Johannes Kepler

Johannes Kepler
File:Kepler.jpg
Born
December 27, 1571 Weil der Stadt, Stuttgart, Germany
Died
November 15, 1630 Regensburg, Bavaria, Germany

Johannes Kepler (December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German Lutheran mathematician, astrologer, and astronomer. He is best known for his laws of planetary motion, based on his Astronomia nova, Harmonice Mundi, and the textbook Epitome of Copernican Astronomy.

Through his career, Kepler was a mathematics teacher at a Graz seminary school (later the University of Graz), an assistant to Tycho Brahe, court mathematician to Emperor Rudolf II, mathematics teacher in Linz, and court astrologer to General Wallenstein. He also did fundamental work in the field of optics and helped legitimate the telescopic discoveries of his contemporary, Galileo Galilei.

Kepler lived in an era when there was no clear distinction between astronomy and astrology, while there was a strong division between astronomy/astrology (a branch of mathematics within the liberal arts) and physics (a branch of the more prestigious discipline of philosophy). He also incorporated religious arguments and reasoning into his work, such that the basis for many of his most important contributions was essentially theological (Barker & Goldstein, 2001).

Kepler was a Pythagorean mystic. He considered mathematical relationships to be at the base of all nature, and all creation to be an integrated whole. This was in contrast to the Platonic and Aristotelian notion that the Earth was fundamentally different from the rest of the universe, being composed of different substances and with different natural laws applying. In his attempt to discover universal laws, Kepler applied terrestrial physics to celestial bodies; famously, his effort produced the three Laws of Planetary Motion. Kepler was also convinced that celestial bodies influence terrestrial events. One result of this belief was his correct assessment of the Moon's role in generating the tides, years before Galileo's incorrect formulation. Another was his belief that someday it would be possible to develop a "scientific astrology", despite his general disdain for most of the astrology of his time.

Life

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 left the family when Johannes was 5. 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.

Introduced to astronomy/astrology at an early age, Kepler developed a love for that discipline that spanned 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.

An abusive household and an absent and irresponsible father must have contributed to Kepler's introverted nature, to the extent that he experienced many of his greatest moments of joy in the contemplation of the order and beauty of the created world. His eyes, although imperfect, were perpetually searching the skies for answers to the riddles of the created universe.

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 eventually proved himself to be a superb mathematician. Under the instruction of Michael Maestlin, he learned both the Ptolemaic and Copernican systems. He became a Copernican at that time, defending heliocentrism from both theoretical and theological perspectives in student debates.

The textbook used by Kepler's instructor Maestlin was Ptolemy's Almagest. The cosmological picture in fashion at that time was Aristotle's and had been accepted as true for nearly 2,000 years. According to Aristotle, the Sun and other planets circled a fixed Earth. Ptolemy provided the mathematical foundation to describe planetary motion in terms of perfect circles. The observed deviations from these circular orbits were explained through the use of "epicycles" (circles drawn around certain points on each planet's orbital circle). Furthermore, it was thought that one set of physical laws applied to the Earth, while a different set of laws applied to the "crystalline spheres" beyond the Moon.

Even in school, Kepler stood out as an iconoclast who critiqued the Ptolemaic Earth-centered system in favor of a Sun-centered planetary system similar to the one advocated by the ancient philosopher, Aristarchus. Nicolaus Copernicus had more recently detailed a system in which the Sun, not the Earth, was at the center of the planetary system. Inspired by Copernicus' work, some of Tycho Brahe's findings, and Plato's ideas, Kepler became convinced of the correctness of the heliocentric model. It appealed to his thinking that the Sun, as God's most brilliant creation, rightly deserved the central position in the planetary system.

In spite of Aristarchus's early assertions, Aristotle's theory of an Earth-centered planetary system had become the popular and accepted model. Ptolemy graphically depicted the geocentric system, which was adopted and taught for over 1,000 years by Church authorities who maintained it was verified in the Holy Bible. The classic example "proving" this worldview was the biblical account mentioned in Joshua's time, when the Sun miraculously stood still in the midst of a battle.

Kepler was still convinced that the orbits of the planets must be circular in order to reflect the perfect nature of the Creator. In fact many of Kepler's writings reflect his deep desire to testify to God's glory.

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 age 23.

Early Career (1594–1601)

As he began teaching in Graz, Kepler simultaneously turned his attention to asking questions about the reasons behind the number of the planets, the nature of their movements, and the structure of the created world in general. In this manner he began developing an original theory of cosmology based on the Copernican system. His theory was published in 1596 as Mysterium Cosmographicum—The Sacred Mystery of the Cosmos.

According to historian of science James R. Volker (Johannes Kepler and the New Astronomy), Kepler asked a unique question: "Why did God choose to construct the solar system in this way and not another?" A partial answer came to him while teaching geometry in the summer of 1595. He noticed that geometrical figures (such as the square and triangle), when inscribed within concentric circles, roughly approximated the relative distances between the orbits of the six known planets. Eventually, Kepler developed a model according to which God had used the five regular Platonic solids in creating the six known planetary orbits around the Sun. He wrote to Maestlin, his old astromony professor, expressing his intention to publish this discovery for the glorification of God. He felt he had found his holy calling in a new venue and wept tears of joy over what he referred to as "stupendous miracles of God."

In April 1597, Kepler married Barbara Müller. That same year he published Cosmological Mystery, a small book in which he first proposed his theories about the regular solids and his insights into the mind of the Creator who had laid the plan for the planets on mathematical foundations. This book is considered the first astronomical publication to support the Copernican theory. It is significant that he sent copies to Tycho Brahe and to Galileo among others.

In December 1599, Tycho Brahe invited Kepler to assist him at Benátky nad Jizerou, outside Prague. Kepler accepted the opportunity to work with the renowned Tycho for more than one reason. First, Graz was becoming an increasingly uncomfortable environment because the institution of Counter-Reformation policies was leading to intolerance of any ideas, especially Protestant ones, that deviated from traditional Catholic views. The atmosphere of free inquiry and expression of opinion required for Kepler's scientific approach would no longer be found in Graz during the Counter-Reformation. Second, the protection and financial security afforded by the new post at Prague must have seemed like a God-given opportunity to the Kepler family. Third, perhaps the most intriguing feature of working with Tycho was access to the best observational data of planetary movements available at the time. Kepler hoped that this data would assist him in his quest to unravel the mystery of the harmony of the universe.

After Tycho's death in 1601, Kepler was appointed Imperial Mathematician in his place, a post Kepler retained 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. It soon became apparent that the perfect circles that he believed to be the perfect form expressed by God in setting up the planetary orbits did not fit Tycho's accurate data.

At first, Tycho assigned Kepler to study the motion of Mars, a relatively minor responsibility. Kepler used the opportunity to examine the behavior of both Mars and Earth and made a suprising discovery. Both planets moved faster when closer to the Sun and slower when farther away. The orbits and motions seemed eccentric. But how could that be? Was there a mathematical relationship that would explain in elegant fashion the handiwork of the Creator? Much to Kepler's delight, his theory that postulated a "planet moving force" flowing from the Sun seemed to be verified by the planets' orbital motion. <<?>>

Kepler went back to Graz to learn that he and his family would be expelled. The Counter-Reformation was in full swing. The Kepler family made a hasty exit to Prague, where Johannes rejoined Tycho. For his part, the Dutch astronomer had been abandoned by several of his work group and needed Kepler more than ever. In a remarkable twist of fate, Tycho recommended Kepler to the Emperor, became ill, and died shortly thereafter, leaving his precious data in Kepler's hands. Shortly thereafter, Kepler was appointed to the position of Imperial Mathematician. He was now free to work with the data that included the most accurate positions of the planets ever observed by the naked eye.

Continuing work on describing the orbit of Mars, he meticulously divided the orbit into 360 segments. William Boerst, historian of science (Johannes Kepler, Discovering the Laws of Celestial Motion, 2003) points out that Kepler was looking for both the accurate distance of Mars from the Sun and the period it took to move from one degree to the next. When Kepler looked at the measured distances with the Sun at the center for each of the 360 degrees, the variance from an ideal circle was enormous.

After five years of painstaking study of the Mars orbit, Kepler began to question his own belief that the orbits must be circular. He decided to attempt a description of the orbit of Earth. This time, he tried aking the question, how much time does it take for the planet to sweep out certain areas described by a line from Sun to Earth moving through a segment of the orbit? In asking this question, Kepler opened the door to revealing what became known as Kepler's Second Law of Planetary Motion. Planets sweep out equal areas in equal times. Mathematical order was preserved in this theory, which seemed to accurately represent the facts of empirical observation.

Applying this law rigorously to the orbits of the other planets led him to what we now refer to as Kepler's First Law of Planetary Motion. Elliptical orbits were the only shape that fit the data accurately. Finally Kepler understood that the planets move in elliptical orbits, with the Sun at one focus. He abandoned the circular theory and wrote that he "felt like I had been awakened from a sleep."

Kepler expounded these two laws in his book Astronomia nova|Astronomia Nova (New Astronomy), which was completed in 1606 and published in 1609. This book captured the imagination of Sir Isaac Newton more than a generation later.

The political backdrop to all that was going on for Kepler was one of great turmoil. While Kepler's star was rising, that of his patron, Emperor Rudolph II, was falling. The Austrian Habsburgs plotted and succeeded in dethroning him by encouraging Matthias, his younger brother, to advance upon Prague. Matthias was crowned King of Bohemia in 1611, and Rudolph died in 1612.

To escape the carnage and turmoil his family had witnessed in Prague, Kepler took the post of provincial mathematician in Linz, a city in Upper Austria. While arranging the move, his wife Barbara died.

Teaching in Linz and Final Years (1612–1630)

Moving to Linz was no panacea for an exhausted and disheartened Kepler. He had lost his wife as well as a stimulating lifestyle that had preceded the horrors of the sacking of Prague. Perhaps he sought to enjoy some peace and quiet in this provincial area of Upper Austria, but the tension between the Catholic Habsburg rulers and the local Protestant leaders was just as much a factor there as everywhere else at that time. To make matters worse, the Protestant leaders fought among themselves and Kepler, with his independent streak, was ultimately excommunicated. He found it tragic and silly that people bickered over minor points of dogma in the face of the magnanimous and glorious God he had come to know through his investigations.

In 1615, Kepler married Susanna Ruettinger, with whom he had several children. Interestingly, he had set about choosing a bride in as systematic a manner as he could conceive, but in the end he settled on marrying a simple, provincial girl whose greatest recommendation was that she genuinely loved him. Demonstrating the type of humility that characterized his desire to develop a personal relationship with God, he pondered, "Can I find God, who in the contemplation of the entire universe I can almost feel in my hands, also in myself?"

In 1617, Kepler's mother, Katharina, was accused of being a witch in Leonberg. Beginning in August 1620, she was imprisoned for 14 months. Thanks in part to the extensive legal defense he drew up for her, she was released in October 1621, after attempts to convict her failed. She was, however, subjected to territio verbalis, a verbal terrorization that included a description of the torture that awaited her if she did not 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 Harmonice 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. It brought together and extended his previous work and became very influential in the acceptance of the Copernican system over the next century. In 1627, he completed the Rudolphine Tables, which provided accurate calculations of future positions of the planets and allowed the prediction of rare astronomical events.

On November 15, 1630, Kepler died of a fever in Regensburg. Two years later, his grave was demolished by the Swedish army in the Thirty Years' War.

Scientific work

Kepler's laws

Kepler inherited from Tycho Brahe a wealth of the most accurate raw data ever collected on the positions of the planets. The difficulty was to make sense of it. The orbital motions of the other planets are viewed from the vantage point of the Earth, which is itself orbiting the Sun. As shown in the example below, this can cause the other planets to appear to move in strange loops. Kepler concentrated on trying to understand the orbit of Mars, but he first had to know the orbit of the Earth accurately. To do this, he needed a surveyor's baseline. In a stroke of pure genius, he used Mars and the Sun as his baseline. He realized that even without knowing the actual orbit of Mars, it would be in the same place in its orbit at times separated by its orbital period. His geometrical analysis needed only the ratios of the distances of the planets from the Sun, not the exact distances. In this manner, he computed the orbital positions of the Earth, and from them, the orbit of Mars.

Unlike Brahe, Kepler held to the heliocentric model of the solar system. Starting from that framework, he invested 20 years of painstaking, trial-and-error efforts to make sense out of the data. He finally arrived at his three laws of planetary motion:

File:Kepler-equal-area.png

Kepler's equal area law. If the time interval taken by the planet to move from P to Q is equal to the time interval from R to S, then according to Kepler's equal area law, the two shaded areas are equal. As Newton later showed, the planet moves faster during interval RS than during PQ because, as it approaches the Sun along QR, the Sun's gravity accelerates it.

1. Kepler's elliptical orbit law: The planets orbit the sun in elliptical orbits, with the Sun at one focus.

2. Kepler's equal-area law: The line connecting a planet to the Sun sweeps out equal areas in equal amounts of time.

3. Kepler's law of periods: The time required for a planet to orbit the Sun, called its period, is proportional to the long axis of the ellipse raised to the power of 3/2. The constant of proportionality is the same for all the planets.

Using these laws, he was the first astronomer to successfully predict a transit of Venus, for the year 1631. Kepler's laws were the first clear evidence in favor of the heliocentric model of the solar system, because they only came out to be so simple under the heliocentric assumption. Kepler, however, never discovered the underlying reasons for the laws, despite many years of what would now be considered non-scientific, mystical speculation. Isaac Newton eventually showed that the laws were a consequence of his laws of motion and law of universal gravitation. (From the modern vantage point, the equal-area law is more easily understood as arising from the conservation of angular momentum.)

Supernova 1604

Remnant of Kepler's Supernova, SN 1604.

On October 17, 1604, Kepler observed that an exceptionally bright star had suddenly appeared in the constellation Ophiuchus. (It was first observed by several others on October 9.) The appearance of the star, which Kepler described in his book De Stella nova in pede Serpentarii (On the New Star in the Foot of Ophiuchus), provided further evidence that the cosmos is not changeless—an observation that influenced Galileo in his argument. It has since been determined that the star was a supernova, the second in a generation, later called "Kepler's Star" or Supernova 1604. No additional supernovae have been observed in the Milky Way, though others outside our galaxy have been seen.

Other scientific and mathematical work

Kepler also made fundamental investigations into combinatorics (a branch of mathematics), geometrical optimization, and natural phenomena such as snowflakes, always with an emphasis on form and design. He was also one of the founders of modern optics, defining, for instance, antiprisms and the Kepler telescope, as detailed in his books Astronomiae Pars Optica and Dioptrice. In addition, he was the first to recognize nonconvex regular solids (such as "stellated dodecahedra"), which have been named "Kepler solids" in his honor.

Mysticism and astrology

Mysticism

Kepler discovered the laws of planetary motion while trying to achieve the Pythagorean purpose of finding harmony of the celestial spheres. He thought it was not a coincidence that the number of perfect polyhedra was one less than the number of known planets. Having embraced the Copernican system, he set out to prove a model in which the distances of the planets from the Sun were given by spheres inside perfect polyhedra, all of which were nested inside each other. The smallest orbit, that of Mercury, was the innermost sphere. He identified the five Platonic solids—cube, tetrahedron, dodecahedron, icosahedron, and octahedron—with the five intervals between the six known planets: Mercury, Venus, Earth, Mars, Jupiter, and Saturn.

In 1596, Kepler published Mysterium Cosmographicum. Here are two selections explaining the relations between the planets and the Platonic solids:

Kepler's "Platonic solids" model of the Solar system, as illustrated in Mysterium Cosmographicum (1596).

… Before the universe was created, there were no numbers except the Trinity, which is God himself… For, the line and the plane imply no numbers: here infinitude itself reigns. Let us consider, therefore, the solids. We must first eliminate the irregular solids, because we are only concerned with orderly creation. There remain six bodies, the sphere and the five regular polyhedra. To the sphere corresponds the heaven. On the other hand, the dynamic world is represented by the flat-faces solids. Of these there are five: when viewed as boundaries, however, these five determine six distinct things: hence the six planets that revolve about the Sun. This is also the reason why there are but six planets…

… I have further shown that the regular solids fall into two groups: three in one, and two in the other. To the larger group belongs, first of all, the Cube, then the Pyramid, and finally the Dodecahedron. To the second group belongs, first, the Octahedron, and second, the Icosahedron. That is why the most important portion of the universe, the Earth—where God's image is reflected in man—separates the two groups. For, as I have proved next, the solids of the first group must lie beyond the Earth's orbit, and those of the second group within… Thus I was led to assign the Cube to Saturn, the Tetrahedron to Jupiter, the Dodecahedron to Mars, the Icosahedron to Venus, and the Octahedron to Mercury…

Closeup of inner section of the model.

In his books Harmonice Mundi and Mysterium Cosmographicum, Kepler further associated the Platonic solids with the classical concept of elements: the tetrahedron was the form of fire, the octahedron was that of air, the cube was earth, the icosahedron was water, and the dodecahedron was the cosmos as a whole or ether. There is some evidence that this association was of ancient origin, as Plato tells of one Timaeus of Locri, who thought of the Universe as being enveloped by a gigantic dodecahedron, while the other four solids represented the elements of fire, air, earth, and water. In 1975, nine years after its founding, the College for Social and Economic Sciences Linz (Austria) was renamed Johannes Kepler University Linz, in Kepler's honor, particularly because he wrote Harmonice Mundi, his magnum opus, in Linz.

To his disappointment, Kepler's attempts to fix the orbits of the planets within a set of polyhedrons never worked out. Yet it is a testimony to his integrity as a scientist that when the evidence mounted against the cherished theory he worked so hard to prove, he abandoned it.

His most significant achievements came from the realization that the planets move in elliptical, not circular, orbits. This realization was a direct consequence of his failed attempt to fit the planetary orbits within polyhedra. Kepler's willingness to abandon his highly cherished theory in the face of precise observational evidence indicates that he had a very modern attitude to scientific research.

Kepler also took important steps in trying to describe the motion of the planets by appealing to a force that resembled magnetism, which he believed emanated from the Sun. Although he did not discover gravity, he seems to have attempted to invoke the first empirical example of a universal law to explain the behavior of both earthly and heavenly bodies.

Astrology

Kepler disdained astrologers who pandered to the tastes of the common man without knowledge of the abstract and general rules, but he saw compiling prognostications as a justified means of supplementing his meagre income. Yet it would be a mistake to take Kepler's astrological interests as merely pecuniary. As one historian, John North, put it, "had he not been an astrologer, he would very probably have failed to produce his planetary astronomy in the form we have it."

Kepler believed in astrology in the sense that he was convinced that astrological aspects physically and really affected humans as well as the weather on Earth. He strove to unravel how and why that was the case and tried to put astrology on a surer footing, which resulted in the publication, On the more certain foundations of astrology (1601). In The Intervening Third Man (1610), (a warning to theologians, physicians, and philosophers), Kepler posed as a third man between the two extreme positions for and against astrology, asserting that a definite relationship between heavenly phenomena and earthly events could be established.

At least 800 horoscopes and natal charts drawn up by Kepler are still extant, several of himself and his family, accompanied by some unflattering remarks. As part of his duties as district mathematician to Graz, Kepler issued a prognostication for 1595 in which he forecast a peasant uprising, Turkish invasion, and bitter cold, all of which happened and brought him renown. He is known to have compiled prognostications for the years 1595 to 1606, and 1617 to 1624.

As court mathematician, Kepler explained to Rudolf II the horoscopes of the Emperor Augustus and Muhammad, and he gave an astrological prognosis for the outcome of a war between the Republic of Venice and Paul V. In On the new star (1606), Kepler interpreted the meaning of the new star of 1604 as the conversion of America, the downfall of Islam, and the return of Christ. His De cometis libelli tres (1619) is also replete with astrological predictions.

Kepler on God

"I was merely thinking God's thoughts after him. Since we astronomers are priests of the highest God in regard to the book of nature," wrote Kepler, "it benefits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God."

Writings by Kepler

Illustration of SN 1604 by Johannes Kepler, from his book De Stella Nova in Pede Serpentarii

• Mysterium cosmographicum (The Sacred Mystery of the Cosmos) (1596)
• Astronomiae Pars Optica (The Optical Part of Astronomy) (1604)
• De Stella nova in pede Serpentarii (On the New Star in the Foot of Ophiuchus) (1604)
• Astronomia nova (New Astronomy) (1609)
• Dioptrice (Dioptre) (1611)
• Nova stereometria doliorum vinariorum (New Stereometry of Wine Barrels) (1615)
• Epitome astronomiae Copernicanae (published in three parts, 1618–1621)
• Harmonice Mundi (Harmony of the Worlds) (1619)
• Tabulae Rudolphinae (Rudolphine Tables) (1627)
• Somnium (The Dream) (1634) (considered the first precursor of science fiction)

References

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• Peter Barker and Bernard R. Goldstein: "Theological Foundations of Kepler's Astronomy". Osiris, Volume 16: Science in Theistic Contexts. University of Chicago Press, 2001.

• Max Caspar: Kepler; transl. and ed. by C. Doris Hellman; with a new introduction and references by Owen Gingerich; bibliographic citations by Owen Gingerich and Alain Segonds. New York: Dover, 1993 ISBN 0-486-67605-6

• James A. Connor: Kepler's Witch: An Astronomer's Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother. HarperSanFrancisco, 2004 ISBN 0-06-052255-0

• J.V. Field: Kepler's geometrical cosmology. Chicago: Chicago University Press, 1988 ISBN 0-226-24823-2

• Owen Gingerich: The eye of heaven: Ptolemy, Copernicus, Kepler. New York: American Institute of Physics, 1993 ISBN 0-88318-863-5 (Masters of modern physics; v. 7)

• Kitty Ferguson: The nobleman and his housedog: Tycho Brahe and Johannes Kepler: the strange partnership that revolutionised science. London : Review, 2002 ISBN 0-747270-22-8 (published in the US as: Tycho & Kepler: the unlikely partnership that forever changed our understanding of the heavens. New York: Walker, 2002 ISBN 0-8027-1390-4)

• Arthur Koestler: The Sleepwalkers: A History of Man's Changing Vision of the Universe. (1959). ISBN 0-140-19246-8

• John Lear: Kepler's Dream. Berkeley: University of California Press, 1965.

• Bruce Stephenson: Kepler's physical astronomy. New York: Springer, 1987 ISBN 0-387-96541-6 (Studies in the history of mathematics and physical sciences; 13)

Kepler in fiction

• John Banville: Kepler: a novel. London: Secker & Warburg, 1981 ISBN 0-436-03264-3 (and later eds.). Also published: Boston, MA:Godine, 1983 ISBN 0-87923-438-5. Draws heavily on Koestler's account of Kepler in The Sleepwalkers.

Named in Kepler's honor

"Kepler Space Observatory," a solar-orbiting, planet-hunting telescope due to be launched by NASA in 2008.

"Kepler Solids," a set of geometrical constructions, two of which were described by him.

"Kepler's Star," Supernova 1604, which he observed and described.

"Kepler," a crater on the Moon, and "Kepler," a crater on Mars.

External links

• Annotation: Posner Family Collection in Electronic Format Harmonices mvndi The Harmony of the Worlds in fulltext facsimile in Latin
• Full text of Kepler by Walter W. Bryant, from Project Gutenberg
• Kepler and the "Music of the Spheres"
• Johannes Kepler Directory
• Gale E. Christianson- Kepler's Somnium: Science Fiction and the Renaissance Scientist
• John J. O'Connor and Edmund F. Robertson. Johannes Kepler at the MacTutor archive

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