2 Scientific work

Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1596) Like previous astronomers, Kepler initially believed that celestial objects moved in perfect circles. These models were consistent with observations and with the Platonic idea that the sphere was the perfect shape. However, after spending twenty years doing calculations with data collected by Tycho Brahe, Kepler concluded that the circular model of planetary motion was inconsistent with that data. Using Tycho's data, Kepler was able to formulate three laws of planetary motion, now known as Kepler's laws, in which planets move in ellipses, not circles. Using that knowledge, he was the first astronomer to successfully predict a transit of Venus (for the year 1631).

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 where 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…

… 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.

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.

Remnant of Kepler's Supernova SN 1604.

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.

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 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.

In 1632, only two years after his death, his grave was demolished by the Swedish army in the Thirty Years' War.

3 Kepler and 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 produced 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 Mohammed, 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.

4 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."

5 Writings by Kepler

• Mysterium cosmographicum ( The Cosmic Mystery ) ( 1596)
• Astronomiae Pars Optica (The Optical Part of Astronomy) ( 1604)
• De Stella nova in pede Serpentarii (On the New Star in Ophiuchus's Foot) ( 1604)
• Astronomia nova ( New Astronomy ) ( 1609)
• Dioptrice ( Dioptre) ( 1611)
• Epitome astronomiae Copernicanae (published in three parts from 1618- 1621)
• Harmonice Mundi ( Harmony of the Worlds ) ( 1619)
• Tabulae Rudolphinae ( 1627)
• Somnium (The Dream) ( 1634) - considered the first precursor of science fiction.

6 See also

• Kepler's laws of planetary motion

7 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
• Johannes Kepler Directory
• Biography from "MacTutor History of Mathematics"

Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes

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