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Johannes Kepler: His Life, Times, and Discoveries

My writing interests are general, with expertise in science, history, biographies, and how-to topics. I have written over 70 books.

Portrait of Johannes Kepler, unknown artist c. 1620.

Portrait of Johannes Kepler, unknown artist c. 1620.

Who Was Johannes Kepler?

Johannes Kepler is most remembered for his discovery of the three laws of planetary motion. Born in what is now Germany during the Renaissance, Kepler became both an astronomer and astrologer. His work provided a transition from the ancient description of the heavens based on a geometrical model to the modern idea of a dynamical astronomy using the concept of force. He was one of the first to embrace the heliocentric model of the solar system originally proposed by Nicolaus Copernicus. In addition, Kepler did fundamental work in optics and made improvements to the refracting telescope.

Early Years

Johannes Kepler was born at Weil der Stadt, near what is now Stuttgart, Germany, on December 27, 1571. Johannes’ father, Heinrich, left home to fight as a mercenary solider in the Protestant uprising in Holland. He returned in 1576, but then again left to fight for the Belgium military. In 1588, he completely abandoned his wife and children. Kepler described his father as “vicious, inflexible, quarrelsome, and doomed to a bad end.” It is believed he died fighting as a mercenary solider in the Netherlands. As for his mother, Katharina, he said she was “thin, garrulous, and bad-tempered.” Late in her life, Katharina would be put on trial for being a witch. The trial and its collateral damage to the family was nearly the death of her and the undoing of her loving son, Johannes.

Johannes’ schooling started at the German Schreibschule in Leonberg, where the family moved to in 1576. From there he transferred to the Latin school, where he became proficient in the language. After attending the Adelberg monastery school and the preparatory academy at Maulbronn, he enrolled at the University of Tübingen in the fall of 1587. As a gifted young man, he won a scholarship from the duke of Württemberg. He passed the examination for the baccalaureate degree in 1588.

At the university he studied astronomy under Michael Maestlin, who believed in the heliocentric model of the solar system proposed by Nicholaus Copernicus in his1543 book De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres). Maestlin planted the seeds of the Copernican model with the Sun at the center of the solar system into Kepler’s fertile mind. Kepler performed well at the university, attaining the highest marks in all of his subjects. When it came time to renew his scholarship, the university’s senate noted that he had “such a superior and magnificent mind that something special may be expected of him.” In 1591, he received his master’s degree and then began his studies in theology, with plans for a career in the clergy.

After nearly completing his third and final year of study, an opportunity came his way that changed the direction of his life. A teacher of mathematics at the Lutheran school in Graz died, and the faculty at Tübingen recommended Kepler to fill the position. Though he was forfeiting his career with the church, this was an opportunity he couldn’t pass up. The 22-year-old Kepler arrived in Graz, a city in southern Austria, in April 1594. There he took up his post as a teacher and the provincial mathematician.

Teacher and Astrologer at Graz

The Protestant Reformation in the early 16th century had lasting consequences throughout central Europe. A fierce conflict was raging between the established Roman Catholic Church and the new Protestant religions, and like nearly everyone in that part of the world, Kepler was drawn into the upheaval. The Catholics had set up a school in the Protestant city of Graz, in what is now Austria. To ensure that the Protestant children of Graz wouldn’t be exposed to the Catholic doctrine, the Protestants set up a rival school. They wanted the best teachers for the school, and Kepler was an obvious choice for the facility.

With few students interested in mathematical astronomy, he was asked to teach a course in Vergil and rhetoric as well as arithmetic. As an aside to his teaching responsibilities, he issued calendars with his predictions on the weather and future events. When a peasant uprising and an invasion by the Turks came to pass, the fulfillment of his prognostications enhanced his reputation with the locals. He continued to issue the calendars for the next five years while at Graz.

In his world, the practical side of his knowledge of mathematics and astronomy was the ability to generate horoscopes. Though Kepler didn’t personally believe in the validity of astrology, the generation of horoscopes did provide additional funds to supplement his meager teaching salary. He referred to astrology as the foolish little daughter of astronomy, writing in 1601, “If astrologers sometimes tell the truth, it ought to be attributed to luck.” In addition to the generation of horoscopes supplementing his income, later it became a significant justification for his position as imperial mathematician.

"Mysterium Cosmographicum" (Cosmographic Mystery)

While at Graz, Kepler arrived at what he thought was the secret key to the universe. When he was not teaching or generating horoscopes, he pondered the mysteries of planetary motion. What came to him, he claimed by divine revelation, was a geometrical interpretation of the planets and their orbits. He wrote, “I believe this all the more because I have constantly prayed to God that I might succeed if what Copernicus had said was true.”

He published his works in Mysterium Cosmographicum (Cosmographic Mystery) in 1596. He based his arguments for the Copernican system on the ratios of regular polygons bound on inscribed one circumscribed circle at defined ratios; this he thought might be the geometrical basis of the orbit of the planets about the Sun. Kepler believed the three-dimensional orbits of the six known planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn—could be described by the five known regular polyhedranes.

There are five regular polyhedrons constructed by faces identical in shape and size; all angles are equal and all sides equal, with the same number of faces meeting at each vertex. The five regular polyhedrons, known as Platonic Solids, are the tetrahedron with four faces, cube with six faces, octahedron with eight faces, dodecahedron with 12 faces, and the icosahedron with 20 faces. Kepler described his model as following:

“The earth’s orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing this will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe with the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of the planets.”

Amazingly, his scheme worked with a fair degree of accuracy when space is allowed for the eccentricities of the planetary orbits. The importance of Kepler’s work in the Mysterium Cosmographicum rests not in its conclusion, which turned out to be a coincidence, but rather its importance is that it was the first Copernican treatise since De revolutionibus. Kepler’s work was strongly tied to his belief in God and his search for the divine hand at work as he explained in a letter to his former teacher Maestlin: “For a long time I was restless, now, however, behold how through my effort God is being celebrated in my astronomy.”

The five Platonic solids.

The five Platonic solids.

Spacing of the Planets

Kepler now tried to explain the regular spacing of the planets. He knew that the further a planet was from the Sun the longer its period of revolution was about the Sun. He reasoned that the long periods had to be due to a diminution of the Sun’s driving force. Kepler demonstrated a relationship between the planetary periods (P1, P2…) to intervals between the planets. After trial and error, he came up with a relationship for the ratios of the distances equivalent to (P1/P2)1/2. He later determined the correct relationship between the distance of the planets was (P1/P2)2/3.

To publish his findings, he submitted his work for review to the faculty of Tübingen University. With approval from the university, he would be clear to publish the Mysterium Cosmographicum. The senate of the university endorsed his work but required he clarify the section on the Copernican model of the solar system. The senate also recommended that he remove his “discussion of the Holy Writ in several thesis.” With the blessing of the university, Kepler had his book published early in 1597.

With his new book in hand, Kepler sent out copies to various scholars seeking their response. From the copy he sent to the Italian astronomer and scientist Galileo Galilei he received a response that he had so far only read the preface. Disheartened by the tepid response from Galileo, he replied, urging the Italian to “believe and step forth” with his endorsement.

From the Danish astronomer Tycho Brahe he received a much more detailed response, calling the nest of inscribed spheres and polyhedrons a clever speculation. Though Kepler’s small book was lacking in scientific rigor, it did thrust him into the first rank of astronomers. His interest in astronomy continued to grow as he was regularly observing lunar and solar eclipses. Though the Mysterium Cosmographicum was erroneous, it was the first publication since the time of Copernicus to embrace the sun-centered model of the solar system. By 1599, he had prepared an outline for a second work.

Illustration from "Mysterium Cosmographicum" showing Kepler’s model of the solar system.

Illustration from "Mysterium Cosmographicum" showing Kepler’s model of the solar system.

Marriage to Barbara Müller

In late 1595 Kepler was introduced to 23-year-old Barbara Müller, the daughter of a wealthy mill owner. According to the young Kepler, she had “set his heart on fire.” She was two years younger than he, had been widowed twice, and had a young daughter. After a lengthy courtship that was nearly scuttled by a seven-month absence when Kepler returned to Tübingen, the wedding took place on April 27, 1597. The initial happiness of the marriage soon faded; she was a simple woman and understood little of his work or aspirations. He later described her as “fat, confused, and simple minded.” When they moved to Prague, she became homesick for old life back in Graz.

Their marriage lasted until 1611 when she died unexpectedly of contagious fever that had been brought to Prague by Austrian troops. Though their marriage was not always a happy one, Kepler mourned her deeply. Out of their marriage came five children, only three of whom lived until adulthood. Though Barbara had family money and inheritance from her two previous husbands, the value was tied up in estates, so it was difficult to transfer the assets when the Lutheran Kepler left Catholic Graz and moved to Prague.

Tycho Brahe

In 1600, Kepler journeyed to Prague to meet the eminent Danish nobleman and astronomer Tycho Brahe. Sponsored by King Frederick II of Denmark, Brahe had built the finest observatory of its time on the island of Hven. There, along with several assistants, he made thousands of very accurate observations of the stars and the planets. However, Brahe fell out of favor with the new Danish king and was exiled. He traveled to Prague and became the official astronomer under Rudolph II, and it was in Prague that Brahe and Kepler met. The two men were very much opposites, Brahe a verbose nobleman and Kepler the pious mathematician, but they made their relationship work for the sake of their science.

When Kepler began to work with Brahe in 1600, it quickly became apparent to him that the quality of Brahe’s astronomical observations were the best available. By the spring of 1601, using Brahe’s observations he calculated the longitudes of Mars with an accuracy that far exceeded the calculations of his predecessors. Brahe was very secretive about his observations and only allowed Kepler to see a limited number of them. The situation changed rapidly in the fall of 1601 when Brahe died unexpectedly. Though Kepler had only worked with Brahe for ten months, Emperor Rudolph appointed Kepler to Tycho’s post as imperial mathematician and astronomer, with a reduced salary, which was often in arrears.

Engraving from Brahe's book "Astronomiae instauratae mechanica", 1598.

Engraving from Brahe's book "Astronomiae instauratae mechanica", 1598.

Improvement on the Calculation for the Orbit of Mars

After the death of Tycho, Kepler continued to work with the Mars observations and developed a quantitative relationship that allowed him to determine the orbit of the planet with an improved degree of accuracy. He was searching for a physically acceptable model that worked accurately to determine both the longitude and latitude of the planet in the sky at any given time. His best effort to date gave an error of eight arc minutes. For comparison, the size of a full moon is 30 arc minutes.

Kepler realized that his predictions were less accurate than Tycho’s observations and set out to refine his method of prediction. He revived his earlier speculation about a planetary driving force, analogous to the attractive force of a magnet to iron, that apparently emanated from the Sun. Kepler had read the works of the English physician and scientist William Gilbert, who had completed an extensive study of magnetism. Gilbert published his research and observations on magnetism in De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet Earth) in 1600.

Through his experimentation, Gilbert concluded that the Earth was a giant magnet and that is why compass needles point toward the north magnetic pole. Kepler speculated that some force, maybe magnetism, was causing the planets to remain in orbit about the Sun. It wasn’t until nearly a century later that Sir Isaac Newton published his explanation of the laws of gravity.

In the process of his analysis, Kepler discovered that a radius vector from the Sun to the planet swept out equal areas in equal times. Today this fact is known as Kepler’s second law of planetary motion; however, nowhere in his great book on Mars is this explicitly stated. Next, he discovered that the orbit of Mars was not circular, although he was not sure exactly what the correct shape of the orbit was. In 1605 he had a breakthrough and realized that an elliptical orbit would satisfy the observations. This allowed him a geometrical way to reconcile the ellipse with his magnetic hypothesis of attraction. Today we call his conclusion of elliptical orbits Kepler’s first law of planetary orbits, where the Sun is at one of the two foci of the ellipse. In 1609, he published his results in Astronomia nova (New Astronomy).

Diagram of an elliptical planetary orbit.

Diagram of an elliptical planetary orbit.

The Italian Astronomer Galileo Galilei

When Galileo completed a short book entitled Sidereus nuncius (Starry Messenger) in 1610, he sent a copy to Kepler and asked for his opinion. The work of the Italian astronomer contained more than seventy drawings and diagrams of the Moon, certain constellations such as Orion and Taurus, the Pleiades star cluster, and the planet Jupiter with its four brightest moons. In the text, Galileo included descriptions and theories to justify his observations. Kepler, now the imperial mathematician, responded quickly to Galileo with a long letter of approval.

That same year, as he revived Galileo’s Sidereus, Kepler published Dissertatio cum Nuncio sidereo (Conversation with the Sidereal Messenger), in which he accepted Galileo’s observations with enthusiasm. In this work he also wrote of the history of the telescope, his own work in optics, and his earlier speculation on the idea of the regular solids and the possibility of inhabitants on the Moon. Later, in the second of the only three known letters that Galileo wrote to Kepler, he thanked Kepler for his endorsement, writing: “I thank you because you were the first one, and practically the only one, to have complete faith in my assertions.”

One of Galileo’s drawings of the Moon, c. 1610.

One of Galileo’s drawings of the Moon, c. 1610.

Kepler’s Telescopic Observations of Jupiter

In the late summer of 1610, Kepler was able to satisfy his desire to look through a telescope himself when Elector Ernest of Cologne lent one to him. For the next two weeks he observed Jupiter and published his results in Narratio de Jovis satellitibus (Narration about Four Satellites of Jupiter observed) in 1611. In the tract, Kepler gave support for Galileo’s observations of Jupiter’s moons, which were in doubt by many. This work and the Dissertatio cum Nuncio sidereo were soon reprinted in Florence, Italy, which did much to validate Galileo’s observations and conclusions.

Linz

In 1611, Kepler’s world began to unravel. The conflict of the Thirty Years’ War reached Prague, forcing Emperor Rudolph to abdicate; his children were stricken with smallpox; and his favorite son and his wife died. After the death of Rudolph in early 1612, Kepler was free to leave Prague and move to Linz, a city in upper Austria, about 150 miles to the south. There he and his children spent the next 14 years. During the first few years in Linz, his scientific research fell off; it was not until 1615 that he began to publish again.

His stay in Linz started off poorly when the local Lutheran pastor excluded him from communion because he had refused to sign a document of Lutheran faith known as the Formula of Concord. Kepler, a deeply religious man, didn’t take the rebuff lightly and made several appeals to church officials, all in vain. When the Counter-reformation swept into Linz in 1625, he was given an exception and was not vanished; however, his library was temporarily sealed, and his children were forced to attend Catholic services.

All was not despair in Linz, however, as he found a second wife, a 24-year-old orphan named Susanna Ruettinger. Though his second wife was considered beneath him socially by his family and friends, the marriage was successful. Out of their union came seven children, five of whom died at childbirth or in their infancy. Similarly, only two of the five children from his first marriage survived into adulthood.

"Harmonice Mundi" (The Harmony of the World)

Kepler’s book Harmonice Mundi (The Harmony of the World), which was published in 1619, was one of his most important works, as it contained the elements of his third law of planetary motion. In 1599, he drafted a plan for this work on the harmonies of the world in a letter to Michael Maestlin. In the letter he detailed the mathematical data and proofs he intended to use for his upcoming text.

It would take him two decades to finish this work due to personal and professional demands on his time. By the summer of 1618, he was putting the final touches on the manuscript and had sent it to the printer. In Harmonice, Kepler developed his theory of harmony in four areas: geometry, music, astrology, and astronomy. Harmonice was divided into five books, each covering a different topic:

Book I – Examines the geometry of polygons and discusses their constructability.

Book II – Investigates the properties of both polygons and polyhedrons. He was the first to introduce the great and small stellated dodecahedrons.

Book III - Expounds on the notion that the principles of the universe are based on geometry rather than on musical harmony. The concept of the "music of the spheres" incorporates the metaphysical principle that mathematical relationships express qualities or "tones" of energy which manifest in numbers and sounds and goes back to the ancient Greek philosopher Pythagoras.

Book IV – This book covers Kepler’s astrological views, which he had previously written about in his works De Stella Nova in Pede Serpentarii (On the New Star in the Foot of the Serpent Handler) and Tertius interveniens (Third-Party Intervention).

Book V – Introduces his third law of planetary motion: the ratio that exists between the period of revolution about the Sun of any two planets is precisely the ratio of the 3/2 power of the mean distances. Though he does not bother to show how accurate the relationship was, he does provide his thoughts in the introduction to book V on his discovery:

“Now, since the dawn eight months ago, since the broad daylight three months ago, and since a few days ago, when the full sun illuminated my wonderful speculations, nothing holds me back. I yield freely to the sacred frenzy; I dare frankly to confess that I have stolen the golden vessels of the Egyptians to build a tabernacle for my God far from the bounds of Egypt. If you pardon me, I shall rejoice; if you reproach me, I shall endure. The die is cast, and I am writing the book—to be read either now or by posterity, it matters not. It can wait a century for a reader, as God himself has waited six thousand years for a witness.”

This would be Kepler’s final contribution to laws that govern the movement of the planets. His work would pave the way for Sir Isaac Newton’s theory of universal gravitation, which effects all the bodies in the physical universe.

The Witch Trial of Kepler’s Mother

While in Linz in 1620, Kepler he got word that his mother had been indicted on charges of being a witch. The charges were serious; if convicted she could be tortured and then burned at the stake. If his mother was convicted, he knew his status as imperial mathematician of the Holy Roman Empire and mathematician of Upper Austria could be threatened. Of his mother’s living children, he was the only one to come to her defense. He prepared a skillful defense of his mother at her trial in Leonberg, resulting in her being acquitted of the charge of witchcraft. The ordeal, which lasted about a year, placed a heavy toll on his mother and she died six months after winning her freedom.

Rudolphine Tables

One of the important tasks that had remained uncompleted since his time working for Brahe was the calculation of the Rudolphine Tables (Latin: Tabulae Rudolphinae), named after the late Rudolf II, emperor of the Holy Roman Empire. The Tables contained a star catalog and predicted planetary positions based on observational data collected by Brahe. Kepler had begun work on the Tables while he was in the employ of Brahe but had delayed work on them due to the sheer volume of calculations that had to be done by hand. Previously produced tables of planetary positions were full of errors, and new, more accurate tables were needed.

After many delays, the Tables were finally published in 1627. In the preface to the work, he mentioned the difficulties of obtaining his salary and of the wartime conditions and “the novelty of my discoveries and the unexpected transfer of the whole of astronomy from fictitious circles to natural causes, which were most profound to investigate, difficult to explain, and difficult to calculate, since mine was the first attempt.” The completed Rudolphine Tablets gave planetary positions with greater accuracy than had previously been accomplished; for example, the prediction for Mars previously erred up to 5˚, but Kepler’s table kept the error to within +/-10 arc minutes of the actual position.

The printed volume of the Rudolphine Tables contained 120 folio pages of text and 119 pages of tables. In addition to the planetary, solar, and lunar tables, it included Tycho Brahe’s catalog of 1,000 fixed stars, a chronological synopsis, and a list of geographical positions. In some of the copies there is a foldout map of the world, measuring 16” x 28”; the map was engraved in 1630 but was not distributed until many years later.

Map of the world from the Rudolphine Tables.

Map of the world from the Rudolphine Tables.

Last Years in Sagan

Before the Rudolphine Tables were complete, Kepler began to search for a new home. In 1627 he traveled to Prague to arrange for further employment. Ferdinand III had just been crowned the king of Bohemia and the imperial commander-in-chief Albrecht von Wallenstein was at the zenith of his power. The king welcomed Kepler and awarded him 4,000 guldens for the dedication of the tables; however, the money, which would be paid by Nuremberg and Ulm, required him to become a Catholic to remain in imperial service.

In Kepler’s new post, he would answer to general Wallenstein, a superstitious man who placed great importance on his horoscope. The general had just received the duchy of Sagan (in western Poland, in the historic region of Silesia) as a fief and wanted direct access to the astrologer Kepler. Wallenstein agreed to support Kepler and a printer in Sagan; Kepler, needing employment, accepted. In the summer of 1628, Kepler and his family reached Sagan. He was not partially happily there, complaining to a close friend in a letter, “I am a guest and stranger…almost completely unknown, and I barely understand the dialect so that I myself am considered a barbarian.”

Johannes Kepler: God’s Mathematician

The Dream

Once a printing press was secured, Kepler started printing a work that had its origin in his school days at Tübingen, his Somnium seu astronomia lunari or, simply, The Dream. The novel is the story of a 14-year-old Icelandic boy who is magically transported to the Moon and his observations of what Earth looks like from the vantage point of the Moon. Both the modern astronomer Dr. Carl Sagan and the popular writer Isaac Asimov have stated that The Dream was the first work of science fiction. Financial trouble, which was Kepler’s constant companion, would come his way once again and delay the publication of the novel.

In the summer of 1630, King Ferdinand III ousted Wallenstein from his position as commander-in-chief; thus Kepler’s financial security was in jeopardy. In the fall, the 58-year-old-astronomer traveled west to collect the interest due on two promissory notes he held in exchange for money he had deposited in Austria. On the way he stopped at Regensburg, possibly to consult with his friends at court about a new residence. There, he became sick with a high fever, his condition worsened, and he died on November 15, 1630. He was buried in a Protestant cemetery that was destroyed during the Thirty Years War.

Kepler’s son-in-law, Jacob Bartsch, became the protector of the bereaved and penniless family. He took over printing of Somnium, completing publication in 1634. He tried in vain to collect the 12,694 guldens owned to Kepler from the state treasury. Kepler composed his own epitaph: “I used to measure the heavens, now measure the shadows of the earth. Although my soul was from heaven, the shadow of my body lies here.”

Statue of Tycho Brahe and Johannes Kepler in Prague, Czech Republic.

Statue of Tycho Brahe and Johannes Kepler in Prague, Czech Republic.

References and Further Reading

Concise Dictionary of Scientific Biography, New York: Charles Scribner’s Sons, 1981.

Couper, Heather and Nigel Henbest. The History of Astronomy. Buffalo, New York: Firefly Books Ltd., 2007.

Gingerich, Owen. Dictionary of Scientific Biography, s.v. “Kepler, Johannes.” New York: Charles Scribner’s Sons, 1981.

Ferguson, Kitty. Tycho & Kepler: The Unlikely Partnership That Forever Changed Our Understanding of the Heavens. New York: Walker & Company, 2002.

The New Encyclopedia Britannica. 15th Edition. Chicago: Encyclopedia Britannia, Inc., 1994.

West, Doug. Nicholaus Copernicus: A Short Biography: The Astronomer Who Moved the Earth. Missouri: C&D Publications, 2018.

West, Doug. The Astronomer Tycho Brahe: A Short Biography. Missouri: C&D Publications, 2022.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2022 Doug West