Johannes Kepler
Johannes Kepler  

A 1610 portrait of Johannes Kepler by an unknown artist


Born 
Free Imperial City of Weil der Stadt, Holy Roman Empire 
December 27, 1571
Died 
November 15, 1630 Regensburg, Electorate of Bavaria, Holy Roman Empire 
(aged 58)
Residence  Württemberg; Styria; Bohemia; Upper Austria 
Nationality  German 
Fields  Astronomy, astrology, mathematics and natural philosophy 
Institutions  University of Linz 
Alma mater  University of Tübingen 
Known for 
Kepler's laws of planetary motion Kepler conjecture 
Signature 
Johannes Kepler (German: ; December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer. A key figure in the 17th century scientific revolution, he is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.
During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and mentioned the telescopic discoveries of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through the natural light of reason.^{[1]} Kepler described his new astronomy as "celestial physics",^{[2]} as "an excursion into Aristotle's Metaphysics",^{[3]} and as "a supplement to Aristotle's On the Heavens",^{[4]} transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.^{[5]}
Contents
 Early years 1

Graz (1594–1600) 2
 Mysterium Cosmographicum 2.1
 Marriage to Barbara Müller 2.2
 Other research 2.3

Prague (1600–1612) 3
 Work for Tycho Brahe 3.1
 Advisor to Emperor Rudolph II 3.2
 Astronomiae Pars Optica 3.3
 The Supernova of 1604 3.4
 Astronomia nova 3.5
 Dioptrice, Somnium manuscript, and other work 3.6

Work in mathematics and physics 4
 Personal and political troubles 4.1

Linz and elsewhere (1612–1630) 5
 Second marriage 5.1
 Epitome of Copernican Astronomy, calendars, and the witch trial of his mother 5.2
 Harmonices Mundi 5.3
 Rudolphine Tables and his last years 5.4
 Reception of his astronomy 6

Historical and cultural legacy 7
 Veneration 7.1
 Works 8

See also 9
 Named in his honor 9.1
 Notes and references 10
 Sources 11
 External links 12
Early years
Johannes Kepler was born on December 27, the feast day of St. John the Evangelist, 1571, at the Free Imperial City of Weil der Stadt (now part of the Stuttgart Region in the German state of BadenWürttemberg, 30 km west of Stuttgart's center). His grandfather, Sebald Kepler, had been Lord Mayor of that town but, by the time Johannes was born, he had two brothers and one sister and the Kepler family fortune was in decline. His father, Heinrich Kepler, 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 Eighty Years' War in the Netherlands. His mother Katharina Guldenmann, an innkeeper's daughter, was a healer and herbalist. Born prematurely, Johannes claimed to have been weak and sickly as a child. Nevertheless, he often impressed travelers at his grandfather's inn with his phenomenal mathematical faculty.^{[6]}
He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great Comet of 1577, writing that he "was taken by [his] mother to a high place to look at it."^{[7]} At age nine, he observed another astronomical event, a lunar eclipse in 1580, recording that he remembered being "called outdoors" to see it and that the moon "appeared quite red".^{[7]} However, childhood smallpox left him with weak vision and crippled hands, limiting his ability in the observational aspects of astronomy.^{[8]}
In 1589, after moving through grammar school, Latin school, and seminary at Maulbronn, Kepler attended Tübinger Stift at the University of Tübingen. There, he studied philosophy under Vitus Müller^{[9]} and theology under Jacob Heerbrand (a student of Philipp Melanchthon at Wittenberg), who also taught Michael Maestlin while he was a student, until he became Chancellor at Tübingen in 1590.^{[10]} He proved himself to be a superb mathematician and earned a reputation as a skillful astrologer, casting horoscopes for fellow students. Under the instruction of Michael Maestlin, Tübingen's professor of mathematics from 1583 to 1631,^{[10]} he learned both the Ptolemaic system and the Copernican system of planetary motion. He became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe.^{[11]} 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 (later the University of Graz). He accepted the position in April 1594, at the age of 23.^{[12]}
Graz (1594–1600)
Mysterium Cosmographicum
Johannes Kepler's first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery), was 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 3dimensional 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, because it was not precise enough.^{[13]}
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 stellar sphere to the Son, and the intervening space between to the Holy Spirit. His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism.^{[14]}
With the support of his mentor Michael Maestlin, Kepler received permission from the Tübingen 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. Mysterium was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; 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 to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system.^{[15]}
Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedralspherist cosmology of Mysterium Cosmographicum. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621, Kepler published an expanded second edition of Mysterium, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.^{[16]}
In terms of the impact of Mysterium, it can be seen as an important first step in modernizing the theory proposed by Nicolaus Copernicus in his "De Revolutionibus". Whilst Copernicus sought to advance a heliocentric system in this book, he resorted to Ptolemaic devices (viz., epicycles and eccentric circles) in order to explain the change in planets' orbital speed, and also continued to use as a point of reference the center of the earth's orbit rather than that of the sun "as an aid to calculation and in order not to confuse the reader by diverging too much from Ptolemy." Modern astronomy owes much to "Mysterium Cosmographicum", despite flaws in its main thesis, "since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it." ^{[17]}
Marriage to Barbara Müller
In December 1595, Kepler was introduced to Barbara Müller, a 23yearold widow (twice over) with a young daughter, Gemma van Dvijneveldt, and he began courting her. Müller, heiress 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; though he had inherited his grandfather's nobility, Kepler's poverty made him an unacceptable match. 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—who had helped set up the match—pressured the Müllers to honor their agreement. Barbara and Johannes were married on April 27, 1597.^{[18]}
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); and in 1607, another son (Ludwig).^{[19]}
Other research
Following the publication of Mysterium and 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.^{[20]}
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.^{[21]}
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.^{[22]}
Prague (1600–1612)
Work for Tycho Brahe
On February 4, 1600, Kepler met Tycho Brahe and his assistants Franz Tengnagel and Longomontanus at Benátky nad Jizerou (35 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^{[23]} from Mysterium Cosmographicum based 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 negotiations 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.^{[24]}
Political and religious difficulties in Graz dashed his hopes of returning immediately to Brahe; 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 forcebased theory of lunar motion: "In Terra inest virtus, quae Lunam ciet" ("There is a force in the earth which causes the moon to move").^{[25]} Though the essay did not earn him a place in Ferdinand's court, it did detail 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 in Astronomiae Pars Optica.^{[26]}
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, who assigned him to analyzing planetary observations and writing a tract against Tycho's (by then deceased) rival, Ursus. In September, Tycho secured him a commission as a collaborator on the new project he had proposed to the emperor: the Rudolphine Tables that should replace the Prutenic Tables of Erasmus Reinhold. Two days after Tycho's unexpected death on October 24, 1601, Kepler was appointed his successor as imperial mathematician with the responsibility to complete his unfinished work. The next 11 years as imperial mathematician would be the most productive of his life.^{[27]}
Advisor 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 wellreceived 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. 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.^{[28]}
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 overextended 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.^{[29]}
Astronomiae Pars Optica
As he slowly continued analyzing Tycho's Mars observations—now available to him 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 to all astronomical 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 as Astronomiae Pars Optica (The Optical Part of Astronomy). In it, Kepler described the inversesquare 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. He also extended his study of optics to the human eye, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the eye's lens onto the retina. The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected "in the hollows of the brain" due to the "activity of the Soul."^{[30]} Today, Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).^{[31]} With respect to the beginnings of projective geometry, Kepler introduced the idea of continuous change of a mathematical entity in this work. He argued that if a focus of a conic section were allowed to move along the line joining the foci, the geometric form would morph or degenerate, one into another. In this way, an ellipse becomes a parabola when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle is formed. As the foci of a hyperbola merge into one another, the hyperbola becomes a pair of straight lines. He also assumed that if a straight line is extended to infinity it will meet itself at a single point at infinity, thus having the properties of a large circle.^{[32]} This idea was later utilized by Pascal, Leibniz, Monge, and Poncelet, among others, and became known as geometric continuity and as the Law or Principle of Continuity.
The Supernova of 1604
In October 1604, a bright new evening star (SN 1604) appeared, but Kepler did not believe the rumors until he saw it himself. Kepler began systematically observing the nova. Astrologically, the end of 1603 marked the beginning of a fiery trigon, the start of the ca. 800year 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. It 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 (the idea accepted since Aristotle that the celestial spheres were perfect and unchanging). The birth of a new star implied the variability of the heavens. In an appendix, Kepler also discussed the recent chronology work of the Polish historian Laurentius Suslyga; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem—analogous to the present new star—would have coincided with the first great conjunction of the earlier 800year cycle.^{[33]}
Astronomia nova
The 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. Kepler calculated and recalculated various approximations of Mars' orbit using an equant (the mathematical tool that Copernicus had eliminated with his system), eventually creating a model that generally agreed with Tycho's observations to within two arcminutes (the average measurement error). But he was not satisfied with the complex and still slightly inaccurate 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 trying to fit an ovoid orbit to the data.^{[34]}
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) and on his own work on optics. Kepler supposed that the motive power (or motive species)^{[35]} radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it.^{[36]}^{[37]} 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—Kepler's second law of planetary motion.^{[38]}
He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an eggshaped 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, he immediately concluded that all planets move in ellipses, with the sun at one focus—Kepler's first law of planetary motion. Because he employed no calculating assistants, however, he did not extend the mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for Astronomia nova, though it would not be published until 1609 due to legal disputes over the use of Tycho's observations, the property of his heirs.^{[39]}
Dioptrice, Somnium manuscript, and other work
In the years following the completion of Astronomia Nova, most of Kepler's research was focused on preparations for the Rudolphine Tables and a comprehensive set of ephemerides (specific predictions of planet and star positions) 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.^{[40]}
Kepler and Roeslin engaged in a series of published attacks and counterattacks, 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 (Thirdparty 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 traditional rules and methods of astrology to be the "evilsmelling dung" in which "an industrious hen" scrapes, there was an "occasional grainseed, indeed, even a pearl or a gold nugget" to be found by the conscientious scientific astrologer.^{[41]}
In the first months of 1610, Galileo Galilei—using his powerful new telescope—discovered four satellites orbiting Jupiter. Upon publishing his account as Sidereus 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 in Narratio de Jovis Satellitibus, providing further support of Galileo. To Kepler's disappointment, however, Galileo never published his reactions (if any) to Astronomia Nova.^{[42]}
After hearing of Galileo's telescopic discoveries, Kepler also started a theoretical and experimental investigation of telescopic optics using a telescope borrowed from Duke Ernest of Cologne.^{[43]} The resulting manuscript was completed in September 1610 and published as Dioptrice in 1611. In it, Kepler set out the theoretical basis of doubleconvex converging lenses and doubleconcave 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 the astronomical or Keplerian telescope—in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.^{[44]}
Around 1611, Kepler circulated a manuscript of what would eventually be published (posthumously) as Somnium (The Dream). Part of the purpose of Somnium was to describe what practicing astronomy would be like from the perspective of another planet, to show the feasibility of a nongeocentric 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 text.^{[45]}
Work in mathematics and physics
As a New Year's gift that year, he also composed for his friend and sometime 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 published the first description of 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.^{[46]}^{[47]} Kepler was one of the pioneers of the mathematical applications of infinitesimals, see Law of Continuity.
Personal and political troubles
In 1611, the growing politicalreligious 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.^{[48]}
Also in that year, Barbara Kepler contracted Hungarian spotted fever, then began having 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.^{[49]}
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 with 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 reaffirmed Kepler's position (and salary) as imperial mathematician but allowed him to move to Linz.^{[50]}
Linz and elsewhere (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 religious freedom relative to his life in Prague—though he was excluded from Eucharist by his Lutheran church over his theological scruples. His first publication in Linz was De 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 treatise Nova stereometria doliorum vinariorum, on measuring the volume of containers such as wine barrels, published in 1615.^{[51]}
Second marriage
On October 30, 1613, Kepler married the 24yearold Susanna Reuttinger. Following the death of his first wife Barbara, Kepler had considered 11 different matches over two years (a decision process formalized later as the marriage problem).^{[52]} He eventually returned to Reuttinger (the fifth match) who, he wrote, "won me over with love, humble loyalty, economy of household, diligence, and the love she gave the stepchildren."^{[53]} The first three children of this marriage (Margareta Regina, Katharina, and Sebald) died in childhood. Three more survived into adulthood: Cordula (b. 1621); Fridmar (b. 1623); and Hildebert (b. 1625). According to Kepler's biographers, this was a much happier marriage than his first.^{[54]}
Epitome of Copernican Astronomy, calendars, and the witch trial of his mother
Since completing the Astronomia nova, Kepler had intended to compose an astronomy textbook.^{[55]} In 1615, he completed the first of three volumes of Epitome astronomiae Copernicanae (Epitome of Copernican Astronomy); the first volume (books IIII) was printed in 1617, the second (book IV) in 1620, and the third (books VVII) in 1621. Despite the title, which referred simply to heliocentrism, Kepler's textbook culminated in his own ellipsebased system. The Epitome became Kepler's most influential work. It contained all three laws of planetary motion and attempted to explain heavenly motions through physical causes.^{[56]} Though it explicitly extended the first two laws of planetary motion (applied to Mars in Astronomia nova) to all the planets as well as the Moon and the Medicean satellites of Jupiter,^{[57]} it did not explain how elliptical orbits could be derived from observational data.^{[58]}
As a spinoff from the Rudolphine Tables and the related Ephemerides, 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.^{[59]}
In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Christoph, 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. Katharina was subjected to territio verbalis, a graphic description of the torture awaiting her as a witch, in a final attempt to make her confess. Throughout the trial, Kepler postponed his other work to focus on his "harmonic theory". The result, published in 1619, was Harmonices Mundi ("Harmony of the World").^{[60]}
Harmonices Mundi
Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world".^{[61]} In Harmony, he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music.^{[62]} The central set of "harmonies" was the musica universalis or "music of the spheres", which had been studied by Pythagoras, Ptolemy and many others before Kepler; in fact, soon after publishing Harmonices Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.^{[63]}
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. Similar relationships had been used by other astronomers, but Kepler—with Tycho's data and his own astronomical theories—treated them much more precisely and attached new physical significance to them.^{[64]}
Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion. He then tried many combinations until he discovered that (approximately) "The square of the periodic times are to each other as the cubes of the mean distances." Although he gives the date of this epiphany (March 8, 1618), he does not give any details about how he arrived at this conclusion.^{[65]} However, the wider significance for planetary dynamics of this purely kinematical law was not realized until the 1660s. When conjoined with Christiaan Huygens' newly discovered law of centrifugal force, it enabled Isaac Newton, Edmund Halley, and perhaps Christopher Wren and Robert Hooke to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them.^{[66]} This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall is uniformly accelerated, and also by Galileo's student Borrelli in his 1666 celestial mechanics.^{[67]} William Gilbert, after experimenting with magnets, decided that the center of the Earth was a huge magnet. His theory led Kepler to think that a magnetic force from the Sun drove planets in their own orbits. This was an interesting explanation for planetary motion, but unfortunately for Kepler, it was wrong. Before scientists could find the right answer, they needed to know more about motion.
Rudolphine Tables and his last years
In 1623, Kepler at last completed the Rudolphine Tables, which at the time was considered his major work. 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 CounterReformation 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 the Tables at his own expense.^{[68]}
In 1628, following the military successes of the Emperor Ferdinand's armies under General Wallenstein, Kepler became an official advisor to Wallenstein. Though not the general's court astrologer per se, Kepler provided astronomical calculations for Wallenstein's astrologers and occasionally wrote horoscopes himself. In his final years, Kepler spent much of his time traveling, from the imperial 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 Swedish army destroyed the churchyard.^{[69]} Only Kepler's selfauthored poetic epitaph survived the times:
 Mensus eram coelos, nunc terrae metior umbras
 Mens coelestis erat, corporis umbra iacet.
 I measured the skies, now the shadows I measure
 Skybound was the mind, earthbound the body rests.^{[70]}
Reception of his astronomy
Kepler's laws were not immediately accepted. Several major figures such as Galileo and René Descartes completely ignored Kepler's Astronomia nova. Many astronomers, including Kepler's teacher, Michael Maestlin, objected to Kepler's introduction of physics into his astronomy. Some adopted compromise positions. Ismael Boulliau accepted elliptical orbits but replaced Kepler's area law with uniform motion in respect to the empty focus of the ellipse, while Seth Ward used an elliptical orbit with motions defined by an equant.^{[71]}^{[72]}^{[73]}
Several astronomers tested Kepler's theory, and its various modifications, against astronomical observations. Two transits of Venus and Mercury across the face of the sun provided sensitive tests of the theory, under circumstances when these planets could not normally be observed. In the case of the transit of Mercury in 1631, Kepler had been extremely uncertain of the parameters for Mercury, and advised observers to look for the transit the day before and after the predicted date. Pierre Gassendi observed the transit on the date predicted, a confirmation of Kepler's prediction.^{[74]} This was the first observation of a transit of Mercury. However, his attempt to observe the transit of Venus just one month later was unsuccessful due to inaccuracies in the Rudolphine Tables. Gassendi did not realize that it was not visible from most of Europe, including Paris.^{[75]} Jeremiah Horrocks, who observed the 1639 Venus transit, had used his own observations to adjust the parameters of the Keplerian model, predicted the transit, and then built apparatus to observe the transit. He remained a firm advocate of the Keplerian model.^{[76]}^{[77]}^{[78]}
Epitome of Copernican Astronomy was read by astronomers throughout Europe, and following Kepler's death it was the main vehicle for spreading Kepler's ideas. Between 1630 and 1650, it was the most widely used astronomy textbook, winning many converts to ellipsebased astronomy.^{[56]} However, few adopted his ideas on the physical basis for celestial motions. In the late 17th century, a number of physical astronomy theories drawing from Kepler's work—notably those of Giovanni Alfonso Borelli and Robert Hooke—began to incorporate attractive forces (though not the quasispiritual motive species postulated by Kepler) and the Cartesian concept of inertia. This culminated in Isaac Newton's Principia Mathematica (1687), in which Newton derived Kepler's laws of planetary motion from a forcebased theory of universal gravitation.^{[79]}
Historical and cultural legacy
Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the philosophy and historiography of science. Kepler and his laws of motion were central to early histories of astronomy such as Jean Etienne Montucla’s 1758 Histoire des mathématiques and JeanBaptiste Delambre's 1821 Histoire de l’astronomie moderne. These and other histories written from an Enlightenment perspective treated Kepler's metaphysical and religious arguments with skepticism and disapproval, but later Romanticera natural philosophers viewed these elements as central to his success. William Whewell, in his influential History of the Inductive Sciences of 1837, found Kepler to be the archetype of the inductive scientific genius; in his Philosophy of the Inductive Sciences of 1840, Whewell held Kepler up as the embodiment of the most advanced forms of scientific method. Similarly, Ernst Friedrich Apelt—the first to extensively study Kepler's manuscripts, after their purchase by Catherine the Great—identified Kepler as a key to the "Revolution of the sciences". Apelt, who saw Kepler's mathematics, aesthetic sensibility, physical ideas, and theology as part of a unified system of thought, produced the first extended analysis of Kepler's life and work.^{[80]}
Modern translations of a number of Kepler's books appeared in the latenineteenth and earlytwentieth centuries, the systematic publication of his collected works began in 1937 (and is nearing completion in the early 21st century), and Max Caspar's Kepler biography was published in 1948.^{[81]} However, Alexandre Koyré's work on Kepler was, after Apelt, the first major milestone in historical interpretations of Kepler's cosmology and its influence. In the 1930s and 1940s, Koyré, and a number of others in the first generation of professional historians of science, described the "Scientific Revolution" as the central event in the history of science, and Kepler as a (perhaps the) central figure in the revolution. Koyré placed Kepler's theorization, rather than his empirical work, at the center of the intellectual transformation from ancient to modern worldviews. Since the 1960s, the volume of historical Kepler scholarship has expanded greatly, including studies of his astrology and meteorology, his geometrical methods, the role of his religious views in his work, his literary and rhetorical methods, his interaction with the broader cultural and philosophical currents of his time, and even his role as an historian of science.^{[82]}
The debate over Kepler's place in the Scientific Revolution has also produced a wide variety of philosophical and popular treatments. One of the most influential is Arthur Koestler's 1959 The Sleepwalkers, in which Kepler is unambiguously the hero (morally and theologically as well as intellectually) of the revolution.^{[83]} Philosophers of science—such as Charles Sanders Peirce, Norwood Russell Hanson, Stephen Toulmin, and Karl Popper—have repeatedly turned to Kepler: examples of incommensurability, analogical reasoning, falsification, and many other philosophical concepts have been found in Kepler's work. Physicist Wolfgang Pauli even used Kepler's priority dispute with Robert Fludd to explore the implications of analytical psychology on scientific investigation.^{[84]} A wellreceived, if fanciful, historical novel by John Banville, Kepler (1981), explored many of the themes developed in Koestler's nonfiction narrative and in the philosophy of science.^{[85]} Somewhat more fanciful is a recent work of nonfiction, Heavenly Intrigue (2004), suggesting that Kepler murdered Tycho Brahe to gain access to his data.^{[86]} Kepler has acquired a popular image as an icon of scientific modernity and a man before his time; science popularizer Carl Sagan described him as "the first astrophysicist and the last scientific astrologer".^{[87]}
The German composer Paul Hindemith wrote an opera about Kepler entitled Die Harmonie der Welt, and a symphony of the same name was derived from music for the opera.
In Austria, Kepler left behind such a historical legacy that he was one of the motifs of a silver collector's coin: the 10euro Johannes Kepler silver coin, minted on September 10, 2002. The reverse side of the coin has a portrait of Kepler, who spent some time teaching in Graz and the surrounding areas. Kepler was acquainted with Prince Hans Ulrich von Eggenberg personally, and he probably influenced the construction of Eggenberg Castle (the motif of the obverse of the coin). In front of him on the coin is the model of nested spheres and polyhedra from Mysterium Cosmographicum.^{[88]}
In 2009, NASA named the Kepler Mission for Kepler's contributions to the field of astronomy.^{[89]}
In New Zealand's Fiordland National Park there is also a range of mountains named after Kepler, called the Kepler Mountains, and a Three Day Walking Trail known as the Kepler Track through the mountains of the same name.
Veneration
Kepler is honored together with Nicolaus Copernicus with a feast day on the liturgical calendar of the Episcopal Church (USA) on May 23.^{[90]}
Works
 Mysterium Cosmographicum (The Sacred Mystery of the Cosmos) (1596)
 De Fundamentis Astrologiae Certioribus (On Firmer Fundaments of Astrology; 1601)
 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 (Thirdparty Interventions) (1610)
 Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610)
 Dioptrice (1611)
 De nive sexangula (On the SixCornered Snowflake) (1611)
 De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit (1614)^{[91]}
 Eclogae Chronicae (1615, published with Dissertatio 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)
 Harmonices Mundi (Harmony of the Worlds) (1619)
 Mysterium cosmographicum (The Sacred Mystery of the Cosmos), 2nd edition (1621)
 Tabulae Rudolphinae (Rudolphine Tables) (1627)
 Somnium (The Dream) (1634)
See also
Named in his honor
 1134 Kepler, an asteroid
 Die Harmonie der Welt, an opera by Paul Hindemith
 The Johannes Kepler ATV, the second Automated Transfer Vehicle (ATV) launched by ESA to resupply the ISS. The ATV launched in February 2011 and deorbited in June 2011.
 Johannes Kepler University Linz: 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 Kepler, since he wrote his magnum opus Harmonice Mundi in Linz.
 Kepler, a crater on Mars
 Kepler, a crater on the moon
 Kepler, a high end graphics processing unit released in 2012 by Nvidia for their GeForce 600 series & 2013 GeForce 700 series GPU series
 Kepler, an opera by Philip Glass
 The Kepler Building, a satellite manufacturing plant for Surrey Satellite Technology Ltd, Surrey, UK.
 Kepler College, Seattle, Washington
 Kepler Launch Site
 The Kepler Mission, a space photometer designed to search for Earthlike planets launched by NASA on March 6, 2009
 The Kepler Mountains and the Kepler Track on the South Island of New Zealand
 The Kepler Solids, a set of geometrical constructions, two of which were described by him
 Kepler's laws of planetary motion for astronomical calculations
 Kepler's Supernova, Supernova 1604, which he observed and described

Numerous schools, streets, observatories and others named after him, e.g.:
 Johannes Kepler Grammar School,^{[92]} at the site where Kepler lived in Prague
 Kepler Gymnasium (high school), Tübingen
 Keplerplatz, a station on the U1 line of the Vienna UBahn rapid transit (Metro) system
 Keplerstraße in Hanau near Frankfurt am Main
 Keplerstraße in Munich, Germany
 Keplerstraße and Keplerbrücke in Graz, Austria
Notes and references
 ^ Barker and Goldstein. "Theological Foundations of Kepler's Astronomy", pp. 112–13.
 ^ Kepler. New Astronomy, title page, tr. Donohue, pp. 26–7
 ^ Kepler. New Astronomy, p. 48
 ^ Epitome of Copernican Astronomy in Great Books of the Western World, Vol 15, p. 845
 ^ Stephenson. Kepler's Physical Astronomy, pp. 1–2; Dear, Revolutionizing the Sciences, pp. 74–78
 ^ Caspar. Kepler, pp. 29–36; Connor. Kepler's Witch, pp. 23–46.
 ^ ^{a} ^{b} Koestler. The Sleepwalkers, p. 234 (translated from Kepler's family horoscope).
 ^ Caspar. Kepler, pp. 36–38; Connor. Kepler's Witch, pp. 25–27.
 ^ Connor, James A. Kepler's Witch (2004), p. 58.
 ^ ^{a} ^{b} Barker, Peter; Goldstein, Bernard R. "Theological Foundations of Kepler's Astronomy", Osiris, 2nd Series, Vol. 16, Science in Theistic Contexts: Cognitive Dimensions (2001), p. 96.
 ^ Westman, Robert S. "Kepler's Early PhysicoAstrological Problematic," Journal for the History of Astronomy, 32 (2001): 227–36.
 ^ Caspar. Kepler, pp. 38–52; Connor. Kepler's Witch, pp. 49–69.
 ^ Caspar. Kepler, pp. 60–65; see also: Barker and Goldstein, "Theological Foundations of Kepler's Astronomy."
 ^ Barker and Goldstein. "Theological Foundations of Kepler's Astronomy," pp. 99–103, 112–113.
 ^ Caspar. Kepler, pp. 65–71.
 ^ Field. Kepler's Geometrical Cosmology, Chapter IV, p 73ff.
 ^ Dreyer, J.L.E. A History of Astronomy from Thales to Kepler, Dover Publications, 1953, pp. 331, 377–379.
 ^ Caspar, Kepler. pp. 71–75.
 ^ Connor. Kepler's Witch, pp. 89–100, 114–116; Caspar. Kepler, pp. 75–77
 ^ Caspar. Kepler, pp. 85–86.
 ^ Caspar, Kepler, pp. 86–89
 ^ Caspar, Kepler, pp. 89–100
 ^ Using Tycho's data, see 'Two views of a system'
 ^ Caspar, Kepler, pp. 100–08.
 ^ Caspar, Kepler, p. 110.
 ^ Caspar, Kepler, pp. 108–11.
 ^ Caspar, Kepler, pp. 111–22.
 ^ Caspar, Kepler, pp. 149–53
 ^ Caspar, Kepler, pp. 146–148, 159–177
 ^ Finger, "Origins of Neuroscience," p 74. Oxford University Press, 2001.
 ^ Caspar, Kepler, pp. 142–146
 ^ Morris Kline, Mathematical Thought from Ancient to Modern Times, p 299. Oxford University Press, 1972.
 ^ Caspar, Kepler, pp. 153–157
 ^ Caspar, Kepler, pp. 123–128
 ^ On motive species, see: Lindberg, "The Genesis of Kepler's Theory of Light," pp. 38–40
 ^ "Kepler's decision to base his causal explanation of planetary motion on a distancevelocity law, rather than on uniform circular motions of compounded spheres, marks a major shift from ancient to modern conceptions of science.... [Kepler] had begun with physical principles and had then derived a trajectory from it, rather than simply constructing new models. In other words, even before discovering the area law, Kepler had abandoned uniform circular motion as a physical principle." Peter Barker and Bernard R. Goldstein, "Distance and Velocity in Kepler's Astronomy", Annals of Science, 51 (1994): 59–73, at p. 60.
 ^ Koyré, The Astronomical Revolution, pp. 199–202
 ^ Caspar, Kepler, pp. 129–132
 ^ Caspar, Kepler, pp. 131–140; Koyré, The Astronomical Revolution, pp. 277–279
 ^ Caspar, Kepler, pp. 178–81
 ^ Caspar, Kepler, pp. 181–85. The full title is Tertius 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 stargazer's superstition do not throw out the child with the bath and hereby unknowingly act contrary to their profession."
 ^ Caspar, Kepler, pp. 192–197
 ^ Koestler, The Sleepwalkers p. 384
 ^ Caspar, Kepler, pp. 198–202
 ^ Lear, Kepler's Dream, pp. 1–78
 ^ Schneer, "Kepler's New Year's Gift of a Snowflake," pp. 531–45
 ^ Kepler, Johannes (1966) [1611]. Hardie, Colin, ed. De nive sexangula [The Sixsided Snowflake]. Oxford: Clarendon Press.
 ^ Caspar, Kepler, pp. 202–204
 ^ Connor, Kepler's Witch, pp. 222–226; Caspar, Kepler, pp. 204–07
 ^ Caspar, Kepler, pp. 208–11
 ^ Caspar, Kepler, pp. 209–20, 227–240
 ^ Ferguson, Thomas S. (1989), "Who solved the secretary problem ?", Statistical Science 4 (3): 282–289,
 ^ Quotation from Connor, Kepler's Witch, p 252, translated from an October 23, 1613 letter from Kepler to an anonymous nobleman
 ^ Caspar, Kepler, pp. 220–223; Connor, Kepler's Witch, pp. 251–54.
 ^ Caspar, Kepler, pp. 239–240, 293–300
 ^ ^{a} ^{b} Gingerich, "Kepler, Johannes" from Dictionary of Scientific Biography, pp. 302–04

^ By 1621 or earlier, Kepler recognized that Jupiter's moons obey his third law.
Kepler contended that rotating massive bodies communicate their rotation to their satellites, so that the satellites are swept around the central body; thus the rotation of the Sun drives the revolutions of the planets and the rotation of the Earth drives the revolution of the Moon. In Kepler's era, no one had any evidence of Jupiter's rotation. However, Kepler argued that the force by which a central body causes its satellites to revolve around it, weakens with distance; consequently, satellites that are farther from the central body revolve slower. Kepler noted that Jupiter's moons obeyed this pattern and he inferred that a similar force was responsible. He also noted that the orbital periods and semimajor axes of Jupiter's satellites were roughly related by a 3/2 power law, as are the orbits of the six (then known) planets. However, this relation was approximate: the periods of Jupiter's moons were known within a few percent of their modern values, but the moons’ semimajor axes were determined less accurately.
Kepler discussed Jupiter's moons in his Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 4, part 2, page 554. (For a more modern and legible edition, see: Christian Frisch, ed., Joannis Kepleri Astronomi Opera Omnia, vol. 6 (FrankfurtamMain, (Germany): Heyder & Zimmer, 1866), page 361.)Original : 4) Confirmatur vero fides hujus rei comparatione quatuor Jovialium et Jovis cum sex planetis et Sole. Etsi enim de corpore Jovis, an et ipsum circa suum axem convertatur, non ea documenta habemus, quae nobis suppetunt in corporibus Terrae et praecipue Solis, quippe a sensu ipso: at illud sensus testatur, plane ut est cum sex planetis circa Solem, sic etiam se rem habere cum quatuor Jovialibus, ut circa corpus Jovis quilibet, quo longius ab illo potest excurrere, hoc tardius redeat, et id quidem proportione non eadem, sed majore, hoc est sescupla proportionis intervallorum cujusque a Jove: quae plane ipsissima est, qua utebantur supra sex planetae. Intervalla enim quatuor Jovialium a Jove prodit Marius in suo Mundo Joviali ista: 3, 5, 8, 13 (vel 14 Galilaeo) … Periodica vero tempora prodit idem Marius ista: dies 1. h. 18 1/2, dies 3 h. 13 1/3, dies 7 h. 3, dies 16 h. 18: ubique proportio est major quam dupla, major igitur quam intervallorum 3, 5, 8, 13 vel 14, minor tamen quam quadratorum, qui duplicant proportiones intervallorum, sc. 9, 25, 64, 169 vel 196, sicut etiam sescupla sunt majora simplis, minora vero duplis.
Translation : (4) However, the credibility of this [argument] is proved by the comparison of the four [moons] of Jupiter and Jupiter with the six planets and the Sun. Because, regarding the body of Jupiter, whether it turns around its axis, we don't have proofs for what suffices for us [regarding the rotation of ] the body of the Earth and especially of the Sun, certainly [as reason proves to us]: but reason attests that, just as it is clearly [true] among the six planets around the Sun, so also it is among the four [moons] of Jupiter, because around the body of Jupiter any [satellite] that can go farther from it orbits slower, and even that [orbit's period] is not in the same proportion, but greater [than the distance from Jupiter]; that is, 3/2 (sescupla ) of the proportion of each of the distances from Jupiter, which is clearly the very [proportion] as [is used for] the six planets above. In his [book] The World of Jupiter [Mundus Jovialis, 1614], [Simon] Mayr [15731624] presents these distances, from Jupiter, of the four [moons] of Jupiter: 3, 5, 8, 13 (or 14 [according to] Galileo) … Mayr presents their time periods: 1 day 18 1/2 hours, 3 days 13 1/3 hours, 7 days 3 hours, 16 days 18 hours: for all [of these data] the proportion is greater than double, thus greater than [the proportion] of the distances 3, 5, 8, 13 or 14, although less than [the proportion] of the squares, which double the proportions of the distances, namely 9, 25, 64, 169 or 196, just as [a power of] 3/2 is also greater than 1 but less than 2.
 ^ Wolf, A History of Science, Technology and Philosophy, pp. 140–41; Pannekoek, A History of Astronomy, p 252
 ^ Caspar, Kepler, pp. 239, 300–01, 307–08
 ^ Caspar, Kepler, pp. 240–264; Connor, Kepler's Witch, chapters I, XIXIII; Lear, Kepler's Dream, pp. 21–39
 ^ Quotation from Caspar, Kepler, pp. 265–266, translated from Harmonices Mundi
 ^ The opening of the movie Mars et Avril by Martin Villeneuve is based on German astronomer Johannes Kepler’s cosmological model from the 17th century, Harmonices Mundi, in which the harmony of the universe is determined by the motion of celestial bodies. Benoît Charest also composed the score according to this theory.
 ^ Caspar, Kepler, pp. 264–66, 290–93
 ^ Caspar, Kepler, pp. 266–90
 ^
 ^ Westfall, Never at Rest, pp. 143, 152, 402–03; Toulmin and Goodfield, The Fabric of the Heavens, p 248; De Gandt, 'Force and Geometry in Newton's Principia', chapter 2; Wolf, History of Science, Technology and Philosophy, p. 150; Westfall, The Construction of Modern Science, chapters 7 and 8
 ^ Koyré, The Astronomical Revolution, p. 502
 ^ Caspar, Kepler, pp. 308–328
 ^ Caspar, Kepler, pp. 332–351, 355–61
 ^ Koestler, The Sleepwalkers, p. 427.
 ^ For a detailed study of the reception of Kepler's astronomy see Wilbur Applebaum, "Keplerian Astronomy after Kepler: Researches and Problems," History of Science, 34(1996): 451–504.
 ^ Koyré, The Astronomical Revolution, pp. 362–364
 ^ North, History of Astronomy and Cosmology, pp. 355–60
 ^ Albert van Helden, "The Importance of the Transit of Mercury of 1631," Journal for the History of Astronomy, 7 (1976): 1–10.
 ^ HM Nautical Almanac Office (June 10, 2004). "1631 Transit of Venus". Archived from the original on October 1, 2006. Retrieved August 28, 2006.
 ^ Allan Chapman, "Jeremiah Horrocks, the transit of Venus, and the 'New Astronomy' in early 17thcentury England," Quarterly Journal of the Royal Astronomical Society, 31 (1990): 333–357.
 ^ North, History of Astronomy and Cosmology, pp. 348–349
 ^ Wilbur Applebaum and Robert Hatch, : Three Unpublished Letters,"Venus in sole visa"Boulliau, Mercator, and Horrock's Journal for the History of Astronomy, 14(1983): 166–179
 ^ Kuhn, The Copernican Revolution, pp. 238, 246–252
 ^ Jardine, "Koyré’s Kepler/Kepler's Koyré," pp. 363–367
 ^ Gingerich, introduction to Caspar's Kepler, pp. 3–4
 ^ Jardine, "Koyré’s Kepler/Kepler's Koyré," pp. 367–372; Shapin, The Scientific Revolution, pp. 1–2
 ^ Stephen Toulmin, Review of The Sleepwalkers in The Journal of Philosophy, Vol. 59, no. 18 (1962), pp. 500–503
 ^ Pauli, "The Influence of Archetypical Ideas"
 ^ William Donahue, "A Novelist's Kepler," Journal for the History of Astronomy, Vol. 13 (1982), pp. 135–136; "Dancing the grave dance: Science, art and religion in John Banville's Kepler," English Studies, Vol. 86, no. 5 (October 2005), pp. 424–438
 ^ Marcelo Gleiser, "Kepler in the Dock", review of Gilder and Gilder's Heavenly Intrigue, Journal for the History of Astronomy, Vol. 35, pt. 4 (2004), pp. 487–489
 ^ Quote from Carl Sagan, Cosmos: A Personal Voyage, episode III: "The Harmony of the Worlds". Kepler was hardly the first to combine physics and astronomy; however, according to the traditional (though disputed) interpretation of the Scientific Revolution, he would be the first astrophysicist in the era of modern science.
 ^ "Eggenberg Palace coin". Austrian Mint. Retrieved September 9, 2009.
 ^ Ng, Jansen (July 3, 2009). "Kepler Mission Sets Out to Find Planets Using CCD Cameras". DailyTech. Retrieved July 3, 2009.
 ^ "Calendar of the Church Year according to the Episcopal Church". Charles Wohlers. Retrieved October 17, 2014.
 ^ "...in 1614, Johannes Kepler published his book "De vero anno quo aeternus dei filius humanum naturam in utero benedictae Virginis Mariae assumpsit", on the chronology related to the Star of Bethlehem.", The Star of Bethlehem, Kapteyn Astronomical Institute
 ^ "GJK.cz". GJK.cz. Retrieved October 17, 2014.
 The most complete 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. Owen Gingerich's The Eye of Heaven builds on Caspar's work to place Kepler in the broader intellectual context of earlymodern astronomy. Many later studies have focused on particular elements of his life and work. Kepler's mathematics, cosmological, philosophical and historical views have been extensively analyzed in books and journal articles, though his astrological work—and its relationship to his astronomy—remains understudied.
Sources
 Andersen, Hanne; Peter Barker; and Xiang Chen. The Cognitive Structure of Scientific Revolutions, chapter 6: "The Copernican Revolution." New York: Cambridge University Press, 2006. ISBN 0521855756
 Armitage, Angus. John Kepler, Faber, 1966.
 Banville, John. Kepler, Martin, Secker and Warburg, London, 1981 (fictionalised biography)
 Barker, Peter 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
 Caspar, Max. 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 0486676056
 Connor, James A. 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 0060522550
 De Gandt, Francois. Force and Geometry in Newton's Principia, Translated by Curtis Wilson, Princeton University Press 1995. ISBN 0691033676
 Dreyer, J. L. E. A History of Astronomy from Thales to Kepler. Dover Publications Inc, 1967. ISBN 0486600793
 Ferguson, Kitty. The nobleman and his housedog: Tycho Brahe and Johannes Kepler: the strange partnership that revolutionized science. London: Review, 2002. ISBN 0747270228 – published in the US as: Tycho & Kepler: the unlikely partnership that forever changed our understanding of the heavens. New York: Walker, 2002. ISBN 0802713904
 Field, J. V.. Kepler's geometrical cosmology. Chicago University Press, 1988. ISBN 0226248232
 Gilder, Joshua and AnneLee Gilder: Heavenly Intrigue: Johannes Kepler, Tycho Brahe, and the Murder Behind One of History's Greatest Scientific Discoveries, Doubleday (May 18, 2004). ISBN 0385508441 Reviews bookpage.com, crisismagazine.com
 Gingerich, Owen. The Eye of Heaven: Ptolemy, Copernicus, Kepler. American Institute of Physics, 1993. ISBN 0883188635 (Masters of modern physics; v. 7)
 Gingerich, Owen: "Kepler, Johannes" in Dictionary of Scientific Biography, Volume VII. Charles Coulston Gillispie, editor. New York: Charles Scribner's Sons, 1973
 Greenbaum and Boockmann: "Kepler's Astrology", Culture and Cosmos Vol. 14. Special Double Issue, 2012.
 Jardine, Nick: "Koyré’s Kepler/Kepler's Koyré," History of Science, Vol. 38 (2000), pp. 363–376
 Kepler, Johannes. Johannes Kepler New Astronomy trans. W. Donahue, forward by O. Gingerich, Cambridge University Press 1993. ISBN 0521301319
 Kepler, Johannes and Christian Frisch. Joannis Kepleri Astronomi Opera Omnia (John Kepler, Astronomer; Complete Works), 8 vols.(1858–1871). vol. 1, 1858, vol. 2, 1859, vol. 3, 1860, vol. 6, 1866, vol. 7, 1868, Frankfurt am Main and Erlangen, Heyder & Zimmer, – Google Books
 Kepler, Johannes, et al. Great Books of the Western World. Volume 16: Ptolemy, Copernicus, Kepler, Chicago: Encyclopædia Britannica, Inc., 1952. (contains English translations by of Kepler's Epitome, Books IV & V and Harmonices Book 5)
 Koestler, Arthur. The Sleepwalkers: A History of Man's Changing Vision of the Universe. (1959). ISBN 0140192468
 Koyré, Alexandre: Galilean Studies Harvester Press 1977. ISBN 0855273542
 Koyré, Alexandre: The Astronomical Revolution: CopernicusKeplerBorelli Ithaca, NY: Cornell University Press, 1973. ISBN 0801405041; Methuen, 1973. ISBN 0416769802; Hermann, 1973. ISBN 2705656480
 Kuhn, Thomas S. The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Cambridge, MA: Harvard University Press, 1957. ISBN 0674171039
 Lindberg, David C.: "The Genesis of Kepler's Theory of Light: Light Metaphysics from Plotinus to Kepler." Osiris, N.S. 2. University of Chicago Press, 1986, pp. 5–42.
 Lear, John. Kepler's Dream. Berkeley: University of California Press, 1965
 M.T.K AlTamimi: Great collapse Kepler's first law, Natural Science 2 (2010), ISBN 2150 – 4091
 North, John. The Fontana History of Astronomy and Cosmology, Fontana Press, 1994. ISBN 0006861776
 Pannekoek, Anton: A History of Astronomy, Dover Publications Inc 1989. ISBN 0486659941
 Pauli, Wolfgang. Wolfgang Pauli — Writings on physics and philosophy, translated by Robert Schlapp and edited by P. Enz and Karl von Meyenn (Springer Verlag, Berlin, 1994). See section 21, The influence of archetypical ideas on the scientific theories of Kepler, concerning Johannes Kepler and Robert Fludd (1574–1637). ISBN 354056859X
 Schneer, Cecil: "Kepler's New Year's Gift of a Snowflake." Isis, Volume 51, No. 4. University of Chicago Press, 1960, pp. 531–545.
 Shapin, Steven. The Scientific Revolution. Chicago: University of Chicago Press, 1996. ISBN 0226750205
 Stephenson, Bruce. Kepler's physical astronomy. New York: Springer, 1987. ISBN 0387965416 (Studies in the history of mathematics and physical sciences; 13); reprinted Princeton:Princeton Univ. Pr., 1994. ISBN 0691036527
 Stephenson, Bruce. The Music of the Heavens: Kepler's Harmonic Astronomy, Princeton University Press, 1994. ISBN 0691034397
 Toulmin, Stephen and June Goodfield. The Fabric of the Heavens: The Development of Astronomy and Dynamics. Pelican, 1963.
 Voelkel, James R. The Composition of Kepler's Astronomia nova, Princeton University Press, 2001. ISBN 0691007381
 Westfall, Richard S.. The Construction of Modern Science: Mechanism and Mechanics. John Wiley and Sons, 1971. ISBN 047193531X; reprinted Cambridge University Press, 1978. ISBN 0521292956
 Westfall, Richard S. Never at Rest: A Biography of Isaac Newton. Cambridge University Press, 1981. ISBN 0521231434
 Wolf, A. A History of Science, Technology and Philosophy in the 16th and 17th centuries. George Allen & Unwin, 1950.
External links
 Works by Johannes Kepler at Project Gutenberg
 Works by or about Johannes Kepler at Internet Archive
 Kommission zur Herausgabe der Werke von Johannes Kepler
 JohannesKepler.Info Kepler information and community website, launched on December 27, 2009
 Harmonices mundi ("The Harmony of the Worlds") in fulltext facsimile; CarnegieMellon University
 Johannes Kepler entry by Daniel A. Di Liscia in the Stanford Encyclopedia of Philosophy
 De Stella Nova in Pede Serpentarii ("On the new star in Ophiuchus's foot") in full text facsimile at Linda Hall Library
 Walter W. Bryant. Kepler at Project Gutenberg (1920 book, part of Men of Science series)
 Electronic facsimileeditions of the rare book collection at the Vienna Institute of Astronomy
 Johannes Kepler at DMOZ
 Audio – Cain/Gay (2010) Astronomy Cast Johannes Kepler and His Laws of Planetary Motion
 Christianson, Gale E., Kepler's Somnium: Science Fiction and the Renaissance Scientist
 Kollerstrom, Nicholas, Kepler's Belief in Astrology
 References for Johannes Kepler
 Plant, David, Kepler and the "Music of the Spheres"
 Kepler, Napier, and the Third Law at MathPages
 Calderón Urreiztieta, Carlos. Harmonice Mundi • Animated and multimedia version of Book V
 Reading the mind of God 1997 drama based on his life by Patrick Gabridge
 Johannes Kepler 2010 drama based on his life by Robert Lalonde
 .
 Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by and/or portraits of Johannes Kepler in .jpg and .tiff format.
 TabvlæRudolphinæ qvibvs astronomicæ scientiæ ... Typis J. Saurii, 1627. From the Rare Book and Special Collections Division at the Library of Congress


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 Johannes Kepler
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