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Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician,
astrologer Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Dif ...
, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his
laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbit ...
, and his books '' Astronomia nova'', '' Harmonice Mundi'', and '' Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton ( ...
's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in
Graz Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...
, 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 Matthias is a name derived from the Greek Ματθαίος, in origin similar to Matthew. People Notable people named Matthias include the following: In religion: * Saint Matthias, chosen as an apostle in Acts 1:21–26 to replace Judas Iscariot * ...
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 A telescope is an instrument designed for the observation of remote objects. Telescope(s) also may refer to: Music * The Telescopes, a British psychedelic band * ''Telescope'' (album), by Circle, 2007 * ''The Telescope'' (album), by Her Space H ...
discoveries of his contemporary Galileo Galilei. He was a corresponding member of the
Accademia dei Lincei The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rom ...
in Rome. 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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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. Kepler described his new astronomy as "celestial physics", as "an excursion into Aristotle's '' Metaphysics''", and as "a supplement to Aristotle's ''
On the Heavens ''On the Heavens'' (Greek: ''Περὶ οὐρανοῦ''; Latin: ''De Caelo'' or ''De Caelo et Mundo'') is Aristotle's chief cosmological treatise: written in 350 BC, it contains his astronomical theory and his ideas on the concrete workings o ...
''", transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.


Early life


Childhood (1571–1590)

Kepler was born on 27 December 1571, in the Free Imperial City of Weil der Stadt (now part of the
Stuttgart Region Stuttgart Region (Baden-Württemberg, Germany) 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 ...
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 The Eighty Years' War or Dutch Revolt ( nl, Nederlandse Opstand) ( c.1566/1568–1648) was an armed conflict in the Habsburg Netherlands between disparate groups of rebels and the Spanish government. The causes of the war included the Refo ...
in the Netherlands. His mother, Katharina Guldenmann, an innkeeper's daughter, was a
healer Healer may refer to: Conventional medicine *Doctor of Medicine *Health professional Alternative medicine * Faith healer * Folk healer * Healer (alternative medicine), someone who purports to aid recovery from ill health * Spiritual healer F ...
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. He was introduced to astronomy at an early age and developed a strong passion for it that would span his entire life. At age six, he observed the
Great Comet of 1577 The Great Comet of 1577 (official designation: C/1577 V1) 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 t ...
, writing that he "was taken by ismother to a high place to look at it." In 1580, at age nine, he observed another astronomical event, a
lunar eclipse A lunar eclipse occurs when the Moon moves into the Earth's shadow. Such alignment occurs during an eclipse season, approximately every six months, during the full moon phase, when the Moon's orbital plane is closest to the plane of the Earth ...
, recording that he remembered being "called outdoors" to see it and that the Moon "appeared quite red".Koestler. ''The Sleepwalkers'', p. 234 (translated from Kepler's family horoscope). However, childhood smallpox left him with weak vision and crippled hands, limiting his ability in the observational aspects of astronomy. 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 and theology under
Jacob Heerbrand Jacob Heerbrand (12 August 1521 – 22 May 1600) was a German Protestant theologian, reformer and controversialist. Life He was born at Giengen in Swabia on 12 August 1521. He was educated at the school at Ulm, and at the universities of Wit ...
(a student of
Philipp Melanchthon Philip Melanchthon. (born Philipp Schwartzerdt; 16 February 1497 – 19 April 1560) was a German Lutheran reformer, collaborator with Martin Luther, the first systematic theologian of the Protestant Reformation, intellectual leader of the Lu ...
at Wittenberg), who also taught Michael Maestlin while he was a student, until he became Chancellor at Tübingen in 1590.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. He proved himself to be a superb mathematician and earned a reputation as a skilful astrologer, casting
horoscope A horoscope (or other commonly used names for the horoscope in English include natal chart, astrological chart, astro-chart, celestial map, sky-map, star-chart, cosmogram, vitasphere, radical chart, radix, chart wheel or simply chart) is an ast ...
s for fellow students. Under the instruction of Michael Maestlin, Tübingen's professor of mathematics from 1583 to 1631, 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 Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at ...
from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe. 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 22.


Graz (1594–1600)

Before concluding his studies at Tübingen, Kepler accepted an offer to teach mathematics as a replacement to Georg Stadius at the Protestant school in Graz (now in Styria, Austria). During this period (1594–1600), he issued many official calendars and prognostications that enhanced his reputation as an astrologer. Although Kepler had mixed feelings about astrology and disparaged many customary practices of astrologers, he believed deeply in a connection between the cosmos and the individual. He eventually published some of the ideas he had entertained while a student in the ''Mysterium Cosmographicum'' (1596), published a little over a year after his arrival at Graz. 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 27 April 1597. In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died in infancy. In 1602, they had a daughter (Susanna); in 1604, a son (Friedrich); and in 1607, another son (Ludwig).


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. He also sought the opinions of many of the astronomers to whom he had sent ''Mysterium'', among them
Reimarus Ursus Nicolaus Reimers Baer (2 February 1551 – 16 October 1600), 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, ...
(Nicolaus Reimers Bär)—the imperial mathematician to
Rudolf II Rudolf II (18 July 1552 – 20 January 1612) was Holy Roman Emperor (1576–1612), King of Hungary and Kingdom of Croatia (Habsburg), Croatia (as Rudolf I, 1572–1608), King of Bohemia (1575–1608/1611) and Archduke of Austria (1576–160 ...
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. Instead, he turned his attention to chronology and "harmony," the
numerological Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...
relationships among music,
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 In astrology, an aspect is an angle that planets make to each other in the Horoscope; as well as to the Ascendant, Midheaven, Descendant, Lower Midheaven, and other points of astrological interest. As viewed from Earth, aspects are measured b ...
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 1 January 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.


Scientific career


Prague (1600–1612)

On 4 February 1600, Kepler met Tycho Brahe and his assistants
Franz Tengnagel Frans Gansneb genaamd Tengnagel van de Camp (1576 in Neede – 1 December 1622 in Vienna) was a Dutch nobleman. He belonged to the nobel ''Gansneb'' family from Gelderland, later called ("genaamd") Tengnagel. This family had as their residence fr ...
and Longomontanus at
Benátky nad Jizerou Benátky nad Jizerou (; german: Benatek) is a town in Mladá Boleslav District in the Central Bohemian Region of the Czech Republic. It has about 7,400 inhabitants. The historic town centre is well preserved and is protected by law as an urban mon ...
(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 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 Jan Jesenius, also written as Jessenius (german: Johannes Jessenius, hu, Jeszenszky János, sk, Ján Jesenský; December 27, 1566 – June 21, 1621), was a Bohemian physician, politician and philosopher. Life Early years He was from an old no ...
, 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 6 April. 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. 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"). 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 10 July eclipse in Graz. These observations formed the basis of his explorations of the laws of optics that would culminate in ''Astronomiae Pars Optica''. On 2 August 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 24 October 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.


Imperial Advisor

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. Rudolf was actively interested in the work of many of his court scholars (including numerous alchemists) and kept up with Kepler's work in physical astronomy as well. Officially, the only acceptable religious doctrines in Prague were Catholic and Utraquist, but Kepler's position in the imperial court allowed him to practice his Lutheran faith unhindered. The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle. Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness. Court life, however, brought Kepler into contact with other prominent scholars (
Johannes Matthäus Wackher von Wackhenfels Johannes Matthaeus Wacker von Wackenfels (1550–1619) was an active diplomat, scholar and author, with an avid interest in history and philosophy. A follower of Neostoicism, he sought to resolve the doubts he still had about his conversion to Catho ...
,
Jost Bürgi Jost Bürgi (also ''Joost, Jobst''; Latinisation of names, Latinized surname ''Burgius'' or ''Byrgius''; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomica ...
,
David Fabricius David Fabricius (9 March 1564 – 7 May 1617) was a German pastor who made two major discoveries in the early days of telescopic astronomy, jointly with his eldest son, Johannes Fabricius (1587–1615). David Fabricius (Latinization of his proper n ...
, Martin Bachazek, and Johannes Brengger, among others) and astronomical work proceeded rapidly.


Supernova of 1604

In October 1604, a bright new evening star (
SN 1604 SN 1604, also known as Kepler's Supernova, Kepler's Nova or Kepler's Star, was a Type Ia supernova that occurred in the Milky Way, in the constellation Ophiuchus. Appearing in 1604, it is the most recent supernova in the Milky Way galaxy to have ...
) appeared, but Kepler did not believe the rumors until he saw it himself. Kepler began systematically observing the supernova. Astrologically, the end of 1603 marked the beginning of a
fiery trigon In Western astrology, astrological signs are the twelve 30-degree sectors that make up Earth's 360-degree orbit around the Sun. The signs enumerate from the first day of spring, known as the First Point of Aries, which is the vernal equinox. ...
, 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 ''De Stella Nova in Pede Serpentarii'' (On the New Star in the Foot of the Serpent Handler), generally known as ''De Stella Nova'' was a book written by Johannes Kepler between 1605 and 1606, when the book was published in Prague. Kepler wrote the ...
''. 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. Kepler also attached an appendix where he discussed the recent chronology work of the Polish historian
Laurentius Suslyga Laurentius Suslyga or Laurence Suslyga (Polish: ''Wawrzyniec Susliga'' or ''Susłyga'') (1570–1640), was a Polish Jesuit historian, chronologist, and an author of Baroque visual poetry. He was the first person to claim that Jesus Christ was b ...
; 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. Over the following years, Kepler attempted (unsuccessfully) to begin a collaboration with Italian astronomer Giovanni Antonio Magini, and dealt with chronology, especially the dating of events in the life of Jesus. Around 1611, Kepler circulated a manuscript of what would eventually be published (posthumously) as ''
Somnium Somnium was originally a Latin word meaning "dream", and may refer to: * ''Somnium'' (novel), a scientific fantasy in Latin by Johannes Kepler * Somnium, a brand name for the drug lorazepam * ''Somnium'' (album) a 7-hour album by the ambient musi ...
''
he Dream He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' in ...
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.


Later life


Troubles

In 1611, the growing political-religious tension in Prague came to a head. Emperor Rudolf—whose health was failing—was forced to abdicate as King of Bohemia by his brother
Matthias Matthias is a name derived from the Greek Ματθαίος, in origin similar to Matthew. People Notable people named Matthias include the following: In religion: * Saint Matthias, chosen as an apostle in Acts 1:21–26 to replace Judas Iscariot * ...
. 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. Also in that year, Barbara Kepler contracted
Hungarian spotted fever ''Rickettsia'' is a genus of nonmotile, gram-negative, nonspore-forming, highly pleomorphic bacteria that may occur in the forms of cocci (0.1 μm in diameter), bacilli (1–4 μm long), or threads (up to about 10 μm long). The term "rickett ...
, 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 The Augsburg Confession, also known as the Augustan Confession or the Augustana from its Latin name, ''Confessio Augustana'', is the primary confession of faith of the Lutheran Church and one of the most important documents of the Protestant Re ...
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. Kepler postponed the move to Linz and remained in Prague until Rudolf'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.


Linz (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 The Eucharist (; from Greek , , ), also known as Holy Communion and the Lord's Supper, is a Christian rite that is considered a sacrament in most churches, and as an ordinance in others. According to the New Testament, the rite was instit ...
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 Leonberg (; swg, Leaberg) is a town in the German federal state of Baden-Württemberg about to the west of Stuttgart, the state capital. About 45,000 people live in Leonberg, making it the third-largest borough in the rural district (''Landkr ...
. 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. 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 Gregory has been the name of sixteen Roman Catholic Popes and two Antipopes: *Pope Gregory I ("the Great"; 590–604), after whom the Gregorian chant is named *Pope Gregory II (715–731) *Pope Gregory III (731–741) *Pope Gregory IV (827–844) * ...
's reformed calendar to Protestant German lands. On 30 October 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). 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." 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. On 8 October 1630, Kepler set out for Regensburg, hoping to collect interest on work he had done previously. A few days after reaching Regensburg, Kepler became sick, and progressively became worse. On 15 November 1630, just over a month after his arrival, he died. He was buried in a Protestant churchyard that was completely destroyed during the Thirty Years' War.


Christianity

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. 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
f nature F, or f, is the sixth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ef'' (pronounced ), and the plural is ''efs''. Hist ...
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.
Kepler advocated for
tolerance Tolerance or toleration is the state of tolerating, or putting up with, conditionally. Economics, business, and politics * Toleration Party, a historic political party active in Connecticut * Tolerant Systems, the former name of Veritas Software ...
among Christian denominations, for example arguing that Catholics and Lutherans should be able to take communion together. He wrote, "Christ the Lord neither was nor is Lutheran, nor Calvinist, nor Papist."


Astronomy


''Mysterium Cosmographicum''

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 Epiphany may refer to: * Epiphany (feeling), an experience of sudden and striking insight Religion * Epiphany (holiday), a Christian holiday celebrating the revelation of God the Son as a human being in Jesus Christ ** Epiphany season, or Epiph ...
on 19 July 1595, while teaching in
Graz Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...
, demonstrating the periodic conjunction of
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
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 Open Relay Behavior-modification System (ORBS), created and run by Alan Brown in New Zealand, was one of the first DNS-based Blackhole Lists (DNSBL), a means by which an internet domain may publish a list of IP addresses, in a database which can ...
; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids selectively— octahedron,
icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
, dodecahedron, tetrahedron,
cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...
—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. Kepler thought the ''Mysterium'' 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 A son is a male offspring; a boy or a man in relation to his parents. The female counterpart is a daughter. From a biological perspective, a son constitutes a first degree relative. Social issues In pre-industrial societies and some current c ...
, and the intervening space between them to the
Holy Spirit In Judaism, the Holy Spirit is the divine force, quality, and influence of God over the Universe or over his creatures. In Nicene Christianity, the Holy Spirit or Holy Ghost is the third person of the Trinity. In Islam, the Holy Spirit acts as ...
. His first manuscript of ''Mysterium'' contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism. With the support of his mentor Michael Maestlin, Kepler received permission from the 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 In politics and government, a spoils system (also known as a patronage system) is a practice in which a political party, after winning an election, gives government jobs to its supporters, friends (cronyism), and relatives (nepotism) as a reward ...
. 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. In terms of impact, the ''Mysterium'' can be seen as an important first step in modernizing the theory proposed by Copernicus in his '' De revolutionibus orbium coelestium''. Whilst Copernicus sought to advance a heliocentric system in this book, he resorted to
Ptolemaic Ptolemaic is the adjective formed from the name Ptolemy, and may refer to: Pertaining to the Ptolemaic dynasty * Ptolemaic dynasty, the Macedonian Greek dynasty that ruled Egypt founded in 305 BC by Ptolemy I Soter * Ptolemaic Kingdom Pertaining ...
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."


''Astronomia Nova''

The extended line of research that culminated in '' Astronomia Nova'' (''A New Astronomy'')—including the first two
laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbit ...
—began with the analysis, under Tycho's direction, of the orbit of Mars. In this work Kepler introduced the revolutionary concept of planetary orbit, a path of a planet in space resulting from the action of physical causes, distinct from previously held notion of planetary orb (a spherical shell to which planet is attached). As a result of this breakthrough astronomical phenomena came to be seen as being governed by physical laws. Kepler calculated and recalculated various approximations of Mars's 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 An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or ...
orbit to the data. In Kepler's religious view of the cosmos, the Sun (a symbol of
God the Father God the Father is a title given to God in Christianity. In mainstream trinitarian Christianity, God the Father is regarded as the first person of the Trinity, followed by the second person, God the Son Jesus Christ, and the third person, God t ...
) 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'') radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. Perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle 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''—his second law of planetary motion. He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped
ovoid An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or ...
orbit. After approximately 40 failed attempts, in late 1604 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 (the
Vicarious Hypothesis The Vicarious Hypothesis, or ''hypothesis vicaria'', was a planetary hypothesis proposed by Johannes Kepler to describe the motion of Mars. The hypothesis adopted the circular orbit and equant of Ptolemy's planetary model as well as the heliocentr ...
), Kepler immediately concluded that ''all planets move in ellipses, with the Sun at one focus''—his first law of planetary motion. Because he employed no calculating assistants, 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.


''Epitome of Copernican Astronomy''

Since completing the ''Astronomia Nova'', Kepler had intended to compose an astronomy textbook that would cover all the fundamentals of heliocentric astronomy. Kepler spent the next several years working on what would become ''Epitome Astronomiae Copernicanae'' (''Epitome of Copernican Astronomy''). Despite its title, which merely hints at heliocentrism, the ''Epitome'' is less about Copernicus's work and more about Kepler's own astronomical system. The ''Epitome'' contained all three laws of planetary motion and attempted to explain heavenly motions through physical causes.Gingerich, "Kepler, Johannes" from ''Dictionary of Scientific Biography'', pp. 302–04 Although 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, it did not explain how elliptical orbits could be derived from observational data. Originally intended as an introduction for the uninitiated, Kepler sought to model his ''Epitome'' after that of his master Michael Maestlin, who published a well-regarded book explaining the basics of geocentric astronomy to non-experts. Kepler completed the first of three volumes, consisting of Books I–III, by 1615 in the same question-answer format of Maestlin's and have it printed in 1617. However, the banning of Copernican books by the Catholic Church, as well as the start of the Thirty Years' War, meant that publication of the next two volumes would be delayed. In the interim, and to avoid being subject to the ban, Kepler switched the audience of the ''Epitome'' from beginners to that of expert astronomers and mathematicians, as the arguments became more and more sophisticated and requiring advanced mathematics to be understood. The second volume, consisting of Book IV, was published in 1620, followed by the third volume, consisting of Books V–VII, in 1621.


''Rudolphine Tables''

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. Kepler, at last, completed the '' Rudolphine Tables'' in 1623, 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.


Astrology

Like Ptolemy, Kepler considered astrology as the counterpart to astronomy, and as being of equal interest and value. However, in the following years, the two subjects drifted apart until astrology was no longer practiced among professional astronomers.
Sir Oliver Lodge Sir Oliver Joseph Lodge, (12 June 1851 – 22 August 1940) was a British physicist and writer involved in the development of, and holder of key patents for, radio. He identified electromagnetic radiation independent of Hertz's proof and at his ...
observed that Kepler was somewhat disdainful of astrology in his own day, as he 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." Nonetheless, Kepler spent a huge amount of time trying to restore astrology on a firmer philosophical footing, composing numerous astrological calendars, more than 800 nativities, and a number of treaties dealing with the subject of astrology proper.


''De Fundamentis''

In his bid to become imperial astronomer, Kepler wrote ''De Fundamentis'' (1601), whose full title can be translated as “On Giving Astrology Sounder Foundations”, as a short foreword to one of his yearly almanacs. In this work, Kepler describes the effects of the Sun, Moon, and the planets in terms of their light and their influences upon humors, finalizing with Kepler's view that the Earth possesses a soul with some sense of geometry. Stimulated by the geometric convergence of rays formed around it, the world-soul is sentient but not conscious. As a shepherd is pleased by the piping of a flute without understanding the theory of musical harmony, so likewise Earth responds to the angles and aspects made by the heavens but not in a conscious manner. Eclipses are important as omens because the animal faculty of the Earth is violently disturbed by the sudden intermission of light, experiencing something like emotion and persisting in it for some time. Kepler surmises that the Earth has "cycles of humors" as living animals do, and gives for an example that "the highest tides of the sea are said by sailors to return after nineteen years around the same days of the year". (This may refer to the 18.6-year lunar node precession cycle.) Kepler advocates searching for such cycles by gathering observations over a period of many years, "and so far this observation has not been made".


''Tertius Interveniens''

Kepler and
Helisaeus Roeslin Helisaeus Roeslin or Helisäus Röslin (17 January 1545 – 14 August 1616) 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 loca ...
engaged in a series of published attacks and counter-attacks on the importance of astrology after the supernova of 1604; around the same time, 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'' (1610). Nominally this work—presented to the common patron of Roeslin and Feselius—was a neutral mediation between the feuding scholars (the titled meaning "Third-party interventions"), 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.


Music


''Harmonice Mundi''

Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world". In ''Harmonice Mundi'' (1619), he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music. The central set of "harmonies" was the '' musica universalis'' or "music of the spheres", which had been studied by Pythagoras, Ptolemy and others before Kepler; in fact, soon after publishing ''Harmonice Mundi'', Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory. Kepler began by exploring regular polygons and
regular solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
s, 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. Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion. He 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 (8 March 1618), he does not give any details about how he arrived at this conclusion. However, the wider significance for planetary dynamics of this purely kinematical law was not realized until the 1660s. When conjoined with
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...
' newly discovered law of centrifugal force, it enabled Isaac Newton, Edmund Halley, and perhaps
Christopher Wren Sir Christopher Wren PRS FRS (; – ) was one of the most highly acclaimed English architects in history, as well as an anatomist, astronomer, geometer, and mathematician-physicist. He was accorded responsibility for rebuilding 52 churches ...
and
Robert Hooke Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them. 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.


Optics


''Astronomiae Pars Optica''

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 eclipse A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby obscuring the view of the Sun from a small part of the Earth, totally or partially. Such an alignment occurs during an eclipse season, approximately every six month ...
s 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 1 January 1604, was published as ''Astronomiae Pars Optica'' (The Optical Part of Astronomy). In it, Kepler described the
inverse-square law In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understo ...
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 Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects ...
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." Today, ''Astronomiae Pars Optica'' is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent). 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 In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
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.


''Dioptrice''

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''
tarry Messenger Tarry is a surname. Notable people with the surname include: * Chris Tarry (born 1970), a Canadian guitarist * Ellen Tarry (1906–2008), African-American journalist, author and centenarian * Gaston Tarry (1843–1913), a French mathematician * ...
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'' onversation 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''. Kepler also started a theoretical and experimental investigation of telescopic lenses using a telescope borrowed from Duke Ernest of Cologne. 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 lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
es and
double-concave diverging lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
es—and how they are combined to produce a
Galilean telescope A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens as its objective to form an image (also referred to a dioptric telescope). The refracting telescope design was originally used in spyglasses and as ...
—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 A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens as its objective to form an image (also referred to a dioptric telescope). The refracting telescope design was originally used in spyglasses and as ...
''—in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.


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. Kepler wrote the influential mathematical treatise ''Nova stereometria doliorum vinariorum'' in 1613, on measuring the volume of containers such as wine barrels, which was published in 1615. Kepler also contributed to the development of infinitesimal methods and numerical analysis, including iterative approximations, infinitesimals, and the early use of logarithms and transcendental equations. Kepler's work on calculating volumes of shapes, and on finding the optimal shape of a wine barrel, were significant steps toward the development of calculus. Simpson's rule, an approximation method used in integral calculus, is known in German as ''Keplersche Fassregel'' (Kepler's barrel rule).


Legacy


Reception of his astronomy

Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...
were not immediately accepted. Several major figures such as
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
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. 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. 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. 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. ''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. 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. 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, a mathematical challenge later known as "solving the
Kepler problem In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force ''F'' that varies in strength as the inverse square of the distance ''r'' between them. The force may be ei ...
".


History of science

Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the
philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
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 Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on th ...
's 1821 ''Histoire de l'astronomie moderne''. These and other histories written from an
Enlightenment Enlightenment or enlighten may refer to: Age of Enlightenment * Age of Enlightenment, period in Western intellectual history from the late 17th to late 18th century, centered in France but also encompassing (alphabetically by country or culture): ...
perspective treated Kepler's metaphysical and religious arguments with skepticism and disapproval, but later
Romantic Romantic may refer to: Genres and eras * The Romantic era, an artistic, literary, musical and intellectual movement of the 18th and 19th centuries ** Romantic music, of that era ** Romantic poetry, of that era ** Romanticism in science, of that e ...
-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 Ernst Friedrich Apelt (3 March 1812 in Reichenau, Saxony – 27 October 1859 in Oppelsdorf, Upper Lusatia, Saxony) was a German philosopher and entrepreneur. He was a student of Jakob Friedrich Fries, succeeding him at the University of Jena. He w ...
—the first to extensively study Kepler's manuscripts, after their purchase by
Catherine the Great , en, Catherine Alexeievna Romanova, link=yes , house = , father = Christian August, Prince of Anhalt-Zerbst , mother = Joanna Elisabeth of Holstein-Gottorp , birth_date = , birth_name = Princess Sophie of Anhal ...
—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. 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. Philosophers of science—such as Charles Sanders Peirce,
Norwood Russell Hanson Norwood Russell Hanson (August 17, 1924 – April 18, 1967) was an American philosopher of science. Hanson was a pioneer in advancing the argument that observation is theory-laden — that observation language and theory language are deeply inter ...
,
Stephen Toulmin Stephen Edelston Toulmin (; 25 March 1922 – 4 December 2009) was a British philosopher, author, and educator. Influenced by Ludwig Wittgenstein, Toulmin devoted his works to the analysis of moral reasoning. Throughout his writings, he sought t ...
, and
Karl Popper Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the cl ...
—have repeatedly turned to Kepler: examples of
incommensurability Two concepts or things are commensurable if they are measurable or comparable by a common standard. Commensurability most commonly refers to commensurability (mathematics). It may also refer to: * Commensurability (astronomy), whether two orbit ...
, 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.


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 (1898–1969), Caspar continued editorial work during World War II. Max Caspar also published a biography of Kepler in 1948. The commission was later chaired by Volker Bialas (during 1976–2003) and
Ulrich Grigull Ulrich Grigull (12 March 1912 – 20 October 2003) was a German engineer. Between 1972 and 1980, he was rector and later president of the Technical University of Munich. Early life After graduating from the Stadtgymnasium in Königsberg, Grigu ...
(during 1984–1999) and
Roland Bulirsch Roland Zdeněk Bulirsch (10 November 1932 – 21 September 2022) was a German mathematician specialising in numerical analysis. He studied and taught at the Technical University of Munich, and taught internationally as visiting professor. He was ...
(1998–2014).


Cultural influence and eponymy

Kepler has acquired a popular image as an icon of scientific modernity and a man before his time; science popularizer
Carl Sagan Carl Edward Sagan (; ; November 9, 1934December 20, 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on ext ...
described him as "the first astrophysicist and the last scientific astrologer". 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 Sleepwalker(s) or The Sleepwalker(s) may refer to: * Sleepwalking or somnambulism, a sleep disorder Film and television Films * ''The Sleepwalker'' (1922 film), an American silent film directed by Edward LeSaint * ''The Sleepwalker'' (1942 film ...
'', in which Kepler is unambiguously the hero (morally and theologically as well as intellectually) of the revolution. A well-received historical novel by
John Banville William John Banville (born 8 December 1945) is an Irish novelist, short story writer, adapter of dramas and screenwriter. Though he has been described as "the heir to Proust, via Nabokov", Banville himself maintains that W. B. Yeats and Henry J ...
, ''Kepler'' (1981), explored many of the themes developed in Koestler's non-fiction narrative and in the philosophy of science. A 2004 nonfiction book, ''Heavenly Intrigue'', suggested that Kepler murdered Tycho Brahe to gain access to his data. In Austria, a silver collector's 10-euro Johannes Kepler silver coin was minted in 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 Eggenberg Palace (german: link=no, Schloss Eggenberg) in Graz, is the most significant Baroque palace complex in the Austrian province of Styria. With its preserved accouterments, the extensive scenic gardens, as well as some special collectio ...
(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''. The German composer Paul Hindemith wrote an opera about Kepler entitled '' Die Harmonie der Welt'' (1957), and during the prolonged process of its creation, he also wrote a symphony of the same name based on the musical ideas he developed for it. Hindemith's opera inspired John Rodgers and Willie Ruff of Yale University to create a
synthesizer A synthesizer (also spelled synthesiser) is an electronic musical instrument that generates audio signals. Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis, additive synthesis and ...
composition based on Kepler's scheme for representing planetary motion with music.
Philip Glass Philip Glass (born January 31, 1937) is an American composer and pianist. He is widely regarded as one of the most influential composers of the late 20th century. Glass's work has been associated with minimal music, minimalism, being built up fr ...
wrote an opera called '' Kepler'' (2009) based on Kepler's life, with a libretto in German and Latin by Martina Winkel. Directly named for Kepler's contribution to science are
Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...
; Kepler's Supernova SN 1604, which he observed and described; the Kepler–Poinsot polyhedra a set of geometrical constructions, two of which were described by him; and the Kepler conjecture on sphere packing. Places and entities named in his honor include multiple city streets and squares, several educational institutions, an asteroid, and both a
lunar Lunar most commonly means "of or relating to the Moon". Lunar may also refer to: Arts and entertainment * ''Lunar'' (series), a series of video games * "Lunar" (song), by David Guetta * "Lunar", a song by Priestess from the 2009 album ''Prior t ...
and a Martian crater.


Works

* '' Mysterium Cosmographicum'' (''The Sacred Mystery of the Cosmos'') (1596) * ''De Fundamentis Astrologiae Certioribus'' (
On Firmer Fundaments of Astrology
') (1601) * * '' De Stella nova in pede Serpentarii'' (''On the New Star in Ophiuchus's Foot'') (1606) * '' Astronomia nova'' (''New Astronomy'') (1609) * ''Tertius Interveniens'' (''Third-party Interventions'') (1610) * ''Dissertatio cum Nuncio Sidereo'' (''Conversation with the Starry Messenger'') (1610) * ''Dioptrice'' (1611) * ''De nive sexangula'' (
On the Six-Cornered Snowflake
') (1611) * ''De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit'' (1614)"... 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 The Kapteyn Astronomical Institute is the department of astronomy of the University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a Public university#Continental Europe, pu ...
* ''Eclogae Chronicae'' (1615, published with ''Dissertatio cum Nuncio Sidereo'') * ''Nova stereometria doliorum vinariorum'' (''New Stereometry of Wine Barrels'') (1615)
''Ephemerides nouae motuum coelestium''
(1617–30) * * ** ** * * '' Harmonice Mundi'' (
Harmony of the Worlds
') (1619) * '' Mysterium cosmographicum'' (''The Sacred Mystery of the Cosmos''), 2nd edition (1621) * '' Tabulae Rudolphinae'' (''Rudolphine Tables'') (1627) * ''
Somnium Somnium was originally a Latin word meaning "dream", and may refer to: * ''Somnium'' (novel), a scientific fantasy in Latin by Johannes Kepler * Somnium, a brand name for the drug lorazepam * ''Somnium'' (album) a 7-hour album by the ambient musi ...
''
''The Dream''
(1634)
English translation on Google Books preview
* ** ** ** ** ** ** ** ** 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 The Bavarian Academy of Sciences and Humanities (german: Bayerische Akademie der Wissenschaften) is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledg ...
. :Vol. 1: ''Mysterium Cosmographicum. De Stella Nova''. Ed. M. Caspar. 1938, 2nd ed. 1993. Paperback . :Vol. 2: ''Astronomiae pars optica''. Ed. F. Hammer. 1939, Paperback . :Vol. 3: ''Astronomia Nova''. Ed. M. Caspar. 1937. IV, 487 p. 2. ed. 1990. Paperback . Semi-parchment . :Vol. 4: ''Kleinere Schriften 1602–1611. Dioptrice''. Ed. M. Caspar, F. Hammer. 1941. . :Vol. 5: ''Chronologische Schriften''. Ed. F. Hammer. 1953. Out-of-print. :Vol. 6: ''Harmonice Mundi''. Ed. M. Caspar. 1940, 2nd ed. 1981, . :Vol. 7: ''Epitome Astronomiae Copernicanae''. Ed. M. Caspar. 1953, 2nd ed. 1991. , Paperback . :Vol. 8: ''Mysterium Cosmographicum. Editio altera cum notis. De Cometis. Hyperaspistes''. Commentary F. Hammer. 1955. Paperback . :Vol 9: ''Mathematische Schriften''. Ed. F. Hammer. 1955, 2nd ed. 1999. Out-of-print. :Vol. 10: ''Tabulae Rudolphinae''. Ed. F. Hammer. 1969. . :Vol. 11,1: ''Ephemerides novae motuum coelestium''. Commentary V. Bialas. 1983. , Paperback . :Vol. 11,2: ''Calendaria et Prognostica. Astronomica minora. Somnium''. Commentary V. Bialas, H. Grössing. 1993. , Paperback . :Vol. 12: ''Theologica. Hexenprozeß. Tacitus-Übersetzung. Gedichte''. Commentary J. Hübner, H. Grössing, F. Boockmann, F. Seck. Directed by V. Bialas. 1990. , Paperback . * Vols. 13–18: Letters: ::Vol. 13: ''Briefe 1590–1599''. Ed. M. Caspar. 1945. 432 p. . ::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. . ::Vol. 16: ''Briefe 1607–1611''. Ed. M. Caspar. 1954. . ::Vol. 17: ''Briefe 1612–1620''. Ed. M. Caspar. 1955. . ::Vol. 18: ''Briefe 1620–1630''. Ed. M. Caspar. 1959. . :Vol. 19: ''Dokumente zu Leben und Werk''. Commentary M. List. 1975. . :Vols. 20–21: manuscripts ::Vol. 20,1: ''Manuscripta astronomica (I). Apologia, De motu Terrae, Hipparchus etc.'' Commentary V. Bialas. 1988. . Paperback . ::Vol. 20,2: ''Manuscripta astronomica (II). Commentaria in Theoriam Martis''. Commentary V. Bialas. 1998. Paperback . ::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

* Theoretical physics *
Cavalieri's principle In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: * 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that pl ...
*
History of astronomy Astronomy is the oldest of the natural sciences, dating back to antiquity, with its origins in the religious, mythological, cosmological, calendrical, and astrological beliefs and practices of prehistory: vestiges of these are still found in ...
* History of physics ** Kepler orbit ** Kepler triangle * Kepler–Bouwkamp constant * Penrose tiling * Radiation pressure


Notes


References


Citations


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. * 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 Clarisse Doris Hellman Pepper (August 28, 1910 – March 28, 1973) was an American historian of science, "one of the first professional historians of science in the United States". She specialized in 16th and 17th century astronomy, wrote a bo ...
; with a new introduction and references by Owen Gingerich; bibliographic citations by Owen Gingerich and Alain Segonds. New York: Dover, 1993. * 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. * De Gandt, Francois. ''Force and Geometry in Newton's'' Principia, Translated by Curtis Wilson, Princeton University Press, 1995. * Dreyer, J. L. E. ''A History of Astronomy from Thales to Kepler''. Dover Publications Inc, 1967. * Ferguson, Kitty. ''The nobleman and his housedog: Tycho Brahe and Johannes Kepler: the strange partnership that revolutionized science.'' London: Review, 2002. – published in the US as: ''Tycho & Kepler: the unlikely partnership that forever changed our understanding of the heavens.'' New York: Walker, 2002. * Field, J. V. ''Kepler's geometrical cosmology''. University of Chicago Press, 1988. * Gilder, Joshua and Anne-Lee Gilder: ''Heavenly Intrigue: Johannes Kepler, Tycho Brahe, and the Murder Behind One of History's Greatest Scientific Discoveries'', Doubleday (18 May 2004). Review
bookpage.com
* Gingerich, Owen. ''The Eye of Heaven: Ptolemy, Copernicus, Kepler''. American Institute of Physics, 1993. (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, foreword by O. Gingerich, Cambridge University Press 1993. * Kepler, Johannes and Christian Frisch. ''Joannis Kepleri Astronomi Opera Omnia'' (''John Kepler, Astronomer; Complete Works''), 8 vols.(1858–1871).
vol. 1, 1858vol. 2, 1859vol. 3, 1860vol. 6, 1866vol. 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 ''Harmonice'' Book 5) * Koestler, Arthur. ''
The Sleepwalkers Sleepwalker(s) or The Sleepwalker(s) may refer to: * Sleepwalking or somnambulism, a sleep disorder Film and television Films * ''The Sleepwalker'' (1922 film), an American silent film directed by Edward LeSaint * ''The Sleepwalker'' (1942 film ...
: A History of Man's Changing Vision of the Universe.'' (1959). * Koyré, Alexandre: ''Galilean Studies'' Harvester Press, 1977. * Koyré, Alexandre: ''The Astronomical Revolution: Copernicus-Kepler-Borelli'' Ithaca, NY: Cornell University Press, 1973. ; Methuen, 1973. ; Hermann, 1973. * Kuhn, Thomas S. ''The Copernican Revolution: Planetary Astronomy in the Development of Western Thought''. Cambridge, MA: Harvard University Press, 1957. * 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 Al-Tamimi. "Great collapse Kepler's first law", ''Natural Science'', 2 (2010), * North, John. ''The Fontana History of Astronomy and Cosmology,'' Fontana Press, 1994. * Pannekoek, Anton: ''A History of Astronomy'', Dover Publications Inc 1989. * 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). * 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. * Stephenson, Bruce. ''Kepler's physical astronomy''. New York: Springer, 1987. (Studies in the history of mathematics and physical sciences; 13); reprinted Princeton:Princeton Univ. Pr., 1994. * Stephenson, Bruce. ''The Music of the Heavens: Kepler's Harmonic Astronomy'', Princeton University Press, 1994. * 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. * Westfall, Richard S. ''The Construction of Modern Science: Mechanism and Mechanics''. John Wiley and Sons, 1971. ; reprinted Cambridge University Press, 1978. * Westfall, Richard S. ''Never at Rest: A Biography of Isaac Newton''. Cambridge University Press, 1981. * Wolf, A. ''A History of Science, Technology and Philosophy in the 16th and 17th centuries''. George Allen & Unwin, 1950.


External links


Kepler's Conversation with the Starry Messenger (English translation of ''Dissertation cum Nuncio Sidereo'')


* * * (1920 book, part of ''Men of Science'' series) * * Plant, David

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