## Johannes Kepler

Born December 27, 1571

Weil der Stadt near Stuttgart, GermanyDied November 15, 1630

Regensburg, Bavaria, Germany

Johannes Kepler(December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German Lutheran mathematician, astronomer, astrologer. He is best known for his laws of planetary motion, based on his worksAstronomia novaandHarmonice Mundi; Kepler's laws would be the foundation of Isaac Newton's theory of universal gravitation.Through his career Kepler was a mathematics teacher at a Graz seminary school (later the University of Graz, Austria), an assistant to Tycho Brahe, court mathematician to Emperor Rudolf II, mathematics teacher in Linz, Austria, and adviser to General Wallenstein. He also did fundamental work in the field of optics and helped to legitimize the telescopic discoveries of his contemporary Galileo Galilei.

Kepler lived in an era when there was no clear distinction between astronomy and astrology, while there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of the more prestigious discipline of philosophy); he also incorporated religious arguments and reasoning into his work, such that the basis for many of his most important contributions was essentially theological.

^{[1]}Nevertheless he was, in the words of Carl Sagan, "the first astrophysicist and the last scientific astrologer."^{[2]}

## Contents

## Life and work

## Childhood and education (1571–1594)

Kepler was born on December 27, 1571 at the Imperial Free City of Weil der Stadt (now part of the Stuttgart Region in the German state of Baden-Württemberg, 30 km west of Stuttgart's center). His grandfather had been Lord Mayor of that town, but by the time Johannes was born, the Kepler family fortunes were in decline. His father earned a precarious living as a mercenary, and he left the family when Johannes was five years old. He was believed to have died in the war in the Netherlands. His mother, an inn-keeper's daughter, was a healer and herbalist who was later tried for witchcraft. Born prematurely, Johannes claimed to have been a weak and sickly child. Despite his ill health, he was precociously brilliant. As a child, he often impressed travelers at his grandfather's inn with his phenomenal mathematical faculty.

He was introduced to astronomy/astrology at an early age, and he developed a love for it that would span his entire life. At age five, he observed the Comet of 1577, writing that he "was taken by [his] mother to a high place to look at it." At age nine, he observed another astronomical event, the Lunar eclipse of 1580, recording that he remembered being "called outdoors" to see it and that the moon "appeared quite red". However, childhood smallpox left him with weak vision, limiting his ability in the observational aspects of astronomy.

In 1589, after moving through grammar school, Latin school, and lower and higher seminary in the Lutheran education system, Kepler began attending the University of Tübingen as a theology student, where he proved himself to be a superb mathematician and earned a reputation as a skillful astrologer. Under the instruction of Michael Maestlin, he learned both the Ptolemaic system and the Copernican system; he became a Copernican at that time, defending heliocentrism from both a theoretical and theological perspective in student debates. Despite his desire to become a minister, near the end of his studies Kepler was recommended for a position as teacher of mathematics and astronomy at the Protestant school in Graz, Austria. He accepted the position in April 1594, at the age of 23.

^{[3]}## Graz (1594–1600)

Mysterium CosmographicumKepler's first major astronomical work,

Mysterium Cosmographicum(The Sacred Mystery of the Cosmos), was also the first published defense of the Copernican system. Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac; he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra. He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path, assuming the planets circle the Sun.Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, as well as his entire geometrical system from

Mysterium, because it was not precise enough. As he indicated in the title, Kepler thought he had revealed God’s geometrical plan for the universe. Much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual; the universe itself was an image of God, with the Sun corresponding to the Father, the stars to the Son, and the intervening space between to the Holy Spirit. His first manuscript ofMysteriumcontained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism. With the support of his mentor Michael Maestlin, Kepler received permission from the Tubingen university senate to publish his manuscript, pending removal of the Bible exegesis and the addition of a simpler, more understandable description of the Copernican system as well as Kepler’s new ideas.Mysteriumwas published late in 1696, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1697; it was not widely read, but it established Kepler’s reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as the men who controlled his position in Graz, also provided a crucial doorway into the patronage system.^{[4]}## Marriage to Barbara Müller

In December 1595, Kepler was introduced to Barbara Müller, a 23-year-old widow (twice over) with a young daughter, and he began courting her. Müller, heir to the estates of her late husbands, was also the daughter of a successful mill owner; her father Jobst initially opposed a marriage despite Kepler's nobility. Jobst relented after Kepler completed work on

Mysterium, but the engagement nearly fell apart while Kepler was away tending to the details of publication. However, church officials pressured the Müllers to honor their agreement; Barbara and Johannes were married on April 27, 1597.In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died in infancy. In 1602, they had a daughter (Susanna); in 1604, a son (Friedrich); in 1607, another son (Ludwig).

^{[5]}## Other research in Graz

Following the publication of

Mysteriumand with the blessing of the Graz school inspectors, Kepler began an ambitious program to extend and elaborate his work. He planned four additional books: one on the stationary aspects of the universe (the Sun and the fixed stars); one on the planets and their motions; one on the physical nature of planets and the formation of geographical features (focused especially on Earth); and one on the effects of the heavens on the Earth, to include atmospheric optics, meteorology and astrology.He also sought the opinions of many of the astronomers to whom he had sent

Mysterium, among them Reimarus Ursus (Nicolaus Reimers Bär)—the imperial mathematician to Rudolph II and a bitter rival of Tycho Brahe. Ursus did not reply directly, but republished Kepler's flattering letter to pursue his priority dispute over (what is now called) the Tychonic system with Tycho. Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler's system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus. Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory (particularly its theological viability). But without the significantly more accurate data of Tycho's observatory, Kepler had no way to address many of these issues.^{[6]}Instead, he turned his attention to chronology and "harmony," the numerological relationships among music, mathematics and the physical world, and their astrological consequences. By assuming the Earth to possess a soul (a property he would later invoke to explain how the sun causes the motion of planets), he established a speculative system connecting astrological aspects and astronomical distances to weather and other earthly phenomena. By 1599, however, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in Graz. In December of that year, Tycho invited Kepler to visit him in Prague; on January 1, 1600 (before he even received the invitation), Kepler set off in the hopes that Tycho's patronage could solve his philosophical problems as well as his social and financial ones.

^{[7]}## Prague (1600–1612)

## Work for Tycho Brahe

On February 4, 1600, Kepler met Tycho and his assistants Franz Tengnagel and Longomontanus at Benátky nad Jizerou (~50 km from Prague), the site where Tycho's new observatory was being constructed. Over the next two months he stayed as a guest, analyzing some of Tycho's observations of Mars; Tycho guarded his data closely, but was impressed by Kepler's theoretical ideas and soon allowed him more access. Kepler planned to test his theory from

Mysterium Cosmographicumbased on the Mars data, but he estimated that the work would take up to two years (since he was not allowed to simply copy the data for his own use). With the help of Johannes Jessenius, Kepler attempted to negotiate a more formal employment arrangement with Tycho, but negotions broke down in an angry argument and Kepler left for Prague on April 6. Kepler and Tycho soon reconciled and eventually reached an agreement on salary and living arrangements, and in June Kepler returned home to Graz to collect his family.^{[8]}Political-religious difficulties in Graz dashed his hopes to return immediately to Tycho; in hopes of continuing his astronomical studies, Kepler sought an appointment as mathematician to Archduke Ferdinand. To that end, Kepler composed an essay—dedicated to Ferdinand—in which he proposed a force-based theory of lunar motion (

In Terra inest virtus, quae Lunam ciet—"There is a force in the earth which causes the moon to move").^{[9]}Though the essay did not earn him a place in Ferdinand's court, its proto-gravitational theory became the basis for his later work on planetary motion. It also detailed a new method for measuring lunar eclipses, which he applied during the July 10 eclipse in Graz. These observations formed the basis of his explorations of the laws of optics that would culminate inAstronomia Pars Optica.^{[10]}On August 2, 1600, after refusing to convert to Catholicism, Kepler and his family were banished from Graz; several months later, Kepler returned, now with the rest of his household, to Prague. Through most of 1601, he was supported directly by Tycho, analyzing planetary observations and writing a tract against Tycho's (now deceased) rival Ursus. In September, Tycho secured him a commission as a collaborator on the new project he proposed to the emperor: the

Rudolphine Tables. Two days after Tycho's unexpected death on October 24, 1601, Kepler was appointed his successor as imperial mathematician; he inherited Tycho's observations as well as the responsibility to complete his unfinished work. The next 11 years as imperial mathematician would be the most productive of his life.^{[11]}## Astrologer to Emperor Rudolph II

Kepler's primary obligation as imperial mathematician was to provide astrological advice to the emperor. Though Kepler took a dim view of the attempts of contemporary astrologers to precisely predict the future or divine specific events, he had been casting detailed horoscopes for friends, family and patrons since his time as a student in Tübingen. In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler's advice in times of political trouble—though Kepler's recommendations were based more on common sense than the stars. Rudolph was actively interested in the work of many of his court scholars (including numerous alchemists), and kept up with Kepler's work in physical astronomy as well.

Officially, the only acceptable religious doctrines in Prague were Catholic and Utraquist, but Kepler's position in the imperial court allowed him to practice his Lutheran faith unhindered. The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle. Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness. Court life, however, brought Kepler into contact with other prominent scholars (Johannes Matthäus Wackher von Wackhenfels, Jost Bürgi, David Fabricius, Martin Bachazek, and Johannes Brengger, among others) and astronomical work proceeded rapidly.

^{[12]}

The Optical Part of AstronomyAs he continued analyzing Tycho's Mars observations—now available in their entirety—and began the slow process of tabulating the

Rudolphine Tables, Kepler also picked up the investigation of the laws of optics from his lunar essay of 1600. Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction applied toallastronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, 1604, was published asAstronomiae Pars Optica(The Optical Part of Astronomy). In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies.Astronomiae Pars Opticais generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).^{[13]}## The supernova of 1604

In October of 1604, a bright new evening star (SN 1604) appeared; Kepler did not believe the rumors until he saw it himself. Kepler began systematically observing the star. Astrologically, the end of 1603 marked the beginning of a fiery trigon, the start of the ca. 800-year cycle of great conjunctions; astrologers associated the two previous such periods with the rise of Charlemagne (ca. 800 years earlier) and the birth of Christ (ca. 1600 years earlier), and thus expected events of great portent, especially regarding the emperor. In was in this context, as the imperial mathematician and astrologer to the emperor, that Kepler described the new star two years later in his

De Stella Nova. In it, Kepler addressed the star's astronomical properties while taking a skeptical approach to the many astrological interpretations then circulating. He noted its fading luminosity, speculated about its origin, and used the lack of observed parallax to argue that it was in the sphere of fixed stars, further undermining the doctrine of the immutability of the heavens. In an appendix, Kepler also discussed the recent chronology work of Laurentius Suslyga; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem—analagous to the present new star—would have coincided with the first great conjunction of the earlier 800-year cycle.^{[14]}

Astronomia novaThe extended line of research that culminated in

Astronomia nova(A New Astronomy)—including the first two laws of planetary motion— began with the analysis, under Tycho's direction, of Mars' orbit. Since antiquity, it was assumeda priorithat the natural motion of planets was circular; retrograge motion was acccounted for, in Ptolemaic astronomy, through circular epicycles, while in the Copernican and Tychonic systems it was a result of Sun-centered paths as viewed from Earth. Further geometrical techniques were necessary to account for observed eccentricities (the equant for Ptolemy, the Tusi-couple for Copernicus), but such devices were not considered cosmologically significant. However, Tycho's data—including observations of ten Mars oppositions, plus two recorded by Kepler—showed that the irregularities of Mars could not be precisely accounted for with an ad hoc mathematical fix.Kepler calculated and recalculated various approximations of Mars orbit using an equant, eventually creating a model that generally agreed with Tycho's observations to within two arcminutes (the typical measurement error). But he was not satisfied with the complex and still slightly innaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about creating—literally—a new astronomy. Though it meant abandoning his system from

Mysterium cosmographicum, he rejected the basic tenet of nearly all astronomy since Aristotle: the primacy of uniform circular motion.^{[15]}Within Kepler's religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert's theory of the magnetic soul of the Earth from

De Magnete(1600). Having given up on circular orbits, Kepler supposed that the Sun's force attenuates with distance, causing faster or slower motion as planets move closer or farther from it; perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle, however, required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry:planets sweep out equal areas in equal times—the second law of planetary motion.He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After approximately 40 failed attempts, in early 1605 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fit the Mars data perfectly, he immediately concluded that

all planets move in ellipses, with the sun at one focus—the first law of planetary motion. By the end of the year, he completed the manuscript forAstronomia nova, though it would not be published until 1609 due legal disputes over the use of Tycho's observations, the property of his heirs.^{[16]}The very idea of an

orbit, a trajectory through space, may have been the most revolutionary aspect of theNew Astronomy. All earlier astronomers, including Copernicus, conceived of the planets as dense spots within a system of orbs, spherical shells that rotated to produced the observed motion of planets; a planet's distance from its center of rotation (whether the Sun or the Earth) was assumed constant. In the new system a planet's distance from the Sun varied in time, making Kepler's theory completely incompatible with traditional cosmology.^{[17]}

Dioptrice, theSomniummanuscript, and other workIn the years following the completion of

Astronomia Nova, most of Kepler's research was focused on preparations for theRudolphine Tablesand a comprehensive set of ephemerides based on the table (though neither would be completed for many years). He also attempted (unsuccessfully) to begin a collaboration with Italian astronomer Giovanni Antonio Magini. Some of his other work dealt with chronology, especially the dating of events in the life of Jesus, and with astrology, especially criticism of dramatic predictions of catastrophe such as those of Helisaeus Roeslin.^{[18]}Kepler and Roeslin engaged in series of published attacks and counter-attacks, while physician Philip Feselius published a work dismissing astrology altogether (and Roeslin's work in particular). In response to what Kepler saw as the excesses of astrology on the one hand and overzealous rejection of it on the other, Kepler prepared

Tertius Interveniens(Third-party Interventions). Nominally this work—presented to the common patron of Roeslin and Feselius—was a neutral mediation between the feuding scholars, but it also set out Kepler's general views on the value of astrology, including some hypothesized mechanisms of interaction between planets and individual souls. While Kepler considered most traditionals rules and methods of astrology to be the "evil-smelling dung" in which "an industrious hen" scrapes, there was "also perhaps a good little grain" to be found by the conscientious scientific astrologer.^{[19]}In the first months of 1610, Galileo Galilei—using his powerful new telescope—discovered four satellites orbiting Jupiter. Upon publishing his account as

Siderus Nuncius(Starry Messenger), Galileo sought the opinion of Kepler, in part to bolster the credibility of his observations. Kepler responded enthusiastically with a short published reply,Dissertatio cum Nuncio Sidereo(Conversation with the Starry Messenger). He endorsed Galileo's observations and offered a range of speculations about the meaning and implications of Galileo's discoveries and telescopic methods, for astronomy and optics as well as cosmology and astrology. Later that year, Kepler published his own telescopic observations of the moons inNarratio de Jovis Satellitibus, providing further support of Galileo. To Kepler's disappointment, however, Galileo never published his reactions (if any) toAstronomia Nova.^{[20]}After hearing of Galileo's telescopic discoveries, Kepler also started a theoretical and experimental investigation of telescopic optics. The resulting manuscript was completed in September of 1610 and published as

Dioptricein 1611. In it, Kepler set out the theoretical basis of double-convex converging lenses and double-concave diverging lenses—and how they are combined to produce a Galilean telescope—as well as the concepts of real vs. virtual images, upright vs. inverted images, and the effects of focal length on magnification and reduction. He also described an improved telescope—now known as theastronomicalorKeplerian telescope—in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.^{[21]}Around 1611, Kepler circulated a manuscript of what would eventually be published (posthumously) as

Somnium(The Dream). Part of the purpose ofSomniumwas to describe what practicing astronomy would be like from the perspective of another planet, to show the feasibility of a non-geocentric system. The manuscript, which disappeared after changing hands several times, described a fantastic trip to the moon; it was part allegory, part autobiography, and part treatise on interplanetary travel (and is sometimes described as the first work of science fiction). Years later, a distorted version of the story may have instigated the witchcraft trial against his mother, as the mother of the narrator consults a demon to learn the means of space travel. Following her eventual acquittal, Kepler composed 223 footnotes to the story—several times longer than the actual text—which explained the allegorical aspects as well as the considerable scientific content (particularly regarding lunar geography) hidden within the the text.^{[22]}As a New Year's gift that year, he also composed for his friend and some-time patron Baron Wackher von Wackhenfels a short pamphlet entitled

Strena Seu de Nive Sexangula(A New Year's Gift of Hexagonal Snow). In this treatise, he investigated the hexagonal symmetry of snowflakes and, extending the discussion into a hypothetical atomistic physical basis for the symmetry, posed what later became known as the Kepler conjecture, a statement about the most efficient arrangement for packing spheres.^{[23]}## Personal and political troubles

In 1611, the growing political-religious tension in Prague came to a head. Emperor Rudolph—whose health was failing—was forced to abdicate as King of Bohemia by his brother Matthias. Both sides sought Kepler's astrological advice, an opportunity he used to deliver conciliatory political advice (with little reference to the stars, except in general statements to discourage drastic action). However, it was clear that Kepler's future prospects in the court of Matthias were dim.

^{[24]}Also in that year, Barbara Kepler contracted Hungarian spotted fever, then began having epileptic seizures. As Barbara was recovering, Kepler's three children all fell sick with smallpox; Friedrich, 6, died. Following his son's death, Kepler sent letters to potential patrons in Württemberg and Padua. At the University of Tübingen in Württemberg, concerns over Kepler's perceived Calvinist heresies in violation of the Augsburg Confession and the Formula of Concord prevented his return. The University of Padua—on the recommendation of the departing Galileo—sought Kepler to fill the mathematics professorship, but Kepler, preferring to keep his family in German territory, instead travelled to Austria to arrange a position as teacher and district mathematician in Linz. However, Barbara relapsed into illness and died shortly after Kepler's return.

^{[25]}Kepler postponed the move to Linz and remained in Prague until Rudolph's death in early 1612, though between political upheaval, religious tension, and family tragedy (along the legal dispute over his wife's estate), Kepler could do no research. Instead, he pieced together a chronology manuscript,

Eclogae Chronicae, from correspondence and earlier work. Upon succession as Holy Roman Emperor, Matthias re-affirmed Kepler's position (and salary) as imperial mathematician but allowed him to move to Linz.^{[26]}## Linz and elswhere (1612–1630)

In Linz, Kepler's primary responsibilities (beyond completing the

Rudolphine Tables) were teaching at the district school and providing astrological and astronomical services. In his first years there, he enjoyed financial security and religous freedom relative to Prague—though he was excluded from communion with Lutheran congregation over his theological scruples. His first publication in Linz wasDe vero Anno(1613), an expanded treatise on the year of Christ's birth; he also participated in deliberations on whether to introduce Pope Gregory's reformed calendar to Protestant German lands; that year he also wrote the influential mathematical treatiseNova stereometria doliorum vinariorum, on measuring the volume of containers such as wine barrels (though it would not be published until 1615).^{[27]}## Second marriage

On October 30, 1613, Kepler married the twenty-four-year-old Susanna Reuttinger, the fifth of eleven matches he had considered following Barbara's death. The first three children of this marriage (Margareta Regina, Katharina, and Sebald) died in childhood. Three more survived: Cordula in 1621; Fridmar in 1623; and Hildebert in 1625. According to Kepler's biographers, this was a much happier marriage than his first.

^{[28]}

Epitome of Copernican Astronomy, calendars, and the witch trial of Kepler's motherSince completing the

Astronomia nova, Kepler had intended to compose an astronomy textbook. In 1615, he completed the first of four volumes ofEpitome astronomia Copernicanae(Epitome of Copernican Astronomy); the first three volumes were printed together 1617, the fourth in 1620. Despite the title, which referred simply to heliocentrism, Kepler's textbook culminated in his own ellipse-based system; according to Kepler scholar Max Caspar, "Epitomeranks next to Ptolemy'sAlmagestand Copernicus'Revolutionesas the first systematic presentation of astronomy to introduce the idea of modern celestial mechanics founded by Kepler."^{[29]}As a spin-off of work on the

Rudolphine Tablesand the relatedEphemerides, Kepler published astrological calendars, which were very popular and helped offset the costs of producing his other work—especially when support from the Imperial treasury was withheld. In his calendars—six between 1617 and 1624—Kepler forecast planetary positions and weather as well as political events; the latter were often cannily accurate, thanks to his keen grasp of contemporary political and theological tensions. By 1624, however, the escalation of those tensions and the ambiguity of the prophecies meant political trouble for Kepler himself; his final calendar was publicly burned in Graz.^{[30]}In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Cristoph, claimed Kepler's mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617, Katharina was accused of witchcraft; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620 she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler; the accusers had no stronger evidence than rumors and (a distorted, second-hand version of) Kepler's

Somniumstory—in which a woman mixes potions and enlists the aid of a demon. However, Katharina was subjected toterritio verbalis, a graphic description of the torture awaiting her as a witch, in a final attempt to make her confess, and she died soon after. Throughout the trial, Kepler postponed his other work to focus on his "harmonic theory". The result, published in 1619, wasHarmonices Mundi("Harmony of the Worlds").^{[31]}

Harmonice MundiKepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world." In

Harmony, he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music. The central set of "harmonies" was themusica universalisor "music of the spheres," which had been studied by Ptolemy and many others before Kepler; in fact, soon after publishingHarmonice Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.^{[32]}Kepler began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler's solids. From there, he extended his harmonic analysis to music, meteorology and astrology; harmony resulted from the tones made by the souls of heavenly bodies—and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the sun. Among many other harmonies, Kepler articulated what came to be the third law of planetary motion: "

The square of the periodic times are to each other as the cubes of the mean distances." However, its significance would not be recognized until much later, when Isaac Newton created his theory of universal gravitation based on (a second-hand account of) Kepler's work.^{[33]}

Rudolphine Tablesand Kepler's last yearsIn 1623, Kepler at last completed the

Rudolphine Tables. However, due to the publishing requirements of the emperor and negotiations with Tycho Brahe's heir, it would not be printed until 1627. In the meantime religious tension—the root of the ongoing Thirty Years' War—once again put Kepler and his family in jeopardy. In 1625, agents of the Catholic Reformation placed most of Kepler's library under seal, and in 1626 the city of Linz was besieged. Kepler moved to Ulm, where he arranged for the printing of theTablesas his own expense.^{[34]}In 1628, following the military successes of the Emperor Ferdinand's armies under General Wallenstein, Kepler became an official adviser to Wallenstein. Though not the general's court astrologer per se, Kepler provided astronomical calculations for Wallenstein's astrologers and occasionally wrote horoscopes himself. Much of Kepler's final years was spent traveling, from court in Prague to Linz and Ulm to a temporary home in Sagan, and finally to Regensburg. Soon after arriving in Regensburg, Kepler fell ill. He died on November 15, 1630, and was buried there; his burial site was lost after the army of Gustavus Adolphus destroyed the churchyard.

^{[35]}## Writings by Kepler

Mysterium cosmographicum(The Sacred Mystery of the Cosmos) (1596)Astronomiae Pars Optica(The Optical Part of Astronomy) (1604)De Stella nova in pede Serpentarii(On the New Star in Ophiuchus's Foot) (1604)Astronomia nova(New Astronomy) (1609)Tertius Interveniens(Third-party Interventions) (1610)Dissertatio cum Nuncio Sidereo(Conversation with the Starry Messenger) (1610)Dioptrice(1611)De nive sexangula(On the Six-Cornered Snowflake) (1611)De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit(1613)Eclogae Chronicae(1615, published withDissertatio cum Nuncio Sidereo)Nova stereometria doliorum vinariorum(New Stereometry of Wine Barrels) (1615)Epitome astronomiae Copernicanae(Epitome of Copernican Astronomy) (published in three parts from 1618-1621)Harmonice Mundi(Harmony of the Worlds) (1619)Tabulae Rudolphinae(Rudolphine Tables) (1627)Somnium(The Dream) (1634)## Trivia

## Kepler in fiction

- John Banville:
Kepler: a novel. London: Secker & Warburg, 1981 ISBN 0-436-03264-3 (and later eds.). Also published: Boston, MA:Godine, 1983 ISBN 0-87923-438-5. Draws heavily on Koestler's account of Kepler inThe Sleepwalkers.## Named in Kepler's honor

- Kepler Space Observatory, a solar-orbiting, planet-hunting telescope due to be launched by NASA in 2008.
- The Kepler Solids, a set of geometrical constructions, two of which were described by him.
- Kepler's Star, Supernova 1604, which he observed and described.
- Kepler, a crater on the moon
- Kepler, a crater on Mars
- 1134 Kepler is an asteroid.
- In 1975, nine years after its founding, the College for Social and Economic Sciences Linz (Austria) was renamed Johannes Kepler University Linz in honor of Johannes Kepler, since he wrote his magnum opus
Harmonice Mundiin Linz.- Johannes Kepler's Gymnasium in Prague
- Keplerstraße in Hanau near Frankfurt am Main
## See also

- Kepler's laws of planetary motion
- Keplerian problem
- Kepler conjecture
- Heliocentrism
- Scientific revolution
## Notes and references

- The most authoritative biography of Kepler is Max Caspar's
Kepler. Though there are a number of more recent biographies, most are based on Caspar's work with minimal original research; much of the information cited from Caspar can also be found in the books by Arthur Koestler, Kitty Ferguson, and James A. Connor. Kepler's mathematics and cosmological views have been extensively analyzed in books and journal articles, though his astrological work—and its relationship to his astronomy—remains understudied.

^Barker and Goldstein, "Theological Foundations of Kepler's Astronomy"^Quote from Carl Sagan,Cosmos: A Personal Voyage, episode III: "The Harmony of the Worlds"^Caspar,Kepler, pp 29-52^Barker and Goldstein, "Theological Foundations of Kepler's Astronomy," pp 88-113^Connor,Kepler's Witch, pp 89-100, 114-116^Caspar,Kepler, pp 85-89^Caspar,Kepler, pp 89-100^Caspar,Kepler, pp 100-108^Translation from Caspar,Kepler, p 110^Caspar,Kepler, pp 108-111^Caspar,Kepler, pp 111-122^Caspar,Kepler, pp 146-153, 159-177^Caspar,Kepler, pp 142-146^Caspar,Kepler, pp 153-157^Caspar,Kepler, pp 123-128^Caspar,Kepler, pp 129-140^Andersen, Barker, and Chen,The Cognitive Structure of Scientific Revolutions, pp 146-163^Caspar,Kepler, pp 178-181^Caspar,Kepler, pp 181-185. The full title isTertius Interveniens, das ist Warnung an etliche Theologos, Medicos vnd Philosophos, sonderlich D. Philippum Feselium, dass sie bey billicher Verwerffung der Sternguckerischen Aberglauben nict das Kindt mit dem Badt aussschütten vnd hiermit jhrer Profession vnwissendt zuwider handlen, translated by C. Doris Hellman as "Tertius Interveniens, that is warning to some theologians, medics and philosophers, especially D. Philip Feselius, that they in cheap condemnation of the star-gazer's superstition do not throw out the child with the bath and hereby unknowingly act contrary to their profession."^Caspar,Kepler, pp 192-197^Caspar,Kepler, pp 198-202^Lear,Kepler's Dream, pp 1-78^Schneer, "Kepler's New Year's Gift of a Snowflake," pp 531-545^Caspar,Kepler, pp 202-204^Connor,Kepler's Witch, pp 222-226; Caspar,Kepler, pp 204-207^Caspar,Kepler, pp 208-211^Caspar,Kepler, pp 209-220, 227-240^Caspar,Kepler, pp 220-223; Connor,Kepler's Witch, pp 251-254^Caspar,Kepler, pp 239-240, 293-300; quotation from p 297^Caspar,Kepler, pp 239, 300-301, 307-308^Caspar,Kepler, pp 240-264; Connor,Kepler's Witch, chapters I, XI-XIII; Lear,Kepler's Dream, pp 21-39^Caspar,Kepler, pp 264-266, 290-293; quotation from pp 265-266^Caspar,Kepler, pp 266-290; quotation from p 286^Caspar,Kepler, pp 308-328^Caspar,Kepler, pp 332-351, 355-361## Bibliography

- Hanne Andersen, Peter Barker, and Xiang Chen:
The Cognitive Structure of Scientific Revolutions, chapter 6: "The Copernican Revolution." New York: Cambridge University Press, 2006 ISBN 0521855756

- Peter Barker and Bernard R. Goldstein: "Theological Foundations of Kepler's Astronomy".
Osiris, Volume 16:Science in Theistic Contexts.University of Chicago Press, 2001, pp 88-113.

- Max Caspar:
Kepler; transl. and ed. by C. Doris Hellman; with a new introduction and references by Owen Gingerich; bibliographic citations by Owen Gingerich and Alain Segonds. New York: Dover, 1993 ISBN 0-486-67605-6

- James A. Connor:
Kepler's Witch: An Astronomer's Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother. HarperSanFrancisco, 2004 ISBN 0-06-052255-0

- Kitty Ferguson:
The nobleman and his housedog: Tycho Brahe and Johannes Kepler: the strange partnership that revolutionized science.London : Review, 2002 ISBN 0-747270-22-8 (published in the US as:Tycho & Kepler: the unlikely partnership that forever changed our understanding of the heavens.New York: Walker, 2002 ISBN 0-8027-1390-4)

- John Lear:
Kepler's Dream. Berkeley: University of California Press, 1965.

- Cecil Schneer: "Kepler's New Year's Gift of a Snowflake."
Isis, Volume 51, No. 4. University of Chicago Press, 1960, pp 531-545.## Further reading

- J.V. Field:
Kepler's geometrical cosmology. Chicago: Chicago University Press, 1988 ISBN 0-226-24823-2

- Johannes Kepler, Christian Frisch:
Joannis Kepleri Astronomi Opera Omnia(John Kepler, Astronomer; Complete Works). 8 vols.(1858-1871), vol. 1, 1858, vol. 6, 1866, Francofurti a.M. et Erlangae, Heyder & Zimmer, 1858. - Google Books

- Owen Gingerich:
The Eye of Heaven: Ptolemy, Copernicus, Kepler. New York: American Institute of Physics, 1993 ISBN 0-88318-863-5 (Masters of modern physics; v. 7)

- Arthur Koestler:
The Sleepwalkers: A History of Man's Changing Vision of the Universe.(1959). ISBN 0-140-19246-8

- Bruce Stephenson:
Kepler's physical astronomy. New York: Springer, 1987 ISBN 0-387-96541-6 (Studies in the history of mathematics and physical sciences; 13)

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