Summary

Johannes Kepler (German: Johannes Kepler, 27 December 1571 - 15 November 1630), formerly known by his Hellenized name Johannes Kepler, was a German astronomer and a catalyst in the scientific revolution of modern times. He was also a mathematician and writer, and occasionally practiced astrology for a living. He is best known as the "Lawgiver of the Sky" from the pheronomic laws concerning the motion of the planets around the Sun described in his Astronomia nova, Harmonices Mundi and Epitome of Copernican. These works form the foundation of Newton's theory of the force of attraction.

During his career, Kepler was a mathematics teacher at a secondary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. He later became an assistant to the astronomer Tycho Brahe and eventually became a mathematician to Emperor Rudolf II and his successors, Matthias and Ferdinand II. He was also a professor of mathematics at Linz, Austria, and an advisor to General Wallenstein. In addition, his work was fundamental in the field of optics since he invented an improved version of a refracting telescope (Kepler's telescope) and cited the telescopic inventions of his contemporary Galileo.

Kepler lived at a time when there was no clear separation between astronomy and astrology, but there was a separation between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler incorporated religious and syllogistic arguments into his work, motivated by the religious belief that God created the world according to a plan 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 "complement to Aristotle of Heaven", transforming the ancient tradition of cosmology by treating astronomy as part of universal mathematical physics.

The first years

Kepler was born on 27 December (feast day of St John the Evangelist) 1571, in the free imperial city of Weil der Stadt in Baden-Württemberg, today 30 km west of Stuttgart. His grandfather, Sebald Kepler, had served as mayor there, but by the time Johannes was born his family had declined. His father Heinrich Kepler was a mercenary soldier and left them when Kepler was five years old. It is believed that he was killed in a war in the Netherlands. His mother, Katharina Guldenmann, the daughter of an innkeeper, practised herbal medicine and was later accused of witchcraft. Born prematurely, Kepler appears to have been a sickly child, although he impressed travellers at his grandfather's inn with his mathematical skills.

He was interested in celestial bodies from a very young age, having observed the comet of 1577 when he was 5 years old, writing later that "his mother took him to a high place to see it". At the age of 9 he watched the lunar eclipse of 1580 and recorded that the moon "looked quite red". But because he contracted smallpox while still a child, which left him with impaired vision, he turned mainly to theoretical and mathematical astronomy instead of observational astronomy.

In 1589, after finishing school, Kepler began studying theology at the University of Tübingen, where he studied philosophy under Vitus Muller and theology under Jacob Heerbrand (a student of Philip Melanchthon in Wittenberg). He became an outstanding mathematician and gained a reputation as a skilled astrologer. He was taught by Michael Maestlin (1550-1631) both the Ptolemaic and heliocentric systems, and from then on embraced the latter, defending it both theoretically and theologically in student debates. Despite his desire to become a chaplain, at the end of his studies he was offered a position as a teacher of mathematics and astronomy at the Protestant School in Graz, Austria. He accepted the post in April 1594, at the age of 23.

Graz (1594-1600)

Kepler's first important astronomical work was Mysterium Cosmographicum, "The Mystery of the Cosmos" (the Universe), which was the first published defence of Copernicus' system. Kepler claimed to have had a revelation on 19 July 1595 during his teaching at Graz, proving the periodic combination of Saturn and Jupiter in the zodiac. He realized that regular polygons are inscribed in a circumscribed circle of definite proportions, which he considered might be the geometric basis of the universe. After failing to find a unique arrangement of polygons that matched known astronomical observations, Kepler began to perform experiments on polygons in three dimensions. He discovered that each of the five Platonic solids could be uniquely inscribed and circumscribed by spheres; placing the solids each in spheres, inside each other so as to produce six layers, corresponding to the six known planets: Mercury, Venus, Venus, Earth, Mars, Jupiter and Saturn. By arranging the solids correctly - octahedron, icosahedron, dodecahedron, tetrahedron, cube - Kepler discovered that the spheres can be spaced at intervals corresponding (within the limits of the precision of available astronomical observations) to the relative sizes of the orbits of each planet, assuming the cycle of the planets around the Sun. Kepler also discovered a formula relating the size of the orbit of each planet to the length of its orbital period: from the interior to the exterior of the planet, the ratio of the increase in orbital period is twice the difference in radius. However, Kepler later rejected this formula because it was not precise enough.

As mentioned above, Kepler believed that he had discovered God's geometric design for the universe. Much of Kepler's enthusiasm for Copernicus' system came from his theological beliefs about the connection between body and spirit; the universe itself was an image of God with the Sun corresponding to the Father, the astral sphere to the Son, and the space in between to the Holy Spirit. The first manuscript from the Mysterium contained an extensive chapter reconciling the concept of heliocentrism with biblical passages referring to the geocentric.

With the support of his mentor Michael Maestlin, Kepler obtained permission from the University of Tybingen to publish his manuscript in anticipation of the removal of the explanation of the Bible and the addition of a simpler, more understandable description of Copernicus' system and Kepler's new ideas. Mysterium was published late in 1596, and Kepler received copies of it and began sending them to noted astronomers and patrons in 1597. It was not widely known but it cemented Kepler's reputation as a skilled scientist. His loyalty to the patrons as well as to those who controlled his position at Graz secured him a place in the patronage system.

Although the details will have to be seen in the light of his last work, Kepler never abandoned the Platonic polyhedral-spherical cosmology to which Mysterium Cosmographicum referred. His later astronomical works dealt in some way with further developments on this, which involved finding greater precision in the inner and outer dimensions than the spheres by calculating the eccentricities of the planetary orbits. In 1621 Kepler published an extended second edition of Mysterium, half the length of the first, which contained footnotes, details and explanations that he had achieved in the 25 years since the first publication of the book.

As far as the impact of Mysterium is concerned, it can be seen as an important first step in the modernization of Copernicus' theory. There is no doubt that Copernicus in De Revolutionibus sought to promote a heliocentric system, but this book resorted to Ptolemaic devices (such as epicycles and eccentric circles) in order to explain the change in the orbital velocity of the planets. In addition, Copernicus continued to use the center of the Earth's orbit as a reference point, not that of the Sun as he states, "as an aid to calculations and so that the reader would not be confused by the large deviation from Ptolemy." Therefore, although Mysterium Cosmographicum''s thesis was wrong, modern astronomy owes much to this work "since it is the first step in cleansing Copernicus' system of the remnants of the Ptolemaic theory and those who remain attached to it."

Marriage with Barbara Mueller

In December 1595, Kepler was introduced to Barbara Müller, a twice-widowed 23-year-old woman with a young daughter, Gemma van Dvijneveldt. In addition to being the heir to the estates of her previous husbands, Müller was the daughter of a successful flour mill owner. Her father, Jobst, had initially opposed their marriage despite Kepler's noble lineage. Although he had inherited his grandfather's noble lineage, Kepler's poverty was an inhibiting factor. Eventually Jobst relented when Kepler completed his book Mysterium Cosmographicum, but the engagement was called off when Kepler was arranging for publication. Nevertheless, church officials - who had been helpful throughout this period - pressed the Mullers to honour their agreement. Mueller and Kepler were married on 27 April 1597.

In the early years of their marriage, Kepler had two children (Heinrich and Susanna), who died in infancy. In 1602 they had a daughter (Susanna), in 1604 a son (Friedrich) and in 1607 another son (Ludwig).

Further research

After the publication of Mysterium, and with the support of the Graz school inspectors, Kepler embarked on an ambitious project to expand and elaborate his work. He planned four books, one on the fixed aspects of the Universe (the Sun and the eclipsing stars), one on the planets and their motions, one on the physical state of the planets and the formation of their physical features (he focused on the Earth), and finally one on the effects of the sky on the Earth, so as to include atmospheric optics, meteorology and astrology.

He also sought the opinions of several astronomers to whom he had sent the Mysterium, among them Reimarus Ursus (Nicolaus Reimers Bär), who was the royal mathematician of Rudolph II and a rival of Tycho Brahe. Ursus did not immediately reply, but sent Kepler a flattering letter to continue his priority on what we now call Tycho Brahe's system. Tycho began a harsh but legitimate critique of Kepler's system, as he began using inaccurate data derived from Copernicus' system, thus causing much tension. Through the letters, Tycho and Kepler discussed a wide range of astronomical problems, including lunar phenomena and Copernicus' theory (especially its theological viability). But without the important data from Tycho's observatory, Kepler was unable to address many of these problems.

Instead, he turned his attention to chronology and "harmony", the numerological relationships between music, mathematics and the physical world, as well as their astrological implications. On the assumption that the Earth possesses a soul (a property he would later invoke to explain how the Sun causes the movement of the planets), he established a speculative system linking astrological aspects and astronomical distances to weather and other earthly phenomena. In 1599, however, he began to feel that his work was limited by the inaccuracy of the available data; as well as that growing religious tension threatened his continued employment at Graz. In December of that year, Tycho invited Kepler to visit him in Prague. On 1 January 1600 (before he even accepted the invitation), Kepler pinned his hopes on Tycho being able to provide answers to his philosophical problems as well as his socio-economic ones.

The collaboration with Tycho Brahe

On 4 February 1600, Kepler met Tycho Brahe and his assistants Franz Tengnagel and Longomontanus at Benátky nad Jizerou (35 km from Prague) where Tycho's observatory had been set up. During the next two months he stayed there as a guest, analysing some of Tycho's observations of Mars; Tycho kept the details of the observations secret but, impressed by Kepler's theoretical ideas, allowed him to study them. Kepler planned to confirm his theory in Mysterium Cosmographicum based on the Mars data, but estimated that the project could take more than two years (since he was not allowed to use the results of the observations for his own personal use). With the help of Johannes Jessenius, Kepler tried to negotiate a more formal collaboration with Tycho Brahe, but the negotiations fell through after a nasty argument and Kepler left for Prague on 6 April. Kepler and Tycho eventually reconciled and were able to agree on salary and survival arrangements, so in June, Kepler returned home to move in with his family.

Graz's religious and political difficulties eliminated his hopes of returning to Brahe. Hoping to continue his astronomical studies, Kepler sought appointment as a mathematician to Archduke Ferdinand II. For this reason, 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 on Earth that causes the Moon to move). Although this essay did not win him a place alongside Ferdinand, he did detail a new method for measuring lunar eclipses, which he used during the July 10 eclipse at Graz. These observations formed the basis of his explorations of the laws of optics that will culminate in Astronomiae Pars Optica.

On August 2, 1600, after refusing to convert to Catholicism, Kepler and his family were exiled from Graz. Several months later, they all returned together to Prague. During 1601, he was openly supported by Tycho, who commissioned him to analyze planetary observations as well as to write a text against Tycho's rival, Ursus (who had died in the meantime). In September Tycho secured his participation in a council as a collaborator, for the new project he had proposed to the emperor: the Rodolfian paintings were to replace Erasmus Reinhold's paintings. Two days after Brahe's sudden death on 24 October 1601, Kepler was appointed his successor as imperial mathematician with the responsibility of completing his unfinished work. The next 11 years as imperial mathematician would be the most productive of his life.

Advisor to the Emperor Rudolph II

As an imperial mathematician, Kepler's main job was to provide astrological advice to the emperor. Although Kepler had a dim view of predicting the future or certain events, he had created detailed horoscopes from friends, family and officials during his studies at Tybingen. In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler's advice in times of political trouble (it is speculated that Kepler's recommendations were based mostly on common sense and less on the stars). Rudolph II had a keen interest in the work of many scholars (including numerous alchemists) and so he also followed Kepler's work in astronomy.

Officially, the only accepted denominations 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 him with a generous income for his family, but the difficulties of the over-loaded imperial treasury meant that getting hold of money sufficient to meet his financial obligations was a perpetually difficult task. Due mainly to his financial problems, his life with Barbara was unpleasant and worsened by arguments and the onset of illness. In his professional life, however, Kepler came into contact with other prominent scientists (Johannes Matthäus Wackher von Wackhenfels, Jost Bürgi, David Fabricius, Martin Bachazek, and Johannes Brengger among others) and thus his astronomical work progressed rapidly.

Astronomiae Pars Optica

Continuing to analyse the results of Tycho's observations of Mars - now available in their entirety - he began the time-consuming process of formulating the Rodolphean tables. Kepler also undertook the investigation of the laws of optics from his 1600 lunar essay. Both lunar and solar eclipses exhibited inexplicable phenomena such as unpredictable shadow sizes, the red color in the lunar eclipse, and unusual light around a total solar eclipse. Related issues of atmospheric refraction apply to all astronomical observations. In 1603, Kepler stopped all his other work to concentrate on optical theory. The manuscript, presented to the emperor on 1 January 1604, was published under the name Astronomiae Pars Optica (The Optical Part of Astronomy). In it, Kepler describes the law of optics concerning the intensity of light being inversely proportional to distance, reflection from flat and convex mirrors, and the principles of the pinhole camera, as well as the astronomical implications of optics, such as parallax, and the apparent sizes of celestial bodies. He also expanded on the study of optics in the human eye, and is considered by neuroscientists to have been the first to recognize that images are projected inverted and upside down from the lens of the eye onto the retina. The solution to this dilemma was of little concern to Kepler, since he did not associate it with optics, although he later suggested that the image was improved in the "cavities of the brain" due to the "activity of the soul". Today Astronomiae Pars Optica is recognized as the foundation of modern optics (although the law of refraction is surprisingly absent). As far as the origins of projective geometry are concerned, Kepler introduced the idea of continuous change of mathematical entity in this work. He argued that if a focus of a conic section was allowed to move along the line joining the foci, the geometric form would transform or degenerate into another. In this way, an ellipse becomes a parabola when one focus moves to infinity, and when the two foci merge into one, a circle is formed. As the foci of a hyperbola merge into one, the hyperbola becomes a pair of straight lines. Also, when a straight line extends to infinity, it will meet its origin at a point at infinity, thus having the properties of a great circle. This idea was used by Pascal, Leibniz, Monge, Poncelet as well as others, and became known as geometric continuity as well as the Law or Principle of Continuity.

The supernova of 1604

In October 1604 a bright new star appeared in the sky, but Kepler did not believe the rumours until he saw it himself. Kepler began systematically observing the newcomer. Astrologically, the end of 1603 marked the beginning of a triangle of fire, the start of an 800-year cycle of grand conjunctions. Astrologers associated the two analogous preceding periods with the rise of Charlemagne (some 800 years earlier) and the birth of Christ (some 1600 years earlier) and therefore anticipated events that would be omens, especially for the emperor. As an imperial mathematician and astrologer, Kepler described the new star two years later in De Stella Nova. In it, Kepler discusses the astronomical properties of the star, taking a skeptical approach to the many astrological interpretations that were circulating. He noted the fading in its brightness, speculated about its origin, and used the lack of observed variation to argue that it was located in the sphere of fixed stars, thus undermining the idea of the uncompleteness of the heavens (the idea was Aristotle's and he argued that the celestial spheres were perfect and unchanging). The birth of a new star meant the mutability of the heavens. In an appendix, Kepler discusses the recent dating work of the Polish historian Laurentius Suslyga. He calculated that if Suslyga was correct in accepting timelines that pointed back four years, then the star of Bethlehem - analogous to the present star - would have coincided with the first great conjunction of the earlier 800-year cycle.

Astronomia nova The extensive line of research that resulted in Astronomia nova - including the first two laws of planetary motion - began with the analysis of the orbit of Mars, under the direction of Tycho. Kepler calculated several times the various approximations of Mars' orbit using an equant (a mathematical tool that Copernicus had eliminated with his system), eventually producing a model that agreed with Tycho's observations within the first two minutes of a degree (the mean measurement error). However, he was not satisfied since there appeared to be deviations from the measurements of up to eight minutes of a degree. Kepler was trying to fit an oval orbit to the data, since the wide range of traditional mathematical astronomical methods had failed.

According to his religious view of the universe, the Sun was the source of the driving force in the solar system (a symbol of God the Father). As a physical basis, Kepler came by analogy to William Gilbert's theory of the magnetic soul of the Earth from De Magnete (1600) and for his work on optics. Kepler hypothesized that the motive force radiating from the sun weakens with distance, causing it to move faster or slower as the planets move closer or farther away from it. Perhaps this hypothesis implies a mathematical relationship that could restore astronomical order. Based on measurements on the perihelion and perihelion of Earth and Mars, he created a formula in which the orbital speed of a planet is inversely proportional to its distance from the Sun. Verifying this relationship over the entire orbital cycle, however, requires very extensive calculation. To simplify this task, by late 1602 Kepler reformulated the ratio in terms of geometry: planets travel equal areas in equal times-Kepler's second law of planetary motion.

He then proceeded to calculate the total orbit of Mars, using the geometric law and assuming an oval orbit. After about 40 unsuccessful attempts, in early 1605 he used the idea of an ellipse, which he considered too simple a solution to have been omitted by previous astronomers. Finding that the elliptical orbit of Mars fit the data, he immediately concluded that all planets move in elliptical orbits, with the sun at one focus - Kepler's first law of planetary motion. Because he did not employ assistants for his work, he did not extend his mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for the Astronomia nova, but it was not published until 1609 because of legal disputes concerning the use of Tycho's observations by his heirs.

In the years after Astronomia nova, Kepler's research focused on preparations for the Rodolfian tables and a complete set of ephemerides (specific predictions of a planet and the position of stars) based on a table (although it should have been completed many years ago). He also attempted (unsuccessfully) to initiate a collaboration with the Italian astronomer Giovanni Antonio Magini. In his other work he was concerned with chronology, and in particular the dating of events in the life of Jesus, and with astrology, especially criticism of dramatic predictions of doom such as those of Helisaeus Roeslin.

Kepler and Roeslin engaged in a series of published attacks and counter-attacks, while physicist Philip Feselius published a paper which was rejected by astrology as a whole (and Roeslin's work in particular). In response to this, Kepler saw the excesses of astrology on the one hand and the overzealousness of the rejection of one in the other. Thus Kepler prepared his work Interveniens Tertius. Nominally this work-presenting the joint patronage of Roeslin and Feselius-was a neutral mediation between the contending scholars, but also Kepler's general views on the merits of astrology, including some hypothetical mechanisms of interaction between the planets.

In the early months of 1610, Galileo, with his new telescope, discovered the four satellites orbiting Jupiter. After being dubbed the Starry Messenger, Galileo consulted Kepler in order to strengthen the reliability of his observations. Kepler was enthusiastic and responded with a published short reply, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger). Kepler endorsed Galileo's observations and offered him a number of speculations on the meaning and implications of his discoveries as well as 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, thus further providing his support for Galileo. To Kepler's disappointment, however, Galileo did not publish his reactions (if any) to Astronomia Nova.

After being informed of Galileo's discoveries with his telescope, Kepler began a theoretical and experimental investigation of optical telescopes, using Duke Ernest's telescope in Cologne. His manuscript was completed in September 1610 and published as Dioptrice in 1611. In it, Kepler defined the theoretical basis of both double convex converging lenses and double concave diverging lenses-and how they combine to produce a telescope similar to Galileo's-as well as the concepts of real versus virtual images, upright versus inverted images, and the effects of focal length for magnification and reduction. He also described an improved telescope-known today as the Kepler astronomical telescope-in which two convex lenses can produce greater magnification than Galileo's combination of convex and concave lenses.

Around 1611, Kepler published a manuscript that would eventually be published (after his death) as Somnium (The Dream). Part of the purpose of Somnium was to describe how astronomy would be practiced from the perspective of another planet, so as to show the feasibility of a non-geocentric system. The manuscript, which disappeared after changing hands several times, described a fictional trip to the moon, was an allegorical part, an autobiography on the one hand, and part of it dealt with interplanetary travel (it can be described as the first work of science fiction). After many years, a twisted version of his story may have instigated a lawsuit against his mother who was accused of practicing witchcraft, as the narrator's mother consults a demon to learn the means of space travel. After her eventual acquittal, Kepler completed 223 footnotes to the story-many times more than the text itself-that explained the allegorical aspects as well as the important scientific content (particularly regarding lunar geography) hidden within the text.

That year, as a New Year's gift, he composed for a friend and patron, Baron Wackher von Wackhenfels, a small pamphlet entitled Strena Seu de Nive Sexangula. In it, he published the first description of the hexagonal symmetry of snowflakes and, extending the discussion to a hypothetical atomistic physical basis for the symmetry, put forward what later became known as Kepler's conjecture, a statement of the most efficient arrangement involving the packing of spheres. Kepler was one of the pioneers of mathematical applications of infinitesimals (see law of continuity).

In 1611, the growing political-religious tension in Prague reached its peak. Emperor Rodolphe II-who was experiencing health problems-was forced to abdicate as King of Bohemia by his brother Matthias. Both sides sought Kepler's astrological advice, an opportunity he used to provide conciliatory political advice (with little reference to the stars, except in his general statements to discourage drastic measures). However, it was clear that the prospects for Kepler's future at Matthias's court were dim.

Also during the same year, Barbara Kepler developed a fever, and then began to have convulsions. When Barbara recovered, three of his children became ill with smallpox, and Friedrich, age 6, died. After his son's death, Kepler sent letters to potential patrons in Württemberg and Padua. At the University of Tybingen in Württemberg, concerns about Calvinist heresies in violation of the Augusta Confession and the Concord formula prevented his return. The University of Padua, on the recommendation of the outgoing Galileo, sought Kepler to fill the vacancy in the chair of mathematics, but Kepler preferred to keep his family on German soil rather than travel to Austria to arrange a position of teacher and mathematician at Linz. However, Barbara relapsed and died shortly after Kepler's return.

Kepler postponed his move to Leeds and remained in Prague until the death of Rudolph II in early 1612, and due to political unrest, religious tension and family tragedy (along with the legal dispute over his wife's estate), Kepler could not engage in any research. Instead, he would piece together a manuscript that is a chronology, Eclogae Chronicae, from his correspondence and earlier work. After the succession of the Holy Roman Empire, Matthias reaffirmed Kepler's position (and his salary) as imperial mathematician, and at the same time allowed him to move to Leeds.

In Leeds and elsewhere (1612 - 1630)

In Leeds Kepler's main responsibilities (apart from completing the Rudolphina Tables project) were to teach in the district school and to provide astrological and astronomical services. In his early years there he enjoyed financial security and religious freedom compared to his life in Prague, although the Lutheran Church had excluded him from the Eucharist because of his theological scruples. His first publication in Leeds was De vero Anno (1613), an extended treatise on the year of Christ's birth. He also took part in studies on the introduction of Pope Gregory III's reformed calendar in the Protestant German lands. In that year he also wrote the very important mathematical treatise Nova stereometria doliorum vinariorum on the measurement of the volume of containers such as wine barrels, published in 1615.

Second Wedding

On 30 October 1613 Kepler married 24-year-old Susanna Reuttinger. After the death of his first wife Barbara, Kepler had considered 11 different candidates. He finally settled on Reuttinger (the fifth girl) who, he wrote, "won me over with her love, humble devotion, economy in the household, diligence and the love she gave to her foster children." The first three children of this marriage (Marguerite Regina, Katharina and Sepald) died in infancy. Three more survived to adulthood: Cordula (b. 1621), Friedmar (b. 1623) and Hildeburt (b. 1625). According to Kepler's biographers, this marriage was much happier than his first.

Compendium of Copernican Astronomy, diaries and his mother's trial for witchcraft

Since completing Astronomia nova, Kepler had intended to compose a textbook on astronomy. In 1615 he completed the first of three volumes of Epitome Astronomiae Copernicanae (Compendium of Copernican Astronomy). The first volume (books 1-3) was printed in 1617, the second (book 4) in 1620 and the third (books 5-7) in 1621. Despite the title simply referring to heliocentrism, Kepler's textbook culminated in his own system based on ellipsis (the oval scheme). The compendium became Kepler's most influential work. It contained all three laws of planetary motion and attempted to explain celestial motions through natural causes. Although he clearly extended the first two laws of planetary motion (applied to Mars in Astronomia nova) to all planets as well as to the Moon and Jupiter's Medici satellites, he did not explain how elliptical orbits could be derived from observational data.

As an offshoot of the Rudolphine Tables and their associated newspapers (Ephemerides), Kepler published astrological calendars, which were very popular and helped offset the production costs of his other works, especially when support from the Imperial Treasury was withdrawn. In his calendars, six between 1617 and 1624, Kepler predicted the positions of the planets, the weather and political events. The latter were usually slyly accurate thanks to his keen understanding of contemporary political and theological tensions. By 1624, however, the escalation of these tensions and the ambiguity of the prophecies meant political trouble for him. His last diary was publicly burned at Graz.

In 1615, Ursula Reingold, a woman who was in a financial dispute with Kepler's brother Christophe, claimed that Kepler's mother, Katharina, had made her sick with an evil potion. The dispute came to a head and in 1617 Katarina was accused of witchcraft. Witchcraft trials were relatively common in Central Europe at the time. First in August 1620 she was imprisoned for 14 months. She was released in October 1621 thanks in part to an extensive legal defense designed by Kepler. Prosecutors had no strong evidence beyond rumors and a doctored second-hand version of Kepler's Somnium, in which a woman mixes magical potions and enlists the help of a demon. Katarina was subjected to territio verbalis, a graphic description of the torture that awaited her as a witch, in a final attempt to get her to confess. During the trial, Kepler put off his other work to concentrate on the "harmonic theory". The result, published in 1619, was Harmonices Mundi (the harmony of the world).

The Harmonices Mundi

Kepler was convinced that geometric things gave the Creator the model to decorate the whole world. In Harmony he attempted to explain the proportions of the physical world, especially the astronomical and astrological aspects, in terms of music. The central group of harmonies was the musica universalis or music of the spheres, which had been studied by Pythagoras, Ptolemy and many others before Kepler. Soon after the publication of Harmonices Mundi Kepler became involved in a priority dispute with Robert Fludd, who had recently published his own harmonic theory. Kepler began by exploring regular polygons and regular solids, including the shapes that would become known as Kepler's solids. From there he extended his harmonic analysis to music, meteorology and astrology. Harmony was derived from the tones emitted by the souls of celestial bodies and, in the case of astrology, from the distinction between these tones and human souls. In the last part of his work (Book 5), Kepler dealt with the motions of the planets, especially the relationships between orbital velocity and the distance of the orbit from the sun. Similar relations had been used by other astronomers, but Kepler, with Tycho's data and his own astronomical theories, worked them out with much more precision and gave them new physical meaning.

Among many other harmonies, Kepler expressed what became known as the third law of planetary motion. He then tried many combinations until he discovered that (roughly) "the square of periodic times are as close to each other as the cubes of mean distances". Although he gives the date of this epiphany, (8 March 1618), he does not give details of how he came to this conclusion. However, the broader significance of this purely kinetic law for the dynamics of the planets was not understood until the 1660s. For when combined with Christian Huyghens' recently discovered law of centrifugal force, it helped Isaac Newton, Edmund Halley, and perhaps Christopher Wren and Robert Hook to show independently that the supposed gravitational attraction between the sun and its planets decreased with the square of the distance between them. This demolished the traditional assumption of scholastic physicists that the force of gravitational attraction remained constant with distance whenever it was applied between two bodies, as Kepler and Galileo assumed in his false universal law that the fall of gravity accelerates uniformly, as did Galileo's student Borelli in his 1666 celestial mechanics. William Gilbert, after experimenting with magnets, decided that the center of the Earth was a huge magnet. His theory led Kepler to think that a magnetic force from the sun was driving the planets into orbit. It was an interesting explanation for planetary motion, but it was wrong. Before scientists could find the right answer, they had to learn more about motion.

The Rosicrucian Tables and his last years

In 1623 Kepler finally completed the Rodolfi Paintings, which at the time was considered his most important work. However, due to the Emperor's demands for publication and negotiations with his heir Tycho Brahe, it was not printed until 1627. Meanwhile, religious tensions - the root of the ongoing Thirty Years' War - once again put Kepler and his family in danger. In 1625 agents of the Catholic Counter-Reformation sealed most of Kepler's library, and in 1626 the city of Leeds was besieged. Kepler moved to Ulm, where he arranged for the printing of the paintings at his own expense. In 1628, following the military successes of Emperor Ferdinand under the command of General Wallenstein, Kepler became an official advisor to the latter. Although he was not himself the court astrologer to the general, Kepler made astronomical calculations for Wallenstein's astrologers and occasionally wrote horoscopes himself. He spent much of his last years travelling 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 5 November 1630 and was buried there. His grave was lost after the Swedish army destroyed the churchyard. Only his poetic epitaph, which he wrote himself, has survived in time "I have measured the heavens, now I count the shadows. The mind had the sky as its limit, the body the earth, where it rests."

Acceptance of his astronomy

Kepler's laws were immediately accepted. Several important figures such as Galileo and René Descartes were completely unaware of Kepler's Astronomia nova. Many astronomers, including his teacher Michael Maestlin, were opposed to the introduction of physics into his astronomy. Some adopted compromise positions. Ismael Boulliau accepted elliptical orbits but replaced the region of Kepler's law with a uniform motion with respect to the empty focus of the ellipse, while Seth Ward used an elliptical orbit with motions defined by an equant. Several astronomers have tested Kepler's theory and its various modifications through astronomical observations. Two passes of Venus and Mercury across the sun provided sensitive evidence for the theory under conditions where these planets could not normally be observed. In the case of the 1631 transit of Mercury, Kepler was extremely uncertain about the parameters and advised observers to look for the transit the day before and after the predicted date. Pierre Gassenti observed the transit on the predicted date, a confirmation of Kepler's prediction. This was the first observation of a Mercury transit. However, his attempt to observe the transit of Venus only a month later was unsuccessful due to inaccuracies in the Rodolfian Tables. Gassenti did not realize that it was not visible from most of Europe including Paris. Jeremiah Horrocks who in 1639 observed the passage of Venus, had used his own observations to adjust the parameters of the Keplerian model, predicted the passage and then constructed equipment to observe it. He remained a staunch defender of the Keplerian model. The Compendium of Copernican Astronomy was read by astronomers throughout Europe and after Kepler's death was the main vehicle for the dissemination of his ideas. Between 1630 and 1650, it was the most widely used textbook, winning many converts to astronomy based on ellipsis. Yet few adopted his ideas about the physical basis of celestial motions. In the late 17th century many physical astronomical theories stemming from Kepler's work-most notably those of Giovanni Borelli and Robert Hook-began to incorporate attractive forces (though not the motivated pseudo-spiritual species that Kepler claimed) and the Cartesian conception of inertia. The culmination was Isaac Newton's Principia Mathematica (1687), in which Newton derived Kepler's laws of planetary motion from a theory based on the forces of universal gravitation.

Historical and cultural heritage

In addition to his role in the historical development of astronomy and natural philosophy, Kepler is important in the philosophy and historiography of science. Kepler and his laws of motion were central to the early history of astronomy, as in Jean Etienne Montucla's 1758 Histoire des mathematiques and Jean Baptiste Delambre's 1821 Histoire de l astronomie moderne. These and other histories written in the light of the Enlightenment treated Kepler's metaphysical and religious arguments with skepticism and disapproval, but later natural philosophers of the Romantic era considered these elements central to his success. William Hewell, in his influential 1837 History of the Inductive Sciences, regarded Kepler as the archetype of the inductive scientific genius. In his 1840 work The Philosophy of the Inductive Sciences, Huel saw in Kepler the embodiment of the most advanced forms of the scientific method. Similarly Ernst Freidrich Apelt - the first to study Kepler's manuscripts in detail after their purchase by Catherine the Great, saw Kepler as the key to the Revolution of Science. Apelt, who saw in Kepler's mathematics his aesthetic sensibility, his ideas about physics, and his theology as parts of a unified system of thought, produced the first extensive analysis of his life and work. Modern translations of many of Kepler's books appeared in the late 19th and early 20th centuries; systematic publication of his collected works began in 1937 (and is nearing completion in the early 21st century); and Max Caspar's biography of Kepler; was published in 1948. However, Alexandre Koyre's work on Kepler was, after Apelt's, the first major milestone in historical interpretations of Kepler's cosmology and its influence. In the 1930s and 1940s Koyre and many others of the first generation of professional historians of science described the scientific revolution as the central event in the history of science and Kepler as perhaps the central figure of the revolution. Koyre placed Kepler's theorizing, despite his empirical work, at the center of the intellectual transformation from ancient to modern worldviews. Since the 1960s the volume of the historian Kepler's scholarship has expanded greatly to include studies of his astrology and meteorology, his geometric methods, his interaction with the broader cultural and philosophical currents of the time, and even his role as a historian of science. The debate over Kepler's place in the Scientific Revolution provoked a variety of philosophical and popular reactions. One of the most important is Arthur Kessler's 1959 work The Sleepwalkers, in which Kepler is clearly the hero (morally, theologically and spiritually) of the revolution. Philosophers of science, such as Charles Sanders Perce, Norwo

Respect - Worship

Kepler is honored along with Nicholas Copernicus with a day of celebration in the liturgical calendar of the Episcopal Church (USA) on May 23.

Kepler was a Pythagorean in his scientific philosophy: he believed that the foundation of all of Nature is mathematical relations and that all of Creation is a single whole. This was in contrast to the Platonic and Aristotelian view that the Earth was fundamentally different from the rest of the Universe (the 'supra-monsterial' world) and that different physical laws applied to it. In his quest to discover universal physical laws, Kepler applied Earth physics to celestial bodies, from which his three laws of planetary motion were derived. Kepler was also convinced that celestial bodies influence terrestrial events. He thus correctly hypothesized that the Moon was related to the cause of tides.

The Laws of Kepler

Kepler inherited from Tychon a large amount of accurate observational data on the positions of the planets ('I confess that when Tychon died, I took advantage of the absence of the heirs and took the observations under my protection, or rather snatched them', he says in a letter in 1605). The difficulty was to interpret them with any reasonable theory. The movements of the other planets on the celestial sphere are observed from the perspective of the Earth, which in turn orbits the Sun. This causes a seemingly odd "orbit", sometimes called "retrograde motion". Kepler focused on the orbit of Mars, but first he needed to know the Earth's orbit accurately. In a stroke of genius, he used the line joining Mars and the Sun, knowing at least that Mars would be at the same point in its orbit at times separated by integer multiples of its (precisely known) orbital period. From this he calculated the positions of the Earth in its own orbit and from these the Martian orbit. He was able to derive his Laws without knowing the (absolute) distances of the planets from the Sun, since his geometric analysis needed only the ratios of their distances from the Sun. Unlike Tychon, Kepler remained faithful to the heliocentric system. Starting from this framework Kepler tried for 20 years to synthesize the data into some theory. Eventually he arrived at the following three "Kepler's Laws" of planetary motion, which are accepted today:

Applying these laws, Kepler was the first astronomer to successfully predict a 1631 transit of Venus. In turn, Kepler's Laws were advocates of the heliocentric system, since they were as simple as assuming that all planets orbit the Sun.

Many decades later, Kepler's Laws were extracted and explained in turn as consequences of Isaac Newton's laws of motion and the Law of Universal Attraction (gravity).

Research work in mathematics and physics

Kepler carried out pioneering research in the fields of combinatorics, geometric optimization and natural phenomena in nature, such as the shape of snowflakes. He was also one of the founders of modern optics, defining e.g. antiprisms and inventing the Keplerian telescope (in his works Astronomiae Pars Optica and Dioptrice). Because he was the first to identify non-curved regular geometric solids (such as asteroidal dodecahedra), these are called "Kepler's solids" in his honour. Kepler was also in contact with Wilhelm Schickard, inventor of the first automatic computer, whose letters to Kepler describe how the mechanism was used to calculate astronomical tables.

In Kepler's time, astronomy and astrology were not separated as they are today. Kepler despised astrologers who satisfied the appetites of ordinary people without knowledge of general and abstract rules, but he saw the writing of astrological forecasts as the only possible way to support his family, especially after the start of the terrible and highly destructive for his country "Thirty Years' War". However, historian John North notes the influence of astrology on his scientific thinking as follows: "if he had not also been an astrologer, he probably would not have produced his astronomical work on the planets in the form we have it today." However, Kepler's views on astrology were radically different from those of his time. He advocated an astrological system based on his "harmonics", i.e. the angles formed between the heavenly bodies and what came to be called "the music of the spheres". Information about these theories can be found in his work Harmonice Mundi. His attempt to put astrology on a firmer footing led to his De Fundamentis Astrologiae Certioribus ('On the more secure foundations of astrology') (1601). In 'The Intermediate Third', a 'warning to theologians, physicians and philosophers' (1610), placing himself as a 'third man' between the two extreme positions 'for' and 'against' Astrology, Kepler advocated the possibility of finding a definite relationship between celestial phenomena and terrestrial events.

Around 800 horoscopes and natal charts compiled by Kepler survive today, including his own and those of his family members. As part of his duties at Graz, Kepler issued a forecast for the year 1595 in which he predicted a peasant uprising, Turkish invasion and severe cold, all of which successfully gave him fame. As an imperial mathematician he explained to Rudolph II the horoscopes of the Emperor Augustus and the Prophet Muhammad, and gave an astrological opinion on the outcome of a war between the Gallic Republic of Venice and Paul V.

In Kepler's thinking as a Pythagorean, it could not be a coincidence that the number of perfect polyhedra was one less than the number of (then known) planets. As he supported the heliocentric system, he tried for years to prove that the distances of the planets from the Sun were given by the radii of spheres inscribed in perfect polyhedra, so that the sphere of one planet was also inscribed in the polyhedron of the planet's interior. The innermost orbit, of Mercury, represented the smallest sphere. In this way he wanted to identify the five Platonic solids with the five intervals between the six then known planets, and also with the five Aristotelian "elements", without ultimately succeeding.

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6. ^ "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."[68]
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