Mysterium Cosmographicum

Kepler's first major astronomical work, Mysterium Cosmographicum (The Sacred Mystery of the Cosmos), was also the first published defense of the Copernican system. Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac; he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra. He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path, assuming the planets circle the Sun.


Closeup of inner section of the modelKepler 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. As he indicated in the title, Kepler thought he had revealed God’s geometrical plan for the universe. Much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son, and the intervening space between to the Holy Spirit. His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism. With the support of his mentor Michael Maestlin, Kepler received permission from the Tubingen 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 the men who controlled his position in Graz, also provided a crucial doorway into the patronage system.

Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherist cosmology of Mysterium Cosmographicum. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621 Kepler published an expanded second edition of Mysterium, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.

Marriage to Barbara Müller

In December 1595, Kepler was introduced to Barbara Müller, a 23-year-old widow (twice over) with a young daughter, and he began courting her. Müller, heir to the estates of her late husbands, was also the daughter of a successful mill owner; her father Jobst initially opposed a marriage despite Kepler's nobility. Jobst relented after Kepler completed work on Mysterium, but the engagement nearly fell apart while Kepler was away tending to the details of publication. However, church officials pressured the Müllers to honor their agreement; Barbara and Johannes were married on April 27, 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); in 1607, another son (Ludwig).

Other research in Graz

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 Bär)—the imperial mathematician to Rudolph II and a bitter rival of Tycho Brahe. Ursus did not reply directly, but republished Kepler's flattering letter to pursue his priority dispute over (what is now called) the Tychonic system with Tycho. Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler's system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus. Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory (particularly its theological viability). But without the significantly more accurate data of Tycho's observatory, Kepler had no way to address many of these issues.[12]

Instead, he turned his attention to chronology and "harmony," the numerological relationships among music, mathematics and the physical world, and their astrological consequences. By assuming the Earth to possess a soul (a property he would later invoke to explain how the sun causes the motion of planets), he established a speculative system connecting astrological aspects and astronomical distances to weather and other earthly phenomena. By 1599, however, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in Graz. In December of that year, Tycho invited Kepler to visit him in Prague; on January 1, 1600 (before he even received the invitation), Kepler set off in the hopes that Tycho's patronage could solve his philosophical problems as well as his social and financial ones

Johannes Kepler

[edit] Childhood and education (1571–1594)
Kepler was born on December 27, 1571 at the Imperial Free City of Weil der Stadt (now part of the Stuttgart Region in the German state of Baden-Württemberg, 30 km west of Stuttgart's center). His grandfather had been Lord Mayor of that town, but by the time Johannes was born, the Kepler family fortunes were in decline. His father 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 war in the Netherlands. His mother, an inn-keeper's daughter, was a healer and herbalist who was later tried for witchcraft. Born prematurely, Johannes claimed to have been a weak and sickly child. Despite his ill health, he was precociously brilliant. As a child, he often impressed travelers at his grandfather's inn with his phenomenal mathematical faculty.

He was introduced to astronomy/astrology at an early age, and he developed a love for it that would span his entire life. At age five, he observed the Comet of 1577, writing that he "was taken by [his] mother to a high place to look at it." At age nine, he observed another astronomical event, the Lunar eclipse of 1580, recording that he remembered being "called outdoors" to see it and that the moon "appeared quite red". However, childhood smallpox left him with weak vision, limiting him to the mathematical rather than observational aspects of astronomy.

In 1589, after moving through grammar school, Latin school, and lower and higher seminary in the Lutheran education system, Kepler began attending the University of Tübingen as a theology student, where he proved himself to be a superb mathematician and earned a reputation as a skillful astrologer. Under the instruction of Michael Maestlin, he learned both the Ptolemaic system and the Copernican system; he became a Copernican at that time, defending heliocentrism from both a theoretical and theological perspective in student debates. 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, Austria. He accepted the position in April 1594, at the age of 23.

Early career (1594–1601)
In Graz, Kepler began developing an original theory of cosmology based on the Copernican system, which was published in 1596 as Mysterium Cosmographicum—The Sacred Mystery of the Cosmos.

In April 1597, Kepler married Barbara Müller. She died in 1611 and was outlived by two of Johannes's children and one by an earlier marriage.

In December 1599, Tycho Brahe wrote to Kepler, inviting Kepler to assist him at Benátky nad Jizerou outside Prague. Pressured to leave Graz by increasingly strict Counter-Reformation policies restricting the religious practices and political rights of Protestants, Kepler joined Tycho in 1600. After Tycho's death in 1601, Kepler was appointed Imperial Mathematician in his place, a post he would retain through the reigns of three Habsburg Emperors (from November 1601 to 1630).

Imperial Mathematician in Prague (1601–1612)
As Imperial Mathematician, Kepler inherited Tycho's responsibility for the Emperor's horoscopes as well as the commission to produce the Rudolphine Tables. Working with Tycho's extensive collection of highly accurate observational data, Kepler also set out to refine his earlier theories but was forced to abandon them. Instead, he began developing the first astronomical system to use non-circular orbits; it was completed in 1606 and published in 1609 as Astronomia Nova—New Astronomy. Astronomia Nova contained what would become the first and second laws of planetary motion.

In October 1604, Kepler observed the supernova which was subsequently named Kepler's Star (a term which may also refer to the stellated octahedron). In 1611, Kepler published (as a letter to a friend) a monograph on the origins of snowflakes, the first known work on the subject. He correctly theorized that their hexagonal nature was due to cold, but did not ascertain a physical cause for this. In January 1612, the Emperor died. To escape the growing religious tension in Prague, Kepler took the post of Provincial Mathematician in Linz.

Teaching in Linz and final years (1612–1630)
In 1615, Kepler married Susanna Ruettinger, with whom he would have several children.

In 1617, Kepler's mother Katharina was accused of being a witch in Leonberg. Beginning in August 1620 she was imprisoned for fourteen months. Thanks in part to the extensive legal defense drawn up by Kepler, she was released in October 1621 after failed attempts to convict her. However, she was subjected to territio verbalis, a graphic description of the torture awaiting her as a witch, in a final attempt to make her confess. Throughout the trial, Kepler postponed his other work (on the Rudolphine Tables and a multi-volume astronomy textbook) to focus on his "harmonic theory". The result, published in 1619 as Harmonices Mundi ("Harmony of the Worlds") contained the third law of planetary motion.

Kepler completed the last of seven volumes of his textbook Epitome of Copernican Astronomy in 1621, which brought together and extended his previous work and would become very influential in the acceptance of the Copernican system over the next century. In 1627 he completed the Rudolphine Tables, which provided accurately calculated future positions of the planets and allowed the prediction of rare astronomical events.

On November 15, 1630 Kepler died of a fever in Regensburg. In 1632, only two years after his death, his grave was demolished by the Swedish army in the Thirty Years' War. Kepler had incidentally composed the epitaph for his own tombstone, which read:

I measured the skies, now the shadows I measure,
Sky-bound was the mind, earth-bound the body rests

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