# Kepler, Johann

# KEPLER, JOHANN

Astronomer, mathematician, discoverer of the three laws of planetary motion; b. Weil der Stadt, Germany, Dec. 27, 1571; d. Regensburg, Germany, Nov. 15, 1630.

He was the son of Heinrich and Katharina (Guldenmann) Kepler. The Keplers, Lutherans in a predominantly Catholic city, were craftsmen, although their ancestors belonged to the minor nobility. Kepler attended German and Latin elementary schools, the Maulbronn seminary, and the Tübingen seminary, passing the master's examination in theology in 1591 but continuing at the university. There, Michael Maestlin, although following Ptolemaic astronomy in his writings, taught Kepler the essence of the Copernican theory.

Not his support of that doctrine, but his doubts about the interpretation of the Sacraments and his unwillingness to condemn the Calvinists completely, caused Kepler to incur his teachers' disfavor. In 1594, having been recommended by them as the best available candidate because of his mathematical and astronomical knowledge, Kepler became a mathematics teacher at the Protestant seminary in Graz, Austria.

In 1595 Kepler, believing that nothing in nature was created by God without a plan and influenced by Pythagoras, Plato, and others, suddenly thought of a geometrical structure of the universe that accounted for the number of planets and their relative distances from the sun by circumscribing the five regular solids about the planet spheres. The *Mysterium Cosmographicum* (1596), describing this, attracted the favorable attention of Tycho Brahe.

Kepler sought a parallax of the fixed stars. He could accept neither Tycho's geo-heliocentric system, which he considered a compromise, nor the enormous diameter of the sphere of fixed stars necessitated by a moving earth. He studied chronological problems, magnetism, the inclination of the ecliptic, and the weather, seeking the stars' influence on it. He planned his later work on the world harmony, noting Copernicus's allusion to the symmetry in the visible universe, and finding the regular solids as the basis of musical harmony. To test his theories, Kepler needed Tycho Brahe's accurate observations.

When the Counter Reformation triumphed in Graz, Kepler, although among those ordered to leave, received permission to return, possibly because of his friendship with the Catholic Bavarian chancellor. He never became Catholic and upheld the Augsburg Confession (see augsburg, confession of).

**Work with Tycho Brahe.** When Graz became unbearable, Kepler accepted Tycho's invitation to visit him near Prague, and he finally moved there with his wife and stepdaughter. The two astronomers first met on Feb. 4,1600. Kepler was assigned work on the Mars observations but did not obtain precise values for the eccentricities of the planet orbits and their distances from the sun that he needed to test his theories, nor was he granted access to the bulk of Tycho's observations.

When Tycho died on Oct. 24, 1601, Kepler succeeded him as imperial mathematician but at a lower and infrequently paid salary. Now all of Tycho's observations were at his disposal. Without acceding to Tycho's dying request to present the planetary motions in accordance with the Tychonic system, Kepler, whenever possible, showed where this system agreed with the observations.

**Laws of Planetary Motion.** Kepler believed that within the sun there was a force that moves the planets, their motion being so much the quicker the nearer they are to the sun. Using Tycho's observations of Mars, as though observing the earth from there, Kepler calculated the eccentricity of the earth's orbit, discovering that at the aphelion and the perihelion, and presumably everywhere, the speed of the earth is inversely proportional to its distance from the sun. Dividing half the earth's circular orbit into 180°, he calculated and added together the distances to the sun of each of these little arcs. Correct distances of the earth from the sun provided correct distances from Mars. His use of Mars was fortunate because of its large eccentricity.

His calculations resulted in the discovery (1602) of the second law of planet motion (the radius vector describes equal areas in equal times) and (1605) of the first law (planets move in ellipses with the sun at one focus), both announced in 1609 in the *Astronomia Nova.* Kepler replaced the geometrical systems with a dynamic one and abandoned the 2,000-year old principle of uniform circular motion. Under William gilbert's influence Kepler explained the deviation in radius vector by considering the planets as composed of magnetic filaments; one end of each filament was attracted by the sun, the other repelled.

In the *Ad Vitellionem* (1604) Kepler explained the inverted image on the retina, improved the formula for refraction, and discussed the apparent diameters of the celestial bodies and of eclipses. This book is important in the history of infinitesimal calculus, as are his *Astronomia Nova* and his work on the shapes of wine casks (Latin, 1615; German, 1616) in which he replaced Archimedes' "exhaustion method" by a direct method and contributed to the theory of regular solids.

Kepler described the 1604 nova in German and Latin tracts. He placed it among the fixed stars, thought it an agglomeration of heavenly material, and considered its appearance to be God's manner of exhorting men. The comet of 1607 received similar treatment.

Galileo's *Sidereus Nuncius* (1610) drew a favorable reply from Kepler, whose *Dioptrice* (1611) gave an exhaustive treatment of the passage of light through lenses.

In 1611 Kepler's wife and one of his three children died. The emperor, deposed in 1611, died early in 1612. Thereupon, Kepler moved to Linz, remaining as district mathematician until 1626. During that time he remarried; fathered six children; witnessed his mother's witch trial; and published the *Epitome of Copernican Astronomy* (1618, 1620, 1621), the *World Harmony* (1619), which announced the third planet law (the squares of the times of the revolution of two planets are to each other as the cubes of their mean distances from the sun), a work on logarithms, and other tracts. He worked on the *Somnium* (1634), begun in Tübingen, describing a journey to the moon and the earth viewed from there, and completed the *Rudolphine Tables* (1627), based on Tycho's observations but on the Copernican-Keplerian system of the universe.

His last years were spent in Ulm and in Sagan, in Wallenstein's employ. He died while seeking funds owed him by the Imperial Treasury.

**Bibliography:** m. caspar, *Kepler,* tr. and ed. c. d. hellman (New York 1959); ed., *Bibliographia Kepleriana* (Munich 1936).

[c. d. hellman]

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