Johannes Kepler

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Johannes Kepler
Johannes Kepler 1610.jpg
Portrait of Kepler by an unknown artist, 1610
BornDecember 27, 1571
DiedNovember 15, 1630(1630-11-15) (aged 58)
Residence Württemberg; Styria; Bohemia; Upper Austria
Alma mater Tübinger Stift, University of Tübingen
Known for Kepler's laws of planetary motion
Kepler conjecture
Rudolphine Tables
Scientific career
Fields Astronomy, astrology, mathematics and natural philosophy
Doctoral advisor Michael Maestlin
Influences Nicolaus Copernicus
Tycho Brahe
Influenced Sir Isaac Newton
Unterschrift Kepler.svg

Johannes Kepler ( /ˈkɛplər/ ; [1] German: [joˈhanəs ˈkɛplɐ, -nɛs -]; [2] [3] December 27, 1571 – November 15, 1630) was a German astronomer, mathematician, and astrologer. He is a key figure in the 17th-century scientific revolution, best known for his laws of planetary motion, and his books Astronomia nova , Harmonices Mundi , and Epitome Astronomiae Copernicanae . These works also provided one of the foundations for Newton's theory of universal gravitation.

Astronomer Scientist who studies celestial bodies

An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets, and galaxies – in either observational or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. Related but distinct subjects like physical cosmology, which studies the Universe as a whole.

Mathematician person with an extensive knowledge of mathematics

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Keplers laws of planetary motion Scientific laws describing motion of planets around the Sun

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.


Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei. He was a corresponding member of the Accademia dei Lincei in Rome. [4]

Seminary, school of theology, theological seminary, and divinity school are educational institutions for educating students in scripture, theology, generally to prepare them for ordination to serve as clergy, in academics, or in Christian ministry. The English word is taken from the Latin seminarium, translated as seed-bed, an image taken from the Council of Trent document Cum adolescentium aetas which called for the first modern seminaries. In the West, the term now refers to Catholic educational institutes and has widened to include other Christian denominations and American Jewish institutions.

Graz Place in Styria, Austria

Graz is the capital of Styria and the second-largest city in Austria after Vienna. On 1 January 2019 it had a population of 328,276. In 2015, the population of the Graz larger urban zone who had principal residence status stood at 633,168.

Hans Ulrich von Eggenberg Czech hofmeister, duke and nobleman

Prince Hans Ulrich von Eggenberg was an Austrian statesman, a son of Seyfried von Eggenberg, Lord of Erbersdorf (1526-1594), and great-grandson of Balthasar Eggenberger. He was a prominent member of the House of Eggenberg and gained the title of Duke of Krumau.

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. [5] Kepler described his new astronomy as "celestial physics", [6] as "an excursion into Aristotle's Metaphysics ", [7] and as "a supplement to Aristotle's On the Heavens ", [8] transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics. [9]

Astronomy Universe events since the Big Bang 13.8 billion years ago

Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics, physics, and chemistry in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets; the phenomena also includes supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, all phenomena that originate outside Earth's atmosphere are within the purview of astronomy. A branch of astronomy called cosmology is the study of the Universe as a whole.

Astrology Pseudoscience claiming celestial objects influence human affairs

Astrology is a pseudoscience that claims to divine information about human affairs and terrestrial events by studying the movements and relative positions of celestial objects. Astrology has been dated to at least the 2nd millennium BCE, and has its roots in calendrical systems used to predict seasonal shifts and to interpret celestial cycles as signs of divine communications. Many cultures have attached importance to astronomical events, and some—such as the Hindus, Chinese, and the Maya—developed elaborate systems for predicting terrestrial events from celestial observations. Western astrology, one of the oldest astrological systems still in use, can trace its roots to 19th–17th century BCE Mesopotamia, from which it spread to Ancient Greece, Rome, the Arab world and eventually Central and Western Europe. Contemporary Western astrology is often associated with systems of horoscopes that purport to explain aspects of a person's personality and predict significant events in their lives based on the positions of celestial objects; the majority of professional astrologers rely on such systems.

Quadrivium liberal arts of astronomy, arithmetic, music and geometry

The quadrivium is the four subjects, or arts, taught after teaching the trivium. The word is Latin, meaning four ways, and its use for the four subjects has been attributed to Boethius or Cassiodorus in the 6th century. Together, the trivium and the quadrivium comprised the seven liberal arts, as distinguished from the practical arts.

Early years

Kepler's birthplace, in Weil der Stadt Kepler-Geburtshaus.jpg
Kepler's birthplace, in Weil der Stadt

Kepler was born on December 27, the feast day of St John the Evangelist, 1571, in the Free Imperial 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, Sebald Kepler, had been Lord Mayor of the city. 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. [10]

John the Evangelist author of the Gospel of John; traditionally identified with John the Apostle of Jesus, John of Patmos (author of Revelation), and John the Presbyter

John the Evangelist is the name traditionally given to the author of the Gospel of John. Christians have traditionally identified him with John the Apostle, John of Patmos, or John the Presbyter, although this has been disputed by modern scholars.

Weil der Stadt Place in Baden-Württemberg, Germany

Weil der Stadt is a town of about 19,000 inhabitants, located in the Stuttgart Region of the German state of Baden-Württemberg. It is about 30 km (19 mi) west of Stuttgart city center, and is often called "Gate to the Black Forest". The town is located in the beautiful valley of the river Würm.

Stuttgart Region human settlement

Stuttgart Region is an urban agglomeration at the heart of the Stuttgart Metropolitan Region. It consists of the city of Stuttgart and the surrounding districts of Ludwigsburg, Esslingen, Böblingen, Rems-Murr and Göppingen. About 2.7 million inhabitants live in that area (3,700 km²). In fact, with 708 people per square kilometre, the Stuttgart Region is one of the most densely populated areas in Germany. Stuttgart Region is governed by a directly elected parliament.

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." [11] In 1580, at age nine, he observed another astronomical event, a lunar eclipse, recording that he remembered being "called outdoors" to see it and that the moon "appeared quite red". [11] However, childhood smallpox left him with weak vision and crippled hands, limiting his ability in the observational aspects of astronomy. [12]

Great Comet of 1577 comet

The Great Comet of 1577 is a non-periodic comet that passed close to Earth during the year 1577 AD. Having an official designation beginning with "C" classes it as a non-periodic comet, and so it is not expected to return. In 1577, the comet was viewed by people all over Europe, including the famous Danish astronomer Tycho Brahe and Turkish astronomer Taqi ad-Din. From his observations of the comet, Brahe was able to discover that comets and similar objects travel above the Earth's atmosphere. The best fit using JPL Horizons suggests that the comet is currently about 320 AU from the Sun.

Lunar eclipse when the Moon passes directly behind the Earth

A lunar eclipse occurs when the Moon passes directly behind Earth and into its shadow. This can occur only when the Sun, Earth, and Moon are exactly or very closely aligned, with Earth between the other two. A lunar eclipse can occur only on the night of a full moon. The type and length of a lunar eclipse depend on the Moon's proximity to either node of its orbit.

Moon Earths natural satellite

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, and the largest among planetary satellites relative to the size of the planet that it orbits. The Moon is after Jupiter's satellite Io the second-densest satellite in the Solar System among those whose densities are known.

As a child, Kepler witnessed the Great Comet of 1577, which attracted the attention of astronomers across Europe. Von einem Schrecklichen vnd Wunderbarlichen Cometen so sich den Dienstag nach Martini dieses lauffenden M. D. Lxxvij. Jahrs am Himmel erzeiget hat (grayscale).png
As a child, Kepler witnessed the Great Comet of 1577, which attracted the attention of astronomers across Europe.

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 [13] 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. [14] He proved himself to be a superb mathematician and earned a reputation as a skilful astrologer, casting horoscopes for fellow students. Under the instruction of Michael Maestlin, Tübingen's professor of mathematics from 1583 to 1631, [14] 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. [15] 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. He accepted the position in April 1594, at the age of 23. [16]

Latin school School type in Europe from the 14th to 19th centuries

The Latin school was the grammar school of 14th- to 19th-century Europe, though the latter term was much more common in England. Emphasis was placed, as the name indicates, on learning to use Latin. The education given at Latin schools gave great emphasis to the complicated grammar of the Latin language, initially in its Medieval Latin form. Grammar was the most basic part of the trivium and the Liberal arts — in artistic personifications Grammar's attribute was the birch rod. Latin school prepared students for university, as well as enabling those of middle class status to rise above their station. It was therefore not unusual for children of commoners to attend Latin schools, especially if they were expected to pursue a career within the church. Although Latin schools existed in many parts of Europe in the 14th century and were more open to the laity, prior to that the Church allowed for Latin schools for the sole purpose of training those who would one day become clergymen. Latin schools began to develop to reflect Renaissance humanism around the 1450s. In some countries, but not England, they later lost their popularity as universities and some Catholic orders began to prefer the vernacular.

Evangelical Seminaries of Maulbronn and Blaubeuren seminary

The Protestant Seminaries of Maulbronn and Blaubeuren in Baden-Württemberg, Germany, are two Gymnasien and Protestant boarding schools in the Württemberg tradition.

Tübinger Stift seminary

The Tübinger Stift is a hall of residence and teaching; it is owned and supported by the Evangelical-Lutheran Church in Württemberg, and located in the university city of Tübingen, in South West Germany. The Stift was founded as an Augustinian monastery in the Middle Ages. After the Reformation, in 1536, Duke Ulrich turned the Stift into a seminary which served to prepare Protestant pastors for Württemberg. To this day the scholarship is still given to students in preparation for the ministry or teaching in Württemberg. Students receive a scholarship which consists of boarding, lodging and further academic support.

Graz (1594–1600)

Mysterium Cosmographicum

Kepler's Platonic solid model of the Solar System, from Mysterium Cosmographicum (1596) Kepler-solar-system-1.png
Kepler's Platonic solid model of the Solar System, from Mysterium Cosmographicum (1596)

Kepler's first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery, 1596), 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 3-dimensional polyhedra. He found that each of the five Platonic solids could be 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 selectively—octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler found that the spheres could be placed at intervals corresponding 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. [17]

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. [18]

Close-up of an inner section of Kepler's model Kepler-solar-system-2.png
Close-up of an inner section of Kepler's model

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. [19]

Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherist 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. [20]

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 orbium coelestium". 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." [21]

Barbara Muller and Johannes Kepler.jpg
Portraits of Kepler and his wife
House of Johannes Kepler.JPG
House of Kepler and Barbara Müller in Gössendorf, near Graz (1597–1599)

Marriage to Barbara Müller

In December 1595, Kepler was introduced to Barbara Müller, a 23-year-old widow (twice over) with a young daughter, Regina Lorenz, and he began courting her. Müller, an heiress to the estates of her late husbands, was also the daughter of a successful mill owner. Her father Jobst initially opposed a marriage. Even though Kepler 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, Protestant officials—who had helped set up the match—pressured the Müllers to honor their agreement. Barbara and Johannes were married on April 27, 1597. [22]

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). [23]

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. [24]

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. [25]

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. [26]

Prague (1600–1612)

Work for Tycho Brahe

Tycho Brahe Tycho Brahe.JPG
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 [27] 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. [28]

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 a 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"). [29] 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. [30]

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 the 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. [31]

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 well-received 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. [32]

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. [33]

Astronomiae Pars Optica

A plate from Astronomiae Pars Optica, illustrating the structure of eyes of various species. Kepler Optica.jpg
A plate from Astronomiae Pars Optica , illustrating the structure of eyes of various species.

As Kepler 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 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. 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." [34] Today, Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent). [35] 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. [36]

Supernova of 1604

Remnant of Kepler's Supernova SN 1604 Keplers supernova.jpg
Remnant of Kepler's Supernova SN 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 about 800-year cycle of great conjunctions; astrologers associated the two previous such periods with the rise of Charlemagne (c. 800 years earlier) and the birth of Christ (c. 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 800-year cycle. [37]

The location of the stella nova, in the foot of Ophiuchus, is marked with an N (8 grid squares down, 4 over from the left). Kepler Drawing of SN 1604.png
The location of the stella nova, in the foot of Ophiuchus, is marked with an N (8 grid squares down, 4 over from the left).

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. [38]

In 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) [39] radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. [40] [lower-alpha 1] 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. [42]

Diagram of the geocentric trajectory of Mars through several periods of apparent retrograde motion (Astronomia nova, Chapter 1, 1609) Kepler Mars retrograde.jpg
Diagram of the geocentric trajectory of Mars through several periods of apparent retrograde motion (Astronomia nova, Chapter 1, 1609)

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. [43] 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. [44]

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. [45]

Kepler and Roeslin engaged in a 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 traditional rules and methods of astrology to be the "evil-smelling dung" in which "an industrious hen" scrapes, there was an "occasional grain-seed, indeed, even a pearl or a gold nugget" to be found by the conscientious scientific astrologer. [46] Conversely, Sir Oliver Lodge observed that Kepler was somewhat disdainful of astrology, as Kepler was "continually attacking and throwing sarcasm at astrology, but it was the only thing for which people would pay him, and on it after a fashion he lived." [47]

Karlova street in Old Town, Prague - house where Kepler lived. Now a museum Karlova str No4, Prague Old Town.jpg
Karlová street in Old Town, Prague  – house where Kepler lived. Now a museum

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. [48]

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. [49] The resulting manuscript was completed in September 1610 and published as Dioptrice in 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 the astronomical or Keplerian telescope —in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses. [50]

One of the diagrams from Strena Seu de Nive Sexangula, illustrating the Kepler conjecture Kepler conjecture 2.jpg
One of the diagrams from Strena Seu de Nive Sexangula, illustrating the Kepler conjecture

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 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 text. [51]

Work in mathematics and physics

As a New Year's gift that year (1611), 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 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. [52] [53]

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. [54]

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. [55]

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 re-affirmed Kepler's position (and salary) as imperial mathematician but allowed him to move to Linz. [56]

Linz and elsewhere (1612–1630)

A statue of Kepler in Linz Kepler Statue Linz.jpg
A statue of Kepler in Linz

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. It was also during his time in Linz that Kepler had to deal with the accusation and ultimate verdict of witchcraft against his mother Katharina in the Protestant town of Leonberg. That blow, happening only a few years after Kepler's excommunication, is not seen as a coincidence but as a symptom of the full-fledged assault waged by the Lutherans against Kepler. [57]

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. [58]

Second marriage

On October 30, 1613, Kepler married the 24-year-old 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). [59] 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." [60] The first three children of this marriage (Margareta Regina, Katharina, and Sebald) died in childhood. Three more survived into adulthood: Cordula (born 1621); Fridmar (born 1623); and Hildebert (born 1625). According to Kepler's biographers, this was a much happier marriage than his first. [61]

Epitome of Copernican Astronomy, calendars, and the witch trial of his mother

Kepler's Figure 'M' from the Epitome, showing the world as belonging to just one of any number of similar stars. Kepler-Bruno.jpg
Kepler's Figure 'M' from the Epitome, showing the world as belonging to just one of any number of similar stars.

Since completing the Astronomia nova, Kepler had intended to compose an astronomy textbook. [62] In 1615, he completed the first of three volumes of Epitome astronomiae Copernicanae (Epitome of Copernican Astronomy); the first volume (books I–III) was printed in 1617, the second (book IV) in 1620, and the third (books V–VII) in 1621. Despite the title, which referred simply to heliocentrism, Kepler's textbook culminated in his own ellipse-based 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. [63] 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, [lower-alpha 2] it did not explain how elliptical orbits could be derived from observational data. [66]

As a spin-off 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. [67]

Geometrical harmonies in the perfect solids from Harmonices Mundi (1619) Kepler-1619-pl-3.jpg
Geometrical harmonies in the perfect solids from Harmonices Mundi (1619)

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"). [68]

Harmonices Mundi

Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world". [69] In Harmony, he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music. [lower-alpha 3] 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. [70]

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. [71]

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. [72] 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. [73] 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. [74]

Rudolphine Tables and his last years

Name "Copernicus" in a manuscript report by Kepler concerning the Rudolphine Tables (1616). Kepler Autograph 1 (cropped) - name Copernicus in Kepler's handwriting.jpg
Name "Copernicus" in a manuscript report by Kepler concerning the Rudolphine Tables (1616).
Title page of the Tabulae Rudolphinae, Ulm, 1627 8107-2Keplertp.png
Title page of the Tabulae Rudolphinae, Ulm, 1627
Kepler's horoscope for General Wallenstein Kepler-Wallenstein-Horoskop.jpg
Kepler's horoscope for General Wallenstein

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 Counter-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 the Tables at his own expense. [75]

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. [76] Only Kepler's self-authored 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. [77]


Kepler's belief that God created the cosmos in an orderly fashion caused him to attempt to determine and comprehend the laws that govern the natural world, most profoundly in astronomy. [78] [79] The phrase "I am merely thinking God's thoughts after Him" has been attributed to him, although this is probably a capsulized version of a writing from his hand:

Those laws [of nature] are within the grasp of the human mind; God wanted us to recognize them by creating us after his own image so that we could share in his own thoughts. [80]

Reception of his astronomy

Kepler's laws of planetary motion 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. Ismaël Bullialdus 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. [81] [82] [83]

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. [84] 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. [85] 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. [86] [87] [88]

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. In the period 1630 – 1650, this book was the most widely used astronomy textbook, winning many converts to ellipse-based astronomy. [63] 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 quasi-spiritual motive species postulated by Kepler) and the Cartesian concept of inertia. [89] This culminated in Isaac Newton's Principia Mathematica (1687), in which Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation. [90]

Historical and cultural legacy

Monument to Tycho Brahe and Kepler in Prague, Czech Republic Brahe kepler.jpg
Monument to Tycho Brahe and Kepler in Prague, Czech Republic
The GDR stamp featuring Kepler Stamps of Germany (DDR) 1971, MiNr 1649.jpg
The GDR stamp featuring Kepler

History of science

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-Étienne Montucla's 1758 Histoire des mathématiques and Jean-Baptiste 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 Romantic-era 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. [91]

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 world-views. 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. [92]

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. [93]

Editions and translations

Modern translations of a number of Kepler's books appeared in the late-nineteenth and early-twentieth centuries, the systematic publication of his collected works began in 1937 (and is nearing completion in the early 21st century).

An edition in eight volumes, Kepleri Opera omnia, was prepared by Christian Frisch (1807–1881), during 1858 to 1871, on the occasion of Kepler's 300th birthday. Frisch's edition only included Kepler's Latin, with a Latin commentary.

A new edition was planned beginning in 1914 by Walther von Dyck (1856–1934). Dyck compiled copies of Kepler's unedited manuscripts, using international diplomatic contacts to convince the Soviet authorities to lend him the manuscripts kept in Leningrad for photographic reproduction. These manuscripts contained several works by Kepler that had not been available to Frisch. Dyck's photographs remain the basis for the modern editions of Kepler's unpublished manuscripts.

Max Caspar (1880–1956) published his German translation of Kepler's Mysterium Cosmographicum in 1923. Both Dyck and Caspar were influenced in their interest in Kepler by mathematician Alexander von Brill (1842–1935). Caspar became Dyck's collaborator, succeeding him as project leader in 1934, establishing the Kepler-Kommission in the following year. Assisted by Martha List (1908–1992) and Franz Hammer (1898–1979), Caspar continued editorial work during World War II. Max Caspar also published a biography of Kepler in 1948. [94] The commission was later chaired by Volker Bialas (during 1976–2003) and Ulrich Grigull (during 1984–1999) and Roland Bulirsch (1998–2014). [95] [96]

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". [97]

The debate over Kepler's place in the Scientific Revolution has 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. [98]

A well-received, if fanciful, historical novel by John Banville, Kepler (1981), explored many of the themes developed in Koestler's non-fiction narrative and in the philosophy of science. [99] Somewhat more fanciful is a recent work of nonfiction, Heavenly Intrigue (2004), suggesting that Kepler murdered Tycho Brahe to gain access to his data. [100]

Veneration and eponymy

In Austria, Kepler left behind such a historical legacy that he was one of the motifs of a silver collector's coin: the 10-euro 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. [101]

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. Philip Glass wrote an opera called Kepler based on Kepler's life (2009).

Kepler is honored together with Nicolaus Copernicus with a feast day on the liturgical calendar of the Episcopal Church (USA) on May 23. [102]

Directly named for Kepler's contribution to science are Kepler's laws of planetary motion, Kepler's Supernova (Supernova 1604, which he observed and described) and the Kepler Solids, a set of geometrical constructions, two of which were described by him, and the Kepler conjecture on sphere packing.

The Kepler crater as photographed by Apollo 12 in 1969 AS12-52-7745.jpg
The Kepler crater as photographed by Apollo 12 in 1969


A critical edition of Kepler's collected works (Johannes Kepler Gesammelte Werke, KGW) in 22 volumes is being edited by the Kepler-Kommission (founded 1935) on behalf of the Bayerische Akademie der Wissenschaften.

Vol. 1: Mysterium Cosmographicum. De Stella Nova. Ed. M. Caspar. 1938, 2nd ed. 1993. Paperback ISBN   3-406-01639-1.
Vol. 2: Astronomiae pars optica. Ed. F. Hammer. 1939, Paperback ISBN   3-406-01641-3.
Vol. 3: Astronomia Nova. Ed. M. Caspar. 1937. IV, 487 p. 2. ed. 1990. Paperback ISBN   3-406-01643-X. Semi-parchment ISBN   3-406-01642-1.
Vol. 4: Kleinere Schriften 1602–1611. Dioptrice. Ed. M. Caspar, F. Hammer. 1941. ISBN   3-406-01644-8.
Vol. 5: Chronologische Schriften. Ed. F. Hammer. 1953. Out-of-print.
Vol. 6: Harmonice Mundi. Ed. M. Caspar. 1940, 2nd ed. 1981, ISBN   3-406-01648-0.
Vol. 7: Epitome Astronomiae Copernicanae. Ed. M. Caspar. 1953, 2nd ed. 1991. ISBN   3-406-01650-2, Paperback ISBN   3-406-01651-0.
Vol. 8: Mysterium Cosmographicum. Editio altera cum notis. De Cometis. Hyperaspistes. Commentary F. Hammer. 1955. Paperback ISBN   3-406-01653-7.
Vol 9: Mathematische Schriften. Ed. F. Hammer. 1955, 2nd ed. 1999. Out-of-print.
Vol. 10: Tabulae Rudolphinae. Ed. F. Hammer. 1969. ISBN   3-406-01656-1.
Vol. 11,1: Ephemerides novae motuum coelestium. Commentary V. Bialas. 1983. ISBN   3-406-01658-8, Paperback ISBN   3-406-01659-6.
Vol. 11,2: Calendaria et Prognostica. Astronomica minora. Somnium. Commentary V. Bialas, H. Grössing. 1993. ISBN   3-406-37510-3, Paperback ISBN   3-406-37511-1.
Vol. 12: Theologica. Hexenprozeß. Tacitus-Übersetzung. Gedichte. Commentary J. Hübner, H. Grössing, F. Boockmann, F. Seck. Directed by V. Bialas. 1990. ISBN   3-406-01660-X, Paperback ISBN   3-406-01661-8.
Vol. 13: Briefe 1590–1599. Ed. M. Caspar. 1945. 432 p. ISBN   3-406-01663-4.
Vol. 14: Briefe 1599–1603. Ed. M. Caspar. 1949. Out-of-print. 2nd ed. in preparation.
Vol 15: Briefe 1604–1607. Ed. M. Caspar. 1951. 2nd ed. 1995. ISBN   3-406-01667-7.
Vol. 16: Briefe 1607–1611. Ed. M. Caspar. 1954. ISBN   3-406-01668-5.
Vol. 17: Briefe 1612–1620. Ed. M. Caspar. 1955. ISBN   3-406-01671-5.
Vol. 18: Briefe 1620–1630. Ed. M. Caspar. 1959. ISBN   3-406-01672-3.
Vol. 19: Dokumente zu Leben und Werk. Commentary M. List. 1975. ISBN   978-3-406-01674-5.
Vols. 20–21: manuscripts
Vol. 20,1: Manuscripta astronomica (I). Apologia, De motu Terrae, Hipparchus etc. Commentary V. Bialas. 1988. ISBN   3-406-31501-1. Paperback ISBN   3-406-31502-X.
Vol. 20,2: Manuscripta astronomica (II). Commentaria in Theoriam Martis. Commentary V. Bialas. 1998. Paperback ISBN   3-406-40593-2.
Vol. 21,1: Manuscripta astronomica (III) et mathematica. De Calendario Gregoriano. In preparation.
Vol. 21,2: Manuscripta varia. In preparation.
Vol. 22: General index, in preparation.

The Kepler-Kommission also publishes Bibliographia Kepleriana (2nd ed. List, 1968), a complete bibliography of editions of Kepler's works, with a supplementary volume to the second edition (ed. Hamel 1998).

See also

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Musica universalis, also called Music of the spheres or Harmony of the Spheres, is an ancient philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of musica. This "music" is not usually thought to be literally audible, but a harmonic, mathematical or religious concept. The idea continued to appeal to thinkers about music until the end of the Renaissance, influencing scholars of many kinds, including humanists. Further scientific exploration has determined specific proportions in some orbital motion, described as orbital resonance.

Celestial spheres Term in ancient times for the heavens

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like jewels set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.

<i>Harmonices Mundi</i> book by Johannes Kepler

Harmonices Mundi is a book by Johannes Kepler. In the work, written entirely in Latin, Kepler discusses harmony and congruence in geometrical forms and physical phenomena. The final section of the work relates his discovery of the so-called "third law of planetary motion".

<i>Astronomia nova</i> Book by Johannes Kepler

Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year-long investigation of the motion of Mars. One of the most significant books in the history of astronomy, the Astronomia nova provided strong arguments for heliocentrism and contributed valuable insight into the movement of the planets. This included the first mention of the planets' elliptical paths and the change of their movement to the movement of free floating bodies as opposed to objects on rotating spheres. It is recognized as one of the most important works of the scientific revolution.

Michael Maestlin German astronomer and mathematician

Michael Maestlin was a German astronomer and mathematician, known for being the mentor of Johannes Kepler. He was a student of Petrus Apianus and was known as the teacher who most influenced Kepler. Maestlin was considered to be one of the most significant astronomers between the time of Copernicus and Kepler.

Copernican Revolution

The Copernican Revolution was the paradigm shift from the Ptolemaic model of the heavens, which described the cosmos as having Earth stationary at the center of the universe, to the heliocentric model with the Sun at the center of the Solar System. Beginning with the publication of Nicolaus Copernicus’s De revolutionibus orbium coelestium, contributions to the “revolution” continued until finally ending with Isaac Newton’s work over a century later.

<i>Mysterium Cosmographicum</i> astronomy book

Mysterium Cosmographicum is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1597 and in a second edition in 1621. Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids, enclosed within a sphere that represented the orbit of Saturn.

Nicolaus Reimers German astronomer

Nicolaus Reimers Baer, also Reimarus Ursus, Nicolaus Reimers Bär or Nicolaus Reymers Baer, was an astronomer and imperial mathematician to Emperor Rudolf II. Due to his family's background, he was also known as Bär, Latinized to Ursus ("bear").

<i>Tantrasamgraha</i> astronomical treatise written by Nilakantha Somayaji

Tantrasamgraha, or Tantrasangraha, is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics. The treatise was completed in 1501 CE. It consists of 432 verses in Sanskrit divided into eight chapters. Tantrasamgraha had spawned a few commentaries: Tantrasamgraha-vyakhya of anonymous authorship and Yuktibhāṣā authored by Jyeshtadeva in about 1550 CE. Tantrasangraha, together with its commentaries, bring forth the depths of the mathematical accomplishments the Kerala school of astronomy and mathematics, in particular the achievements of the remarkable mathematician of the school Sangamagrama Madhava. In his Tantrasangraha, Nilakantha revised Aryabhata's model for the planets Mercury and Venus. His equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.

Copernican heliocentrism Concept that the Earth rotates around the Sun

Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths modified by epicycles and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, placing Earth at the center of the Universe. It is often regarded as the launching point to modern astronomy and the Scientific Revolution.

Paul Wittich German astronomer

Paul Wittich was a German mathematician and astronomer whose Capellan geoheliocentric model, in which the inner planets Mercury and Venus orbit the sun but the outer planets Mars, Jupiter and Saturn orbit the Earth, may have directly inspired Tycho Brahe's more radically heliocentric geoheliocentric model in which all the 5 known primary planets orbited the Sun, which in turn orbited the stationary Earth.

Helisaeus Roeslin or Helisäus Röslin (17 January 1545, Plieningen – 14 August 1616, Buchsweiler was a German physician and astrologer who adopted a geoheliocentric model of the universe. He was one of five observers who concluded that the Great Comet of 1577 was located beyond the moon. His representation of the comet, described as "an interesting, though crude, attempt," was among the earliest and was highly complex.

Johannes Remus Quietanus

Johann Ruderauf or Johannes Remus Quietanus was a German astronomer, astrologer and doctor. He maintained correspondence with Galileo Galilei, Johannes Kepler and Giovanni Faber, a pontifical botanist. He is one of the first four observers of Transit of Mercury that happened on 7 November 1631.

<i>Epitome Astronomiae Copernicanae</i> book by Johannes Kepler

The Epitome Astronomiae Copernicanae was an astronomy book on the heliocentric system published by Johannes Kepler in the period 1617 to 1621. The first volume was printed in 1617, the second in 1620, and the third in 1621.



  1. "Kepler's decision to base his causal explanation of planetary motion on a distance-velocity 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." [41]
  2. 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 semi-major 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' semi-major axes were determined less accurately. Kepler discussed Jupiter's moons in his Summary of Copernican Astronomy : [64] [65]
    (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 [1573–1624] 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.
  3. 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.


  1. "Kepler". Random House Webster's Unabridged Dictionary .
  2. Dudenredaktion; Kleiner, Stefan; Knöbl, Ralf (2015) [First published 1962]. Das Aussprachewörterbuch [The Pronunciation Dictionary] (in German) (7th ed.). Berlin: Dudenverlag. pp. 487, 505. ISBN   978-3-411-04067-4.
  3. Krech, Eva-Maria; Stock, Eberhard; Hirschfeld, Ursula; Anders, Lutz Christian (2009). Deutsches Aussprachewörterbuch [German Pronunciation Dictionary] (in German). Berlin: Walter de Gruyter. pp. 628, 646. ISBN   978-3-11-018202-6.
  4. accessed 9/7/2017
  5. Barker and Goldstein. "Theological Foundations of Kepler's Astronomy", pp. 112–13.
  6. Kepler. New Astronomy, title page, tr. Donohue, pp. 26–7
  7. Kepler. New Astronomy, p. 48
  8. Epitome of Copernican Astronomy in Great Books of the Western World, Vol 15, p. 845
  9. Stephenson. Kepler's Physical Astronomy, pp. 1–2; Dear, Revolutionizing the Sciences, pp. 74–78
  10. Caspar. Kepler, pp. 29–36; Connor. Kepler's Witch, pp. 23–46.
  11. 1 2 Koestler. The Sleepwalkers, p. 234 (translated from Kepler's family horoscope).
  12. Caspar. Kepler, pp. 36–38; Connor. Kepler's Witch, pp. 25–27.
  13. Connor, James A. Kepler's Witch (2004), p. 58.
  14. 1 2 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.
  15. Westman, Robert S. "Kepler's Early Physico-Astrological Problematic," Journal for the History of Astronomy , 32 (2001): 227–36.
  16. Caspar. Kepler, pp.  38–52; Connor. Kepler's Witch, pp.  49–69.
  17. Caspar. Kepler, pp. 60–65; see also: Barker and Goldstein, "Theological Foundations of Kepler's Astronomy."
  18. Barker and Goldstein. "Theological Foundations of Kepler's Astronomy," pp. 99–103, 112–113.
  19. Caspar. Kepler, pp. 65–71.
  20. Field. Kepler's Geometrical Cosmology, Chapter IV, p 73ff.
  21. Dreyer, J.L.E. A History of Astronomy from Thales to Kepler, Dover Publications, 1953, pp. 331, 377–379.
  22. Caspar, Kepler. pp. 71–75.
  23. Connor. Kepler's Witch, pp. 89–100, 114–116; Caspar. Kepler, pp. 75–77
  24. Caspar. Kepler, pp. 85–86.
  25. Caspar, Kepler, pp. 86–89
  26. Caspar, Kepler, pp. 89–100
  27. Using Tycho's data, see 'Two views of a system' Archived July 21, 2011, at the Wayback Machine
  28. Caspar, Kepler, pp. 100–08.
  29. Caspar, Kepler, p. 110.
  30. Caspar, Kepler, pp. 108–11.
  31. Caspar, Kepler, pp. 111–22.
  32. Caspar, Kepler, pp. 149–53
  33. Caspar, Kepler, pp. 146–148, 159–177
  34. Finger, "Origins of Neuroscience," p. 74. Oxford University Press, 2001.
  35. Caspar, Kepler, pp. 142–146
  36. Morris Kline, Mathematical Thought from Ancient to Modern Times , p. 299. Oxford University Press, 1972.
  37. Caspar, Kepler, pp. 153–157
  38. Caspar, Kepler, pp. 123–128
  39. On motive species, see Lindberg, "The Genesis of Kepler's Theory of Light," pp. 38–40.
  40. Koyré, The Astronomical Revolution, pp. 199–202.
  41. Peter Barker and Bernard R. Goldstein, "Distance and Velocity in Kepler's Astronomy", Annals of Science, 51 (1994): 59–73, at p. 60.
  42. Caspar, Kepler, pp. 129–132
  43. Caspar, Kepler, p. 133
  44. Caspar, Kepler, pp. 131–140; Koyré, The Astronomical Revolution, pp. 277–279
  45. Caspar, Kepler, pp. 178–81
  46. 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 star-gazer's superstition do not throw out the child with the bath and hereby unknowingly act contrary to their profession."
  47. Lodge, O.J., "Johann Kepler" in The World of Mathematics, Vol. 1 (1956) Ed. Newman, J.R., Simon and Schuster, pp. 231.
  48. Caspar, Kepler, pp. 192–197
  49. Koestler, The Sleepwalkers p. 384
  50. Caspar, Kepler, pp. 198–202
  51. Lear, Kepler's Dream, pp. 1–78
  52. Schneer, "Kepler's New Year's Gift of a Snowflake," pp. 531–45
  53. Kepler, Johannes (1966) [1611]. Hardie, Colin (ed.). De nive sexangula[The Six-sided Snowflake]. Oxford: Clarendon Press. OCLC   974730.
  54. Caspar, Kepler, pp. 202–204
  55. Connor, Kepler's Witch, pp. 222–226; Caspar, Kepler, pp. 204–07
  56. Caspar, Kepler, pp. 208–11
  57. Mazer, Arthur (2010). Shifting the Earth: The Mathematica Quest to Understand the Motion of the Universe. Hoboken, NJ: John Wiley & Sons, Inc. ISBN   978-1-118-02427--0.
  58. Caspar, Kepler, pp. 209–20, 227–240
  59. Ferguson, Thomas S. (1989), "Who solved the secretary problem ?", Statistical Science, 4 (3): 282–289, doi:10.1214/ss/1177012493, JSTOR   2245639, When the celebrated German astronomer, Johannes Kepler (1571–1630), lost his first wife to cholera in 1611, he set about finding a new wife using the same methodical thoroughness and careful consideration of the data that he used in finding the orbit of Mars to be an ellipse ... The process consumed much of his attention and energy for nearly 2 years ...
  60. Quotation from Connor, Kepler's Witch, p 252, translated from an October 23, 1613 letter from Kepler to an anonymous nobleman
  61. Caspar, Kepler, pp. 220–223; Connor, Kepler's Witch, pp. 251–54.
  62. Caspar, Kepler, pp. 239–240, 293–300
  63. 1 2 Gingerich, "Kepler, Johannes" from Dictionary of Scientific Biography, pp. 302–04
  64. Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 4, part 2, page 554
  65. Christian Frisch, ed., Joannis Kepleri Astronomi Opera Omnia, vol. 6 (Frankfurt-am-Main, (Germany): Heyder & Zimmer, 1866), page 361.)
  66. Wolf, A History of Science, Technology and Philosophy, pp. 140–41; Pannekoek, A History of Astronomy, p 252
  67. Caspar, Kepler, pp. 239, 300–01, 307–08
  68. Caspar, Kepler, pp. 240–264; Connor, Kepler's Witch, chapters I, XI-XIII; Lear, Kepler's Dream, pp. 21–39
  69. Quotation from Caspar, Kepler, pp. 265–266, translated from Harmonices Mundi
  70. Caspar, Kepler, pp. 264–66, 290–93
  71. Caspar, Kepler, pp. 266–90
  72. Miller, Arthur I. (March 24, 2009). Deciphering the cosmic number: the strange friendship of Wolfgang Pauli and Carl Jung. W. W. Norton & Company. p. 80. ISBN   978-0-393-06532-9 . Retrieved March 7, 2011.
  73. 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
  74. Koyré, The Astronomical Revolution, p. 502
  75. Caspar, Kepler, pp. 308–328
  76. Caspar, Kepler, pp. 332–351, 355–61
  77. Koestler, The Sleepwalkers, p. 427.
  78. "Johannes Kepler | Biography, Discoveries, & Facts".
  79. "Astronomy - the techniques of astronomy".
  80. Letter (9/10 Apr 1599) to the Bavarian chancellor Herwart von Hohenburg. Collected in Carola Baumgardt and Jamie Callan, Johannes Kepler Life and Letters (1953), 50
  81. 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.
  82. Koyré, The Astronomical Revolution, pp. 362–364
  83. North, History of Astronomy and Cosmology, pp.  355–60
  84. Helden, Albert van (1976). "The Importance of the Transit of Mercury of 1631". Journal for the History of Astronomy. 7: 1–10. Bibcode:1976JHA.....7....1V. doi:10.1177/002182867600700101.
  85. HM Nautical Almanac Office (June 10, 2004). "1631 Transit of Venus". Archived from the original on October 1, 2006. Retrieved August 28, 2006.
  86. Allan Chapman, "Jeremiah Horrocks, the transit of Venus, and the 'New Astronomy' in early 17th-century England," Quarterly Journal of the Royal Astronomical Society, 31 (1990): 333–357.
  87. North, History of Astronomy and Cosmology, pp.  348–349
  88. Wilbur Applebaum and Robert Hatch, "Boulliau, Mercator, and Horrock's Venus in sole visa: Three Unpublished Letters," Journal for the History of Astronomy , 14(1983): 166–179
  89. Lawrence Nolan (ed.), The Cambridge Descartes Lexicon, Cambridge University Press, 2016, "Inertia."
  90. Kuhn, The Copernican Revolution, pp. 238, 246–252
  91. Jardine, "Koyré's Kepler/Kepler's Koyré," pp. 363–367
  92. Jardine, "Koyré's Kepler/Kepler's Koyré," pp. 367–372; Shapin, The Scientific Revolution, pp. 1–2
  93. Pauli, "The Influence of Archetypical Ideas"
  94. Gingerich, introduction to Caspar's Kepler, pp. 3–4
  95. Ulrich Grigull, "Sechzig Jahre Kepler-Kommission", in: Sitzungsberichte der Bayerischen Akademie der Wissenschaften [Sitzung vom 5. Juli 1996], 1996.
  96. Ulf Hashagen, Walther von Dyck (1856–1934). Mathematik, Technik und Wissenschaftsorganisation an der TH München, Stuttgart, 2003.
  97. 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.
  98. Stephen Toulmin, Review of The Sleepwalkers in The Journal of Philosophy, Vol. 59, no. 18 (1962), pp. 500–503
  99. 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
  100. 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
  101. "Eggenberg Palace coin". Austrian Mint. Archived from the original on May 31, 2011. Retrieved September 9, 2009.
  102. "Calendar of the Church Year according to the Episcopal Church". Charles Wohlers. Retrieved October 17, 2014.
  103. Ng, Jansen (July 3, 2009). "Kepler Mission Sets Out to Find Planets Using CCD Cameras". DailyTech. Archived from the original on March 10, 2009. Retrieved July 3, 2009.
  104. "". Retrieved October 17, 2014.
  105. "... 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


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From the Lessing J. Rosenwald Collection at the Library of Congress: