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Johannes Kepler

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                Johannes Kepler
   Born December 27, 1571
        Weil der Stadt near 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 mathematician, astronomer,
   astrologer, and an early writer of science fiction stories. He is best
   known for his laws of planetary motion, based on his works 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, Austria), an assistant to Tycho
   Brahe, court mathematician to Emperor Rudolf II, mathematics teacher in
   Linz, Austria, and court astrologer to General Wallenstein. He also did
   fundamental work in the field of optics and helped to legitimize the
   telescopic discoveries of his contemporary Galileo Galilei.

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

Life

Childhood and education (1571–1594)

   Kepler was born on December 29, 1571 in the Free Imperial City of Weil
   der Stadt (now part of the Stuttgart Region in the German state of
   Baden-Württemberg, 30 km west of Stuttgart's centre). 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 he left the family when Johannes
   was five years old. 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. Whether Kepler was born
   prematurely is disputable. But it is indisputable that he was
   frequently ill. 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.

   He was introduced to astronomy/astrology at an early age, and he
   developed a love for it that would span 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.

   In 1589, after moving through grammar school, Latin school, and after
   passing the "Landexamen" (state-wide examination), Kepler attended the
   lower and higher seminary in the scholarship-based education system of
   the Duchy of Württemberg. Kepler enrolled in the University of Tübingen
   as a theology student, where he proved himself to be a superb
   mathematician and earned a reputation as a skillful astrologer. Under
   the instruction of Michael Maestlin, he learned both the Ptolemaic
   system and the Copernican system; he became a Copernican at that time,
   defending heliocentrism from both a theoretical and theological
   perspective in student debates. 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 the
   age of 23.
   Monument of Johannes Kepler and Tycho Brahe in Prague
   Enlarge
   Monument of Johannes Kepler and Tycho Brahe in Prague

Early career (1594–1601)

   In Graz, Kepler began developing an original theory of cosmology based
   on the Copernican system, which was published in 1596 as Mysterium
   Cosmographicum— The Sacred Mystery of the Cosmos.

   In April 1597, Kepler married Barbara Müller. She died in 1611 and was
   outlived by two of Johannes's children and one by an earlier marriage.

   In December 1599, Tycho Brahe wrote to Kepler, inviting Kepler to
   assist him at Benátky nad Jizerou outside Prague. Pressured to leave
   Graz by increasingly strict Counter-Reformation policies restricting
   the religious practices and political rights of Protestants, Kepler
   joined Tycho in 1600. After Tycho's death in 1601, Kepler was appointed
   Imperial Mathematician in his place, a post he would retain 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. Instead, he began developing
   the first astronomical system to use non-circular orbits; it was
   completed in 1606 and published in 1609 as Astronomia Nova—New
   Astronomy. Astronomia Nova contained what would become the first and
   second laws of planetary motion.

   In October 1604, Kepler observed the supernova which was subsequently
   named Kepler's Star (a term which may also refer to the stellated
   octahedron). In 1611, Kepler published (as a letter to a friend) 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. In January 1612,
   the Emperor died. To escape the growing religious tension in Prague,
   Kepler took the post of Provincial Mathematician in Linz.

Teaching in Linz and final years (1612–1630)

   In 1615, Kepler married Susanna Ruettinger, with whom he would have
   several children.

   In 1617, Kepler's mother Katharina was accused of being a witch in
   Leonberg. Beginning in August 1620 she was imprisoned for fourteen
   months. Thanks in part to the extensive legal defense drawn up by
   Kepler, she was released in October 1621 after failed attempts to
   convict her. However, she was subjected to territio verbalis, a graphic
   description of the torture awaiting her as a witch, in a final attempt
   to make her 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
   Harmonices 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, which brought together and extended his
   previous work and would become very influential in the acceptance of
   the Copernican system over the next century. In 1627 he completed the
   Rudolphine Tables, which provided accurately calculated future
   positions of the planets and allowed the prediction of rare
   astronomical events.

   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 had incidentally composed the
   epitaph for his own tombstone, which read:

          I measured the skies, now the shadows I measure,
          Sky-bound was the mind, earth-bound the body rests

Work

   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).

   For instance, Kepler was explicit about the intellectual safeguards
   that, in his view, the Christian faith provided for scientific
   speculation. In connection with the apriorism of the world view of
   antiquity (a good example is the Platonic dictum Ex nihilo nihil
   fit—nothing is made from nothing), he wrote: "Christian religion has
   put up some fences around false speculation in order that error may not
   rush headlong" (Introduction to Book IV of Epitome astronomae
   copernicanae, c1620, in Werke Vol. VII p. 254).

   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.

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 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.

   Image:Retrograde-motion-of-mars.png

   Unlike Brahe, Kepler had accepted Copernicus's heliocentric model of
   the solar system. Starting from that framework, Kepler 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.
   Enlarge
   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 favour 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.

   Kepler first discovered his distance-cubed-over-time-squared (or
   'third') law of planetary motion on March 8, 1618 but rejected the idea
   until May 15, 1618, when he verified his result. This result was
   published in his Harmonices Mundi (1619).

Supernova 1604

   Remnant of Kepler's Supernova SN 1604
   Enlarge
   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 were not changeless; this was to influence Galileo Galilei
   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 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,
   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 example antiprisms and the
   Keplerian 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 honour.

   Kepler also was in contact with Wilhelm Schickard, inventor of the
   first automatic calculator, whose letters to Kepler show how to use the
   machine for calculating astronomical tables.

Mysticism and astrology

Mysticism

   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 Sacred
   Mystery of the Cosmos. 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…MS

   Kepler's Platonic solid model of the Solar system from Mysterium
   Cosmographicum (1596)
   Enlarge
   Kepler's Platonic solid model of the Solar system from Mysterium
   Cosmographicum (1596)
   Closeup of inner section of the model
   Enlarge
   Closeup of inner section 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.

   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.

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
   meager 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." However,
   Kepler's views on astrology were quite unconventional for his time; he
   argued for a system of astrology based largely on harmonics, a type of
   'planetary harmonics' based almost entirely upon the astrological
   aspects and what has been traditionally been termed " the music of the
   spheres." Information relating to his theories can be found in his book
   Harmonice Mundi.

   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 Fundamentals of Astrology (1601), in which,
   among other technical innovations, he was the first to propose a number
   of new aspects such as 18°, 24°, 30° (semi-sextile), 36°, 45°
   (semi-square), 72° (quintile), 108°, 135° (sesquiquadrate), 144°
   (bi-quintile), and 150° ( quincunx). 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, Kepler explained to Rudolf II the horoscopes of the
   Emperor Augustus and the Prophet Muhammad, and Kepler 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.

Writings by Kepler

   Illustration of SN 1604 by Johannes Kepler from his book De Stella Nova
   in Pede Serpentarii
   Enlarge
   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)
     * De Fundamentis Astrologiae Certioribus (On The More Certain
       Fundamentals of Astrology) (1601)
     * 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)
     * Nova stereometria doliorum vinariorum (New Stereometry of wine
       barrels) (1615)
     * 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.

Named in Kepler's honour

   The GDR stamp featuring Johannes Kepler.
   Enlarge
   The GDR stamp featuring Johannes Kepler.
     * Kepler Space Observatory, a solar-orbiting, planet-hunting
       telescope due to be launched by NASA in 2008.
     * The 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 conjecture about sphere packing, proved true 400 years
       later.
     * Kepler, a crater on the moon
     * Kepler, a crater on Mars
     * 1134 Kepler is an asteroid.
     * In 1975, nine years after its founding, the College for Social and
       Economic Sciences Linz (Austria) was renamed Johannes Kepler
       University Linz in honour of Johannes Kepler, since he wrote his
       magnum opus Harmonice Mundi in Linz.
     * Johannes Kepler's Gymnasium in Prague
     * Keplerstraße in Hanau near Frankfurt am Main
     * Kepler-Gymnasium in Pforzheim, Germany.

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.

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