Johannes Kepler

From Example Problems
Jump to navigation Jump to search
Johannes Kepler
December 27, 1571
Weil der Stadt, Stuttgart, Germany
November 15, 1630
Regensburg, Bavaria, Germany

Johannes Kepler (December 27, 1571November 15, 1630), a key figure in the scientific revolution, was a German mathematician, astronomer and astrologer of famed brilliance. He is best known for his laws of planetary motion, expounded in the two books Astronomia nova and Harmonice Mundi.

Kepler was a professor of mathematics at the University of Graz, court mathematician to Emperor Rudolf II, and court astrologer to General Wallenstein. Early in his career, Kepler was an assistant to Tycho Brahe. Kepler's career also coincided with that of Galileo Galilei.

He is sometimes referred to as "the first theoretical astrophysicist", although Carl Sagan also referred to him as the last scientific astrologer.


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 so 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 abandoned the family when Johannes was 17. His mother, an inn-keeper's daughter, had a reputation for involvement in witchcraft. Born prematurely, Johannes is said to have been a weak and sickly child, but despite his ill health, he was precociously brilliant - he often impressed travelers at the inn [aforementioned] with his phenomenal mathematical faculty as a child.

Though he excelled in his schooling, Kepler was frequently bullied, and was plagued by a belief that he was physically repulsive, thoroughly unlikable and, compared to the other pupils, an outsider. This ostracizing probably led him to turn to the world of ideas, as well as an abiding religious conviction, for solace.

He was introduced to astronomy/astrology at an early age, and developed a love for that discipline that would span his entire life. At age six, 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."

In 1587, Kepler began attending the University of Tübingen, where he proved himself to be a superb mathematician. Upon his graduation from that school in 1591, he went on to pursue study in theology, becoming a part of the Tübingen faculty. However, before he took his final exams he was recommended for the vacant post of teacher of mathematics and astronomy at the Protestant school in Graz, Austria. He accepted the position in April of 1594, at the age of 23.

In April 1597, Kepler married Barbara Müller. She died in 1611 and was outlived by two children.

In December 1599, Tycho Brahe wrote to Kepler, inviting Kepler to assist him at Benátky nad Jizerou outside Prague. After Tycho's death, Kepler was appointed Imperial Mathematician (from November 1601 to 1630) to the Habsburg Emperors.

In October 1604, Kepler observed the supernova which was subsequently named Kepler's Star. In January 1612 the Emperor died, and Kepler took the post of provincial mathematician in Linz.

In 1611, Kepler published 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. The question of snowflakes was not resolved until the 20th century.

On March 8, 1618 Kepler discovered the third law of planetary motion: distance cubed over time squared. He initially rejected this idea, but later confirmed it on May 15 of the same year.

In August of 1620, Katherine, Kepler's mother, was arrested in Leonberg as a witch; she was imprisoned for 14 months. She was released in October 1621 after attempts to convict her failed. Even though she was subjected to torture, she refused to confess to the charges. However, only the courageous personal intervention of Kepler (despite the risk to be arrested as well) and his reputation as the famous Imperial Mathematician rescued her.


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 lived in an era when there was no clear distinction between astronomy and astrology, and no consensus on the scientific method as the correct way to decide what was correct or incorrect in science. His ideas are therefore a fascinating mixture of what would today be considered mathematical physics and nonsensical mysticism. Although the subsections below separate the two, Kepler did not see them as separate.

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 the orbit of Mars, but he had to know the orbit of the Earth accurately first. In order to do this, he needed a surveyor's baseline. In a stroke of pure genius, he used Mars and the Sun as his baseline, since without knowing the actual orbit of Mars, he knew that it would be in the same place in its orbit at times separated by its orbital period. Thus the orbital positions of the Earth could be computed, and from them the orbit of Mars. He was able to deduce his planetary laws without knowing the exact distances of the planets from the sun, since his geometrical analysis needed only the ratios of their solar distances.


Kepler, unlike Brahe, held to the heliocentric model of the solar system, and starting from that framework, he made twenty years of painstaking trial-and-error attempts at making some sense out of the data. He finally arrived at his three laws of planetary motion:

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. The reason it speeds up, as later found by Newton, is that the planet is moving faster during interval RS than it did during PQ, because as it approached the sun along QR, the Sun's gravity accelerated 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 3/2 power. 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 deeper 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 conservation of angular momentum.)

1604 supernova

File:Keplers supernova.jpg
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 Ophiuchus's Foot'), provided further evidence that the cosmos was not changeless; this was to influence 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 further supernovae have since been observed with certainty in the Milky Way, though others outside our galaxy have been seen.

Other scientific and mathematical work

Kepler also made fundamental investigations into combinatorics, 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 e.g. antiprisms and the Kepler telescope (see Kepler's books Astronomiae Pars Optica — i.a. theoretical explanation of the camera obscura — and Dioptrice). In addition, since he was the first to recognize the non-convex regular solids (such as the stellated dodecahedra), they are named Kepler solids in his honor.

Mysticism and astrology


Kepler discovered the laws of planetary motion while trying to achieve the Pythagorean purpose of finding the harmony of the celestial spheres. In his cosmologic vision, 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 that the distances from the planets to 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 thereby identified the five Platonic solids with the five intervals between the six known planets — Mercury, Venus, Earth, Mars, Jupiter, Saturn; and the five classical elements.

In 1596 Kepler published Mysterium Cosmographicum, or The Cosmic Mystery. Here is a selection explaining the relation between the planets and the Platonic solids:

… 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…
Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1596)
Closeup of the model
… 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…

To emphasize his theory, Kepler envisaged an impressive model of the universe which shows a cube, inside a sphere, with a tetrahedron inscribed in it; another sphere inside it with a dodecahedron inscribed; a sphere with an icosahedron inscribed inside; and finally a sphere with an octahedron inscribed. Each of these celestial spheres had a planet embedded within them, and thus defined the planet's orbit.

In his 1619 book, Harmonice Mundi or Harmony of the Worlds, as well as the aforementioned Mysterium Cosmographicum, he also made an association between the Platonic solids with the classical conception of the 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 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 represent 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 honor of Johannes Kepler, since he wrote his magnum opus harmonice mundi in Linz.

To his disappointment, Kepler's attempts to fix the orbits of the planets within a set of polyhedrons never worked out, but 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 moved 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 most cherished theory in the face of precise observational evidence also indicates that he had a very modern attitude to scientific research. Kepler also made great steps in trying to describe the motion of the planets by appealing to a force which 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 behaviour of both earthly and heavenly bodies.


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 On the more certain foundations of astrology (1601), in which, among other technical innovations, he was the first to propose the quincunx aspect. In The Intervening Third Man, or a warning to theologians, physicians and philosophers (1610), posing as a third man between the two extreme positions for and against astrology, Kepler advocated 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. Kepler is known to have compiled prognostications for 1595 to 1606, and from 1617 to 1624. As court mathematician, he explained to Rudolf II the horoscopes of the Emperor Augustus and Muhammad, and gave astrological prognosis for the outcome of a war between the Republic of Venice and Paul V. In the On the new star (1606) Kepler explicated the meaning of the new star of 1604 as the conversion of America, downfall of Islam and return of Christ. The 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

See also

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

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.

Machines named in Kepler's honor

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

External links

Template:Link FA

als:Johannes Kepler bg:Йоханес Кеплер ca:Johannes Kepler cs:Johannes Kepler da:Johannes Kepler de:Johannes Kepler et:Johannes Kepler es:Johannes Kepler eo:Keplero eu:Johannes Kepler fa:یوهانس کپلر fr:Johannes Kepler gl:Johannes Kepler ko:요하네스 케플러 hr:Johannes Kepler io:Johannes Kepler id:Johannes Kepler is:Johannes Kepler it:Johannes Kepler he:יוהנס קפלר la:Iohannes Keplerus hu:Johannes Kepler nl:Johannes Kepler ja:ヨハネス・ケプラー no:Johannes Kepler pl:Jan Kepler pt:Johannes Kepler ro:Johannes Kepler ru:Кеплер, Иоганн sco:Johannes Kepler sk:Johannes Kepler sl:Johannes Kepler fi:Johannes Kepler sv:Johannes Kepler zh:约翰内斯·开普勒