## Introduction

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Johannes Kepler 1571–1630
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German astronomer, essayist, and nonfiction writer.

Kepler is regarded as a towering figure of the scientific renaissance and a seminal catalyst in bridging the medieval cosmology and the modern world-view. Building on the heliocentric theory of the Polish astronomer Nicolaus Copernicus, Kepler established the three laws of planetary motion and corrected the central fault of Copemican astronomy, which had wrongly determined the orbital paths of the planets to be circular. Kepler described a universe in which planets spinning on their axis rotate around the sun in elliptical orbits and provided the mathematical equations to verify his premise. The new astronomy replaced the earth-centered Ptolemaic system that had prevailed since the second century. Utilizing the skillful observations of the Danish astronomer Tycho Brahe, Kepler was the first to demand irrefutable mathematical proof to validate his scientific theories. He is also considered the father of modern optics for first correctly describing both the physics and physiology of vision. He further utilized his optical knowledge in making important contributions to the design of the refracting telescope. His extensive work in mathematics led to the development of infinitesimal calculus. A deeply religious man, Kepler viewed the universe as the perfect creation of God, the prime mover and perfect geometrician. It was up to the scientist to unravel the natural laws of providential design. But Kepler's insistence that all theories must be confirmed by precise, verifiable data made him a seminal figure in the development of empiricism and the scientific method. His groundbreaking theories and rigorous methodologies laid the path for Newtonian physics and the laws of universal gravity, which clearly marked the arrival of the modern era.

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Biographical Information
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Kepler was born at Weil der Stadt, Swabia in south-west Germany on December 27, 1571. His father, Heinrich, was a ne'er-do-well mercenary who often left his family for long periods before permanently abandoning them during Kepler's teen-age years. His mother Katharina was a meddlesome, disagreeable woman who was charged with being a witch in her later years. Kepler's childhood was unhappy and marked by recurring sickness, and it was apparent early on that he was ill suited for manual labor. His keen intelligence was noted, however, and he was the fortuitous beneficiary

of a practice of the dukes of Württemberg that provided educational scholarships for intellectually gifted but impoverished students. Kepler attended several elementary and secondary schools where part of his early schooling stressed learning a very formal and ornate Latin writing style that would be reflected in Kepler's later writings. He attended the Protestant University of Tübingen on scholarship, graduating in 1587. He continued his studies there and received his master's degree in 1591. Intending to enter the Lutheran ministry, Kepler pursed a curriculum in the arts. While at Tübingen he studied astronomy with Michael Maestlin who introduced him to both the Ptolemaic and Copernican systems. They began a friendship that would be of lasting importance throughout Kepler's life. Upon graduation Kepler began theological studies. But shortly before completing his course, Lutheran officials decided that Kepler's religious heterodoxy and refusal to sign the Formula of Concord made him an unsuitable candidate for the clergy. They recommended instead that he take a mathematics teaching post at a Protestant school at Graz in Austria. It was while giving a lecture one day that Kepler experienced a brilliant insight that explained the architectural order of the solar system. Kepler based his vision on what he believed to be an integral relationship between the six known planets and the five regular solids of Pythagorean mathematics. Kepler published his theory in the *Mysterium Cosmographicum* (1596; *Mystery of the Universe*) when he was twenty-six and sent copies of his work to both Tycho Brahe and Galileo. Even though he rejected the thesis of Kepler's work, Tycho immediately recognized Kepler's brilliance and was especially impressed by his mathematical skills. When religious turmoil forced Kepler to leave Graz in 1600, he traveled to Prague to meet with Tycho who had just been appointed as the Imperial Mathematician by Emperor Rudolph II. Tycho had been working on his own theory of the universe which was a hybrid of the Ptolemaic and Copernican systems; the sun revolved around the Earth while all the other planets revolved around then sun. He invited Kepler to join him in his work in his observatory and to work particularly on determining the orbit of Mars. Expecting to be considered more as a colleague, the relationship was a bit strained when Tycho treated Kepler as a subordinate. The alliance had also been tested by the revelation of some old correspondence between Kepler and Nicolaus Raymarus Ursus who had also once served as Imperial Mathematician. Their exchanges had begun in 1595 with a letter Kepler sent to Ursus praising him for his work. Tycho and Ursus were nemeses and rivals, the former having accused the latter of plagiarism. Brahe assigned Kepler the uncomfortable task of writing a major defense of his work against Ursus in which Kepler had to explain away his early correspondence as the fawning of a novice. Kepler and Tycho worked together, if a bit tenuously, for ten months before Tycho's unexpected death in 1601. Within two months Rudolph II named Kepler to the position of Imperial Mathematician. Besides formal scientific work Kepler's duties included providing astrological forecasts for the royal family. Kepler assumed numerous posts during his lifetime and the moves were generally precipitated by his having to leave an area due to reoccurring religious turmoil. A man of great faith, Kepler was nonetheless very tolerant of dissident views and his heterodoxy often placed him in disfavor with the authorities. The peaks and valleys that marked Kepler's professional life touched his personal life as well. In 1597 he married Barbara von Müller, a prosperous heiress, who at age twenty-three had already been widowed twice. Though Kepler had initially been much in love with her, it soon became an unhappy marriage as Kepler found his wife to be undereducated and ill mannered, unable to comprehend or appreciate the importance of his work. Still the marriage endured for fourteen years until her death in 1611. Together they had five children of whom only two survived. She did not leave a will and Kepler was left virtually penniless. In 1612 Rudolph II was deposed and Kepler lost his post as Imperial Mathematician while increasing religious strife made it impossible for Lutherans to remain in Prague. Kepler moved to Linz and took the assignment of district mathematician. In 1613 Kepler wed Susanna Reutlinger, age twenty-four, who had been an orphan. It proved to be a much happier marriage and together they had seven children, but once again only two survived childhood. Beginning in 1615 Kepler's mother, still living in Württemberg, had become the subject of rumors involving sorcery. Kepler, living in Linz, became aware in 1617 of the seriousness of his mother's plight and became actively involved in her defense. Although formally charged as a witch in 1621, she was eventually freed but died within several months of her release. Kepler's efforts on her behalf were partly motivated by filial duty and partly by self-defense. If his mother had been convicted both his mathematics career and personal safety would be imperiled. Still Kepler suffered more religious persecution during the Counter-Reformation and was forced once again to relinquish a job and leave his home. Beginning in 1628 Kepler spent the last years of his life studying and publishing at Zagao in Silesia under the patronage of Albrecht von Wallenstein, a duke and prosperous soldier of fortune. While traveling to Austria to collect a debt Kepler became ill and succumbed to fever at age fifty-nine at Regensburg, Germany on November 15, 1630.

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Major Works
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Kepler published The *Mysterium Cosmographicum* when he was twenty-six and the work reveals both the mystical and empirical elements in Kepler's intellectual orientation. Kepler posited that the five polyhedral shapes of Pythagorean mathematics were essential elements in the design of the universe. In Kepler's Platonic vision, each of the five shapes fit nearly into the spaces between the orbits of the six known planets. Neptune, Uranus, and Pluto had yet to be discovered. While the first part of the book reveals Kepler's mystical orientation in suggesting that the geometrical perfection of the universe is the manifestation of a divinely inspired plan, the second half reflects Kepler's commitment to empiricism. He simply states that if observable and verifiable data cannot prove his theory, the thesis must be jettisoned. *Astronomiae Pars Optica* (1604; *The Optical Part of Astronomy*) contains Kepler's theories on how vision occurs through the process of refraction within the eye, discusses the development of glasses for both near sightedness and far sightedness, and explains how both eyes work together for depth perception. In the treatise Kepler also examines why the sun appears to vary in size at different times and discusses the creation of images using the pinhole camera. *Astronomia Nova* (1609; *The New Astronomy*) is Kepler's most important work and contains his first two laws on planetary motion. Tycho's observational data on Mars played a seminal role in Kepler's calculations. Copernican cosmology was a highly complicated system that resembled clockwork architecture with complex orbits and epicycles that were not precise or provable. This work established Kepler's first two laws of planetary motion. The first law states that all planets travel on an elliptical orbit that has the sun as one point of its focus. The sun is off-center in the ellipse and a planet's distance from the sun varies according to where the planet is during its rotation. The second law postulates that the line connecting the sun and a planet will sweep through equal area in equal time regardless of where the planet is in its orbit. At the points when the planet is closer to the sun it travels faster; conversely, when a planet is farther from the sun the speed of its rotation is slower. But the area transversed in any period by a planet remains the same regardless of the speed at which the planet is traveling. *Somnium Seu Astronomia* (1634; *A Dream of the Moon*), Kepler's early experiment in writing science fiction, is the tale of an imaginary voyage to the moon. Although the story began circulating in manuscript form shortly after its completion in 1609, it was not published until after Kepler's death. In *Dioptrice* (1611) Kepler discussed the refraction of the lens in human eyesight leading to the concept of the inverted telescope indispensable to astronomical observation. The *Harmonice Mundi* (1619; *Harmony of the World)* actually had its genesis as early as 1599 as Kepler sought to reconcile the natural harmony of the universe with the objectivity of scientific proof. This work contains Kepler's third law, which describes the relationship between planetary movements and their distances from the sun. His third law states that the cube of the average distance of each individual planet from the sun is proportional to the square of the time required for the planet to complete one full orbit. The treatise also contains elaborate musical equations and scales correlated with Pythagorean theory and to suggest the natural order, symmetry, and harmony of the universe. As a Platonist, Kepler sought to correlate musical forms with heavenly bodies as part of God's design for a flawless universe. In *Epitome Astronomiae Copernicanae* (1621; *The Epitomy of Copernican Astronomy*) Kepler established the true orbits of all the planets as well the satellites of Jupiter. In the *Tabulae Rudolphinae* (1629; *Rudolphine Tables*), Kepler's last major work, he expanded on Tycho's observation and established in a comprehensive catalog of known celestial bodies the positions of the planets and of over 1000 stars. Besides major treatises Kepler's work also includes over 800 existing astrology forecasts done for himself, as part of his duties as Imperial Mathematician, and for wealthy patrons when financial need required him to do so.

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Critical Reception
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Kepler's scientific contemporaries immediately regarded his work as serious and important contributions to astronomy and cosmology, yet his writings were not widely disseminated for forty or fifty years after his death. But by the time Isaac Newton was building on Kepler's work, however, Kepler's theories were becoming increasingly known even in the popular culture. Critics have suggested that Kepler's highly formal Latin writing style made his work difficult to read in its original. He also had a habit of interjecting into his work all of his self-doubts suggesting where he may be in error—a practice that led to a very digressive writing style that many readers found tedious. Kepler explained that these frequent sidebars were merely intended to provide guidance to future students and readers of his work, something he wished his scientific predecessors would have done. While newer data and observations have supplanted some of Kepler's theories and calculations, the bulk of his work remains accurate and applicable to modern physics, astronomy, optics, and mathematics. Much recent Kepler criticism focuses on the unique blend of mysticism and empiricism that is the hallmark of Kepler's vision.