Johannes Kepler
1571-1630

The German astronomer Johannes Kepler was one of the chief founders of modern astronomy because of his discovery of three basic laws underlying the motion of planets.

Johannes Kepler was born on Dec. 27, 1571, in the Swabian town of Weil. His father, Heinrich Kepler, was a mercenary; although a Protestant, he enlisted in the troops of the Duke of Alba fighting the Reformed insurgents in the Low Countries. Kepler's grandmother brought him up; for years he was a sickly child. At 13 he was accepted at a theological seminary at Adelberg.

Kepler wanted to become a theologian, and following his graduation from the University of Tübingen, as bachelor of arts in 1591, he enrolled in its theological faculty. But he was also interested in French literature and astronomy. His poor health and proclivity to morbidness singled him out no less than did his precocious advocacy of the doctrine of Copernicus.

It seems that the University of Tübingen gladly presented Kepler for the post of the "mathematician of the province" when request for a candidate came from Graz. He arrived there in April 1594 and set himself to work on one of his duties, the composition of the almanac, in which the main events of the coming year were to be duly predicted. His first almanac was a signal success. The occurrence of two not too unlikely events, an invasion by the Turks and a severe winter, which he had predicted, established his reputation.

Far more important for astronomy was the idea that seized Kepler on July 9, 1595. It appeared to him that the respective radii of the orbits of the planets corresponded to the lengths determined by a specific sequence in which the five regular solids were placed within one another, with a sphere separating each solid from the other. The sphere (orbit) of Saturn enveloped a cube which in turn enveloped another sphere, the orbit of Jupiter. This circumscribed a tetrahedron, a sphere (the orbit of Mars), a dodecahedron, a sphere (the orbit of earth), an icosahedron, a sphere (the orbit of Venus), an octahedron, and the smallest sphere (the orbit of Mercury). The idea was the main theme of his Mysterium cosmographicum (1596).

The next year Kepler married Barbara Muehleck, already twice widowed, "under an ominous sky," according to Kepler's own horoscope. Of their five children only one boy and one girl reached adulthood. It was with reluctance that Kepler, a convinced Copernican, first sought the job of assistant to Tycho Brahe, the astrologer-mathematician of Rudolph II in Prague. He took his new position in 1600. On the death of Tycho the following year, Kepler was appointed his successor.


His Three Laws

Kepler's immediate duty was to prepare for publication Tycho's collection of astronomical studies, Astronomiae instauratae progymnasmata (1601-1602). Kepler fell heir to Tycho's immensely valuable records. Their outstanding feature lay in the precision by which Tycho surpassed all astronomers before him in observing the position of stars and planets. Kepler tried to utilize Tycho's data in support of his own layout of the circular planetary orbits. The facts, that is, Tycho's observations, forced him to make one of the most revolutionary assumptions in the history of astronomy. A difference of 8 minutes of arc between his theory and Tycho's data could be explained only if the orbit of Mars was not circular but elliptical. In a generalized form this meant that the orbits of all planets were elliptical (Kepler's first law). On this basis a proper meaning could be given to another statement of his which he had already made in the same context. It is known as Kepler's second law, according to which the line joining the planet to the sun sweeps over equal areas in equal times in its elliptical orbit.

Kepler published these laws in his lengthy discussion of the orbit of the planet Mars, the Astronomia nova (1609). The two laws were clearly spelled out also in the book's detailed table of contents. Thus they must have struck the eyes of any careful reader sensitive to an astronomical novelty of such major proportion. Still, Galileo failed to take cognizance of them in his printed works, although he could have used them to great advantage to buttress his advocacy of the Copernican system.

The relations between Galileo and Kepler were rather strange. Although Galileo remained distinctly unappreciative of Kepler's achievements, the latter wrote a booklet to celebrate Galileo's Starry Messenger immediately upon its publication in 1610. On the other hand, Kepler argued rather vainly in his Conversation with the Starry Messenger (1610) that in his Astronomiae pars optica (1604), or Optics, which he presented as a commentary to Witelo's 13th-century work, one could find all the principles needed to construct a telescope.

In 1611 came Rudolph's abdication, and Kepler immediately looked for a new job. He obtained in Linz the post of provincial mathematician. By the time he moved to Linz in 1612 with his two children, his wife and his favorite son, Friedrich, were dead. Kepler's 14 years in Linz were marked, as far as his personal life was concerned, with his marriage in 1613 to Suzanna Reuttinger and by his repeated efforts to save his aged mother from being tried as a witch.

As for Kepler the scientist, he published two important works while he was in Linz. One was the Harmonice mundi (1618), in which his third law was announced. According to it the squares of the sidereal periods of any two planets are to each other as the cubes of their mean distances from the sun. The law was, however, derived not from celestial mechanics (Newton's Principia was still 6 decades away) but from Kepler's conviction that nature had to be patterned along quantitative relationships since God created it according to "weight, measure and number." Shortly after his first book appeared, he wrote in a letter: "Since God established everything in the universe along quantitative norms, he endowed man with a mind to comprehend them. For just as the eye is fitted for the perception of colours, the ear for sounds, so is man's mind created not for anything but for the grasping of quantities." In the Harmonice mundi he wrote merely a variation on the same theme as he spoke of geometry which "supplied God with a model for the creation of the world. Geometry was implanted into human nature along with God's image and not through man's visual perception and experience." The second work was the Epitome astronomiae Copernicanae, published in parts between 1618 and 1621. It was the first astronomical treatise in which the doctrine of circles really or hypothetically carrying the various planets was completely abandoned in favor of a physical explanation of planetary motions. It consisted in "magnetic arms" emanating from the sun.

Kepler was already in Ulm, the first stopover of the wanderings of the last 3 years of his life, when his Tabulae Rudolphinae (1628) was published. It not only added the carefully determined position of 223 stars to the 777 contained in Tycho's Astronomiae instauratae progymnasmata but also provided planetary tables which became the standard for the next century. Kepler died on Nov. 15, 1630. He was a unique embodiment of the transition from the old to the new spirit of science.

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Johannes Kepler was born in Weil der Stadt in Swabia, in southwest Germany. His paternal grandfather, Sebald Kepler, was a respected craftsman who served as mayor of the city; his maternal grandfather, Melchior Guldenmann, was an innkeeper and mayor of the nearby village of Eltingen. His father, Heinrich Kepler, was "an immoral, rough and quarrelsome soldier," according to Kepler, and he described his mother in similar unflattering terms. From 1574 to 1576 Johannes lived with his grandparents; in 1576 his parents moved to nearby Leonberg, where Johannes entered the Latin school. In 1584 he entered the Protestant seminary at Adelberg, and in 1589 he began his university education at the Protestant university of Tübingen. Here he studied theology and read widely. He passed the M.A. examination in 1591 and continued his studies as a graduate student.

Kepler's teacher in the mathematical subjects was Michael Maestlin (1550-1635). Maestlin was one of the earliest astronomers to subscribe to Copernicus's heliocentric theory, although in his university lectures he taught only the Ptolemaic system. Only in what we might call graduate seminars did he acquaint his students, among whom was Kepler, with the technical details of the Copernican system. Kepler stated later that at this time he became a Copernican for "physical or, if you prefer, metaphysical reasons."

In 1594 Kepler accepted an appointment as professor of mathematics at the Protestant seminary in Graz (in the Austrian province of Styria). He was also appointed district mathematician and calendar maker. Kepler remained in Graz until 1600, when all Protestants were forced to convert to Catholicism or leave the province, as part of Counter Reformation measures. For six years, Kepler taught arithmetic, geometry (when there were interested students), Virgil, and rhetoric. In his spare time he pursued his private studies in astronomy and astrology. In 1597 Kepler married Barbara Müller. In that same year he published his first important work, The Cosmographic Mystery, in which he argued that the distances of the planets from the Sun in the Copernican system were determined by the five regular solids, if one supposed that a planet's orbit was circumscribed about one solid and inscribed in another.

Except for Mercury, Kepler's construction produced remarkably accurate results. Because of his talent as a mathematician, displayed in this volume, Kepler was invited by Tycho Brahe to Prague to become his assistant and calculate new orbits for the planets from Tycho's observations. Kepler moved to Prague in 1600.

Kepler served as Tycho Brahe's assistant until the latter's death in 1601 and was then appointed Tycho's successor as Imperial Mathematician, the most prestigious appointment in mathematics in Europe. He occupied this post until, in 1612, Emperor Rudolph II was deposed. In Prague Kepler published a number of important books. In 1604 Astronomia pars Optica ("The Optical Part of Astronomy") appeared, in which he treated atmospheric refraction but also treated lenses and gave the modern explanation of the workings of the eye; in 1606 he published De Stella Nova ("Concerning the New Star") on the new star that had appeared in 1604; and in 1609 his Astronomia Nova ("New Astronomy") appeared, which contained his first two laws (planets move in elliptical orbits with the sun as one of the foci, and a planet sweeps out equal areas in equal times). Whereas other astronomers still followed the ancient precept that the study of the planets is a problem only in kinematics, Kepler took an openly dynamic approach, introducing physics into the heavens.

In 1610 Kepler heard and read about Galileo's discoveries with the spyglass. He quickly composed a long letter of support which he published as Dissertatio cum Nuncio Sidereo ("Conversation with the Sidereal Messenger"), and when, later that year, he obtained the use of a suitable telescope, he published his observations of Jupiter's satellites under the title Narratio de Observatis Quatuor Jovis Satellitibus ("Narration about Four Satellites of Jupiter observed"). These tracts were an enormous support to Galileo, whose discoveries were doubted or denied by many. Both of Kepler's tracts were quickly reprinted in Florence. Kepler went on to provide the beginning of a theory of the telescope in his Dioptrice, published in 1611.

During this period the Keplers had three children (two had been born in Graz but died within months), Susanna (1602), who married Kepler's assistant Jakob Bartsch in 1630, Friedrich (1604-1611), and Ludwig (1607-1663). Kepler's wife, Barbara, died in 1612. In that year Kepler accepted the position of district mathematician in the city of Linz, a position he occupied until 1626. In Linz Kepler married Susanna Reuttinger. The couple had six children, of whom three died very early.

In Linz Kepler published first a work on chronology and the year of Jesus's birth, In German in 1613 and more amply in Latin in 1614: De Vero Anno quo Aeternus Dei Filius Humanam Naturam in Utero Benedictae Virginis Mariae Assumpsit (Concerning the True Year in which the Son of God assumed a Human Nature in the Uterus of the Blessed Virgin Mary"). In this work Kepler demonstrated that the Christian calendar was in error by five years, and that Jesus had been born in 4 BC, a conclusion that is now universally accepted. Between 1617 and 1621 Kepler published Epitome Astronomiae Copernicanae ("Epitome of Copernican Astronomy"), which became the most influential introduction to heliocentric astronomy; in 1619 he published Harmonice Mundi ("Harmony of the World"), in which he derived the heliocentric distances of the planets and their periods from considerations of musical harmony. In this work we find his third law, relating the periods of the planets to their mean orbital radii.

In 1615-16 there was a witch hunt in Kepler's native region, and his own mother was accused of being a witch. It was not until late in 1620 that the proceedings against her ended with her being set free. At her trial, her defense was conducted by her son Johannes.

1618 marked the beginning of the Thirty Years War, a war that devastated the German and Austrian region. Kepler's position in Linz now became progressively worse, as Counter Reformation measures put pressure on Protestants in the Upper Austria province of which Linz was the capital. Because he was a court official, Kepler was exempted from a decree that banished all Protestants from the province, but he nevertheless suffered persecution. During this time Kepler was having his Tabulae Rudolphinae ("Rudolphine Tables") printed, the new tables, based on Tycho Brahe's accurate observations, calculated according to Kepler's elliptical astronomy. When a peasant rebellion broke out and Linz was besieged, a fire destroyed the printer's house and shop, and with it much of the printed edition. Soldiers were garrisoned in Kepler's house. He and his family left Linz in 1626. The Tabulae Rudolphinae were published in Ulm in 1627.

Kepler now had no position and no salary. He tried to obtain appointments from various courts and returned to Prague in an effort to pry salary that was owed him from his years as Imperial Mathematician from the imperial treasury. He died in Regensburg in 1630. Besides the works mentioned here, Kepler published numerous smaller works on a variety of subjects.

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Kepler, Johannes (1571–1630), German astronomer and mathematician; discoverer of the laws of planetary motion. Born into the Protestant minority in the free city of Weil der Stadt, within the Lutheran duchy of Württemberg, Kepler's family was poised at the boundary between the aristocracy and the artisan class. His father and brother Heinrich both served as soldiers; his youngest brother worked as a tinsmith. Kepler was educated at religious schools supported by the duke of Württemberg, and at the University of Tübingen. Here he studied with theologians trained by Philipp Melanchthon (1497–1560), the great German religious and educational reformer, and began a lifelong friendship with his mathematics teacher, the Copernican astronomer Michael Mästlin (1550–1631).

Unable to follow a church career because his scruples prevented him from signing the Formula of Concord, Kepler began his professional life as a teacher in the Protestant gymnasium at Graz, in southern Austria. From here he rose to become an imperial courtier, and achieved lasting fame as an innovator in astronomy. Kepler married twice (1597 and 1613). He was a devoted father who suffered deeply at the early deaths of many of his children, and he seems to have used mathematical research as a solace. Kepler's publication of the Mysterium Cosmographicum (1596; The secret of the universe) began a meteoric rise. Compelled to leave Graz with other Protestants in 1598, he attached himself to the court of Emperor Rudolf II (ruled 1576–1612) in Prague, and succeeded Tycho Brahe as imperial mathematician in 1601. Thus, in only three years, Kepler ascended from the position of a provincial schoolteacher to become the astrological and astronomical adviser to the most powerful monarch in the Christian world, although the emperor proved unreliable as a source of financial support. Kepler immediately began to produce a series of major works, especially the Optics (Astronomiae pars Optica, 1604) and the New Astronomy (1609), which extended and refounded their subjects. Other works (1601, 1610) attempted to reform astrology. In 1612, after the forced abdication and death of Rudolf, Kepler left Prague, but retained his title of imperial mathematician under later emperors. From 1612 to 1626 he and his family made their home in Linz, in Upper Austria, although Kepler traveled widely. While in Linz he produced the Epitome of Copernican Astronomy (1618–1621) and the Harmony of the World (1619). The latter precipitated a violent exchange with the English theosophist Robert Fludd (1574–1637), but Kepler declined an invitation to visit England despite his long-standing admiration for King James I (ruled 1603–1625). During this period his mother was accused of witchcraft. Kepler directed the defense that led to her acquittal in 1620–1621. The work that had secured the favor of the imperial house for so long, the Rudolfine Tables, was completed in 1627.

With the increasing violence and disorder of the Thirty Years' War, Kepler again sought the protection of a powerfulpatron, and he became astrological adviser to A. W. E. von Wallenstein, the leading Catholic general, in 1628. His patron's fall from power immediately preceded his own death, at Regensburg, in 1630. In the Mysterium Cosmographicum, Kepler presented the most important defense of Sun-centered astronomy since the appearance of Nicolaus Copernicus's De Revolutionibus Orbium Coelestium in 1543. Uniting ideas from his education in mathematics and religion, Kepler proposed that God had employed each regular geometrical solid exactly once in the plan of the world. Nesting the solids within each other, the orbs defining the limits of the planets' motions could be inscribed between them. The five regular solids provided the spacing between six orbs, explaining both their relative distances and the number of planets (the Earth-Moon system forms one unit). On both counts Kepler's Sun-centred model could be argued to be superior to the Earth-centred Ptolemaic system. But Kepler's defense of Copernicus faced another rival: the newly proposed hybrid system of Tycho Brahe, in which Earth was central and stationary, the Moonand Sunwent aroundthe Earth, butall the other planets circled the Sun.

On arriving in Prague in 1600, Kepler was effectively subordinated to Brahe, who first set him to writing an attack on an earlier imperial mathematician (A Defense of Tycho against Ursus). Although not actually published during Kepler's lifetime, this work gives valuable insights into both the state of astronomy and Kepler's novel methodological ideas. Brahe had presented Kepler to Rudolf II as the man who would distill Brahe's decades of observations into new astronomical tables that would carry the emperor's name. When Brahe died unexpectedly in 1601, the importance of this project helped Kepler to succeed Brahe as imperial mathematician. Kepler used the superlatively accurate and complete observations to show that Brahe's cosmic scheme was untenable, and to replace Copernicus's circle-based models with elliptical orbits.

In 1604 Kepler published an important work on optics, which treated the nature of light and vision, the phenomena of refraction, and the applications of optics in astronomy. During the same period he established that the path of Mars was an ellipse and introduced a new way of calculating the planet's position based on the novel concept of an orbit with the Sun at one focus (a principle now called the first law of planetary motion). He showed that his new approach was superior not only to the models of Ptolemy and Brahe, but also to the original form of Copernicus's system. Also improving on Copernicus, he was able to show that the planes of the planet's orbits intersected in the Sun. He also suggested that the Sun was the origin of a quasi-magnetic force responsible for the planets' motions. Based on these physical ideas, he argued for a connection between the speed of a planet along its path and the area swept out by the line connecting it to the Sun (now called the second, or area, law). He demonstrated this result first for a circular path, then for an ellipse. Although originally presented only for the case of Mars, the elliptical orbit and the mathematical principles governing its motion were intended to extend to all planets, based on universal physical principles. Kepler advertised the new connection between physics and astronomy in his book's title, A New Astronomy, Based on Causes, or Celestial Physics. It appeared in 1609 after a delay caused by Brahe's heirs.

In Prague, Kepler also produced two important works attempting to reform astrology, On More Certain Foundations for Astrology (1601) and Tertius Interveniens (1610; The intermediary third position [between two extremes]). He rejected the traditional astrological machinery of houses, but retained the idea that geometrical configurations of celestial objects influenced human judgment and caused terrestrial weather. Also in 1610 he gave enthusiastic support to Galileo Galilei (in Conversation with the Sidereal Messenger, 1610, and preface to the Dioptrice, 1611), and confirmed the latter's telescopic discovery of the moons of Jupiter.

During his time in Linz, Kepler's two most important productions were the Harmony of the World (1619) and the Epitome of Copernican Astronomy (which appeared in several volumes, 1617–1621). The former attempted a grand synthesis of geometry, harmonics, astrology, and astronomy, and presented the music of the spheres, in the form of tones generated as planets vary in speed throughout their orbits. Here also Kepler stated the third law of planetary motion, connecting the square of the planetary year with the cube of its mean distance. The Epitome of Copernican Astronomy was a systematic presentation of Kepler's version of the Copernican system, intended as a textbook, and as a basis for understanding Kepler's approach in the Rudolfine Tables. Appearing in 1627, the tables successfully predicted that Mercury would pass across the face of the sun in November 1631, showing that Kepler had improved the accuracy of positional calculations by a factor of ten.

Kepler was an innovator where Copernicus was a renovator. Copernicus had re-centred the planetary system, but his calculations of planetary positions took as their geometrical centre the mean sun, a constructed point, located elsewhere than the Sun itself. The Sun played no physical role in Copernicus's system and he retained celestial spheres to move the planets. Like Ptolemy, Copernicus continued to use circles carrying circles to predict the positions of planets against the background of fixed stars, and although distances were calculable in his system, they played no role in predicting positions. Kepler introduced the modern form of Copernicanism. His planets moved freely through the heavens, propelled by a force originating in the Sun, along orbits that intersected at the Sun. They obeyed mathematical laws that united physics and astronomy in a new way. Their path through space was an ellipse, not a circle, and their distances and velocities were linked in the second law.

Kepler's insights were not immediately accepted by contemporaries, but they were vindicated by Isaac Newton (1642–1727), who replaced Kepler's solar force with universal gravitation, and demonstrated that the three laws of planetary motion followed from his own more general laws of motion in the case of a planet moving around the Sun. Although the laws of planetary motion became central results of the later mechanical philosophy, Kepler himself was not a mechanical philosopher. Kepler's sun rotates because of an animating spirit; the planet Earth has a spirit that perceives celestial alignments and creates weather; in the 1609 presentation of Kepler's theory, planets are capable of directing their own motion of approach to or recession from the Sun. In his last work, the Somnium, published posthumously in 1634, another kind of spirit narrates the appearance of the heavens as seen from the Moon. In Kepler's cosmos, mathematical regularities are evidence of controlling minds, and the structure of the universe, which Kepler spent his life uncovering, testifies to the architectonic mind of its Creator.
 

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