Johannes KeplerGB

							Johannes Kepler
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
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 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
Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler
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.



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

Quelle: http://en.wikipedia.org/wiki/Johannes_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.

Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler
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.




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
Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler
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.

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
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 honor.

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.




Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler
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)

         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




                                             Closeup of inner section of the mode


Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler
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

Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler
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
•        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 honor
•        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 honor 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 Forum e.V. in Regensburg, Germany.




Quelle: http://en.wikipedia.org/wiki/Johannes_Kepler