Johannes Kepler

• 1. The Boy Who Watched the Sky

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  At age six, Johannes Kepler was taken by his mother to a high place to look at the Great Comet of 1577. Three years later, in 1580, he was called outdoors to watch a lunar eclipse, and he remembered that the Moon appeared quite red. These two scenes, recorded in his own words, opened a life that would never stop staring upward. Yet the same childhood that gave Kepler the sky nearly took his sight. Smallpox left him with weak vision and crippled hands, limiting the very observational astronomy he loved.

  Kepler was born on the 27th of December 1571, in the Free Imperial City of Weil der Stadt. He grew into a German polymath who worked as an astronomer, mathematician, astrologer, natural philosopher and music theorist. He became a key figure in the 17th-century Scientific Revolution. How does a sickly child of a declining family end up advising emperors and reshaping how humanity understands the heavens? Why would a man devoted to God spend decades fitting curves to the path of Mars? And how did the same person who wrote laws of planetary motion also defend his own mother against a charge of witchcraft? The answers run through war, faith, grief, and a stubborn refusal to accept an orbit that was eight arcminutes off.

• 2. Faith Against Authority

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  Kepler was denied ordination in the Lutheran church because of beliefs contrary to the Formula of Concord, the statement of faith adopted in 1577. The man who wanted to be a minister was instead pushed toward a classroom in Graz. His religious convictions never left his science. Kepler believed God had created the world according to an intelligible plan, one accessible through the natural light of reason. He wrote that God wanted humans to recognize the laws of nature, having created us after his own image so that we could share in his own thoughts.

  The Counter-Reformation made his faith a danger. In September 1598, Ferdinand II ordered all Protestant preachers and teachers to leave Graz. Kepler was exempted at first, but on the 17th of July 1600 a new decree forced everyone to renounce the Protestant faith or leave the province. This time there was no exception, and Kepler left for Prague with his wife and step-daughter on the 30th of September 1600.

  In Linz, the pastor Daniel Hitzler refused Kepler communion over his unwillingness to fully endorse the Formula of Concord. The dispute centered on the doctrine of ubiquity, the belief in the real presence of Christ's body and blood in the Eucharist, which Kepler could not accept. In 1619 his excommunication was finally and unequivocally declared. Through all of it Kepler argued for tolerance, writing that Christ the Lord was neither Lutheran, nor Calvinist, nor Papist. That plea for unity would echo in his political advice during the worst war of his century.

• 3. Tycho's Data, Kepler's Orbit

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  On the 4th of February 1600, Kepler met Tycho Brahe at Benatky nad Jizerou, 35 km from Prague, where Tycho's new observatory was being built. Tycho guarded his observations closely, but he was impressed by Kepler's theoretical ideas and slowly granted more access. Two days after Tycho's unexpected death on the 24th of October 1601, Kepler was appointed his successor as imperial mathematician, charged with completing the unfinished work. The next 11 years would be the most productive of his life.

  The orbit of Mars became Kepler's great battle. He built a model that agreed with Tycho's observations to within two arcminutes, the average measurement error, yet at certain points it differed by up to eight arcminutes. He refused to accept that gap. After roughly 40 failed attempts, in late 1604 he hit upon the idea of an ellipse, a solution he had assumed was too simple for earlier astronomers to have overlooked.

  Finding that an elliptical orbit fit the Mars data, Kepler concluded that all planets move in ellipses, with the Sun at one focus. This became his first law of planetary motion. Earlier, by late 1602, he had reformulated another relationship into geometry: planets sweep out equal areas in equal times, his second law. Both appeared in Astronomia Nova, the manuscript he finished by the end of 1604. It would not be published until 1609, held up by legal disputes over Tycho's observations, which were the property of his heirs.

• 4. Harmony of the Spheres

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  Kepler claimed an epiphany on the 19th of July 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac. He came to believe the five Platonic solids could be nested inside one another to explain the spacing of the six known planets: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. He published this vision in Mysterium Cosmographicum in 1596 and never abandoned it, issuing an expanded second edition in 1621.

  Kepler was convinced that geometrical things had provided the Creator with the model for decorating the whole world. In Harmonice Mundi, published in 1619, he tried to explain the proportions of nature through music, drawing on the musica universalis, the music of the spheres studied by Pythagoras and Ptolemy before him. Soon after publishing it, Kepler was drawn into a priority dispute with Robert Fludd, who had released his own harmonic theory.

  Buried in that work was the third law of planetary motion. After trying many combinations, Kepler found that the square of the periodic times are to each other as the cubes of the mean distances. He gives the date of this discovery as the 8th of March 1618, but offers no details on how he reached it. The wider significance of this law for planetary dynamics was not realized until the 1660s, when it helped others connect gravity to the inverse square of distance.

• 5. The Optics of Sight

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  Through most of 1603, Kepler paused his other work to focus on optical theory, and on the 1st of January 1604 he presented the resulting manuscript to the emperor. Published as Astronomiae Pars Optica, it described the inverse-square law governing the intensity of light, reflection by mirrors, and the principles of pinhole cameras. Today it is generally recognized as the foundation of modern optics, though the law of refraction is conspicuously absent.

  Kepler turned the same study toward the human eye. Neuroscientists generally credit him as the first to recognize that images are projected inverted and reversed by the eye's lens onto the retina. The correction of that upside-down image did not much interest him, though he suggested it was fixed in the hollows of the brain through the activity of the Soul.

  In the first months of 1610, Galileo Galilei used his new telescope to discover four satellites orbiting Jupiter and sought Kepler's opinion. Kepler replied enthusiastically and endorsed the observations. Later that year, borrowing a telescope from Duke Ernest of Cologne, Kepler completed his own investigation of lenses, published as Dioptrice in 1611. In it he described an improved instrument, now known as the Keplerian telescope, in which two convex lenses produce higher magnification than Galileo's mix of convex and concave lenses.

• 6. A Mother on Trial

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  In December 1615, Kepler received a letter from his family informing him that his mother Katharina had been accused of witchcraft. Katharina Guldenmann, an innkeeper's daughter, was a healer and herbalist who lived in the Protestant town of Leonberg. The initial accusation came from Ursula Reinbold, who claimed Katharina had given her a drink that made her ill. As the case spread, more rumours circulated, and the family raised an action for slander against the accusers.

  Kepler vowed to defend his mother, sending despatches to the authorities in Leonberg and travelling there in person. The case dragged on for years, with Katharina held in prison from 1620-1621. The final stage was held in Tubingen, where it was determined she should be questioned under the threat of torture. She refused to confess, saying she trusted God to bring the truth to light. She was absolved and discharged, released on the 4th of October 1621, and died about six months later.

  A distorted version of Kepler's own writing may have helped instigate the trial. Around 1611 he had circulated a manuscript later published as Somnium, a fantastic trip to the Moon in which the narrator's mother consults a demon to learn the means of space travel. Sometimes described as the first work of science fiction, it earned Kepler the label father of science fiction. After his mother's acquittal, he composed 223 footnotes to the story, several times longer than the text itself, explaining its allegory and its science.

• 7. Tables Amid the Flames

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  Kepler's primary obligation as imperial mathematician was to provide astrological advice to Emperor Rudolf II. Though he took a dim view of astrologers who claimed to predict specific events, he had been casting horoscopes since his student days in Tubingen, eventually producing more than 800 nativities. He spent enormous effort trying to put astrology on a firmer philosophical footing, even as the subject would later drift away from professional astronomy entirely.

  War shadowed his greatest project. The Thirty Years' War began in 1618 with the Bohemian Revolt against Habsburg rule. In July 1620 the Bavarian army entered Linz, and in November the Bohemian forces were defeated at the Battle of White Mountain. Kepler's central charge, the Rudolphine Tables, was meant to replace the older Prutenic Tables. He completed the work in 1623, but disputes with Tycho Brahe's heirs and the emperor's publishing demands delayed printing.

  The city of Linz was besieged from June to August 1626 during the Peasant War. Kepler survived, but his house and printing works on the outskirts of the city were destroyed by fire. With permission from the emperor, he moved to Ulm, where his manuscript had escaped damage, and the Rudolphine Tables were finally completed in September 1627. The tables would soon face their first great test: a transit of Mercury across the face of the Sun, predicted by Kepler and observed by Pierre Gassendi in 1631.

• 8. The Last Journey

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  Wallenstein, recently granted the Dukedom of Sagan in Silesia, invited Kepler to take up residence there, and Kepler arrived on the 20th of July 1628. He felt isolated in the North German city with its unfamiliar dialect. He wrote to his friend Matthias Bernegger in March 1629 that it was loneliness which made him oppressed, far from the large cities, with letters coming and going only slowly and at great expense.

  Still owed considerable sums by the Imperial treasury, Kepler set out for Regensburg on the 8th of October 1630, hoping to collect at least some of it. A few days after arriving he became sick and steadily worsened. Kepler died on the 15th of November 1630, just over a month after reaching the city. He was buried in a Protestant churchyard in Regensburg, which was later completely destroyed during the war.

  Kepler's laws were not immediately accepted. Galileo and Rene Descartes completely ignored Astronomia Nova, and many astronomers objected to his introduction of physics into the heavens. Yet in Principia Mathematica in 1687, Isaac Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation. The problem of recovering those laws from gravity later became known, fittingly, as solving the Kepler problem.