section on Kepler, which has been published separately as The Watershed (Garden City, N.Y.: Anchor Books, 1960). The author describes Kepler's scientific achievement; he is most successful at analyzing Kepler's psychology.

Koyre, Alexander. The Astronomical Revolution. Ithaca, N.Y.: Cornell University Press, 1973. Originally published in French, this detailed description of Kepler's scientific thought includes extensive translations from Kepler's original text. It is practically an anthology of the major works.

Stevenson, Bruce. Kepler's Physical Astronomy. New York: Springer-Verlag, 1987. A review of physics and mathematics in the Mysterium Cosmographicum, Astronomia Nova, and the Epitome, the author shows the importance of Kepler's speculations in physics for the development of his astronomical laws.

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Author: | RILEY, MARK T. |
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Publication: | Great Thinkers of the Western World |

Article Type: | Biography |

Date: | Jan 1, 1999 |

Words: | 2874 |

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