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JOHANNES KEPLER

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Bianca
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« on: October 25, 2008, 09:38:56 am »



A 1610 portrait of Johannes Kepler by an unknown artist









Born

December 27, 1571(1571-12-27)
Weil der Stadt near Stuttgart, Germany



Died

November 15, 1630 (aged 58)
Regensburg, Bavaria, Germany
 


Residence

Baden-Württemberg;
Styria; Bohemia;
Upper Austria



Fields

Astronomy,
Astrology,
Mathematics and
Natural Philosophy



Institutions

University of Linz
Alma mater - University of Tübingen
Known for Kepler's Laws Of Planetary Motion
Kepler Conjecture
 


Religious stance

Lutheran
« Last Edit: October 25, 2008, 09:43:10 am by Bianca » Report Spam   Logged

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Bianca
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« Reply #1 on: October 25, 2008, 09:45:09 am »



The Great Comet of 1577, which Kepler witnessed as a child, attracted the attention of
astronomers across Europe.
« Last Edit: October 25, 2008, 09:46:30 am by Bianca » Report Spam   Logged

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« Reply #2 on: October 25, 2008, 09:49:50 am »











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, Sebald Kepler, had been Lord Mayor of that town, but by the time Johannes was born, the Kepler family fortune was on the decline. His father, Heinrich Kepler, 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 Eighty Years' War in the Netherlands. His mother Katharina Guldenmann, 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. He was, however, a brilliant child; he often impressed travelers at his grandfather's inn with his phenomenal mathematical faculty.

He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great 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 and crippled hands, limiting his
ability in the observational aspects of astronomy.

In 1589, after moving through grammar school, Latin school, and lower and higher seminary in the Württemberg state-run Protestant education system, Kepler began attending the University of Tübingen as a theology student, and studied philosophy under Vitus Müller. He proved himself to be
a superb mathematician and earned a reputation as a skillful astrologer, casting horoscopes for fellow students.

Under the instruction of Michael Maestlin, he learned both the Ptolemaic system and the Copernican system of planetary motion. He became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe.  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 (later the University of Graz). He accepted the position in April 1594, at the age of 23.






GERMANY
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« Reply #3 on: October 25, 2008, 09:51:25 am »



Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum
(1596)
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« Reply #4 on: October 25, 2008, 09:53:11 am »






                         

                          CLOSE UP OF THE INNER SECTION
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« Reply #5 on: October 25, 2008, 09:58:17 am »












                                                            Graz (1594–1600)





Mysterium Cosmographicum
 


Johannes Kepler's first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery), was the first published defense of the Copernican system. Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn
and Jupiter in the zodiac; he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe.

After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra.
He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by
spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler
found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, because it was not precise enough.

 
As he indicated in the title, Kepler thought he had revealed God’s geometrical plan for the universe. Much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son, and the intervening space between to the Holy Spirit. His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism.

With the support of his mentor Michael Maestlin, Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible exegesis and the addition
of a simpler, more understandable description of the Copernican system as well as Kepler’s new ideas. Mysterium was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; it was not widely read, but it established Kepler’s reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as to
the men who controlled his position in Graz, also provided a crucial doorway into the patronage system.

Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherist cosmology of Mysterium Cosmographicum. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621 Kepler published an expanded second edition of Mysterium, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.
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« Reply #6 on: October 25, 2008, 10:00:25 am »











Marriage to Barbara Müller
 


In December 1595, Kepler was introduced to Barbara Müller, a 23-year-old widow (twice over) with a young daughter, and he began courting her.

Müller, heir to the estates of her late husbands, was also the daughter of a successful mill owner. Her father Jobst initially opposed a marriage despite Kepler's nobility; though he had inherited his grandfather's nobility, Kepler's poverty made him an unacceptable match. Jobst relented after Kepler completed work on Mysterium, but the engagement nearly fell apart while Kepler was away tending to the details of publication.

However, church officials — who had helped set up the match — pressured the Müllers to honor their agreement.

Barbara and Johannes were married on April 27, 1597.

In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died
in infancy. In 1602, they had a daughter (Susanna); in 1604, a son (Friedrich); and in 1607, another son (Ludwig).
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« Reply #7 on: October 25, 2008, 10:14:23 am »










Other research in Graz



Following the publication of Mysterium and with the blessing of the Graz school inspectors, Kepler began an ambitious program to extend and elaborate his work. He planned four additional books: one on the stationary aspects of the universe (the Sun and the fixed stars); one on the planets and their motions; one on the physical nature of planets and the formation of geographical features (focused especially on Earth); and one on the effects of the heavens on the Earth, to include atmospheric optics, meteorology and astrology.

He also sought the opinions of many of the astronomers to whom he had sent Mysterium, among them Reimarus Ursus (Nicolaus Reimers Bär) — the imperial mathematician to Rudolph II and a bitter rival of Tycho Brahe. Ursus did not reply directly, but republished Kepler's flattering letter to pursue his priority dispute over (what is now called) the Tychonic system with Tycho.

Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler's system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus. Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory (particularly its theological viability).

But without the significantly more accurate data of Tycho's observatory, Kepler had no way to
address many of these issues.

Instead, he turned his attention to chronology and "harmony," the numerological relationships among music, mathematics and the physical world, and their astrological consequences.

By assuming the Earth to possess a soul (a property he would later invoke to explain how the sun causes the motion of planets), he established a speculative system connecting astrological aspects
and astronomical distances to weather and other earthly phenomena.

By 1599, however, he again felt his work limited by the inaccuracy of available data — just as growing religious tension was also threatening his continued employment in Graz. In December of that year, Tycho invited Kepler to visit him in Prague; on January 1, 1600 (before he even received the invitation), Kepler set off in the hopes that Tycho's patronage could solve his philosophical problems as well as his social and financial ones.
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« Reply #8 on: October 25, 2008, 10:18:16 am »








                                                              Prague (1600–1612)






Work for Tycho Brahe
 


Tycho BraheOn February 4, 1600, Kepler met Tycho Brahe and his assistants Franz Tengnagel and Longomontanus at Benátky nad Jizerou (~50 km from Prague), the site where Tycho's new observatory was being constructed. Over the next two months he stayed as a guest, analyzing some of Tycho's observations of Mars; Tycho guarded his data closely, but was impressed by Kepler's theoretical ideas and soon allowed him more access. Kepler planned to test his theory from Mysterium Cosmographicum based on the Mars data, but he estimated that the work would take up to two years (since he was not allowed to simply copy the data for his own use). With the help of Johannes Jessenius, Kepler attempted to negotiate a more formal employment arrangement with Tycho, but negotiations broke down in an angry argument and Kepler left for Prague on April 6. Kepler and Tycho soon reconciled and eventually reached an agreement on salary and living arrangements, and in June, Kepler returned home to Graz to collect his family.

Political and religious difficulties in Graz dashed his hopes of returning immediately to Tycho; in hopes
of continuing his astronomical studies, Kepler sought an appointment as mathematician to Archduke Ferdinand. To that end, Kepler composed an essay — dedicated to Ferdinand — in which he proposed
a force-based theory of lunar motion (In Terra inest virtus, quae Lunam ciet — "There is a force in the earth which causes the moon to move").  Though the essay did not earn him a place in Ferdinand's court, it did detail a new method for measuring lunar eclipses, which he applied during the July 10 eclipse in Graz. These observations formed the basis of his explorations of the laws of optics that
would culminate in Astronomiae Pars Optica.

On August 2, 1600, after refusing to convert to Catholicism, Kepler and his family were banished from Graz; several months later, Kepler returned, now with the rest of his household, to Prague. Through most of 1601, he was supported directly by Tycho, who assigned him to analyzing planetary observations and writing a tract against Tycho's (now deceased) rival Ursus. In September, Tycho secured him a commission as a collaborator on the new project he had proposed to the emperor: the Rudolphine Tables that should replace the Prussian Tables of Erasmus Reinhold. Two days after Tycho's unexpected death on October 24, 1601, Kepler was appointed his successor as imperial mathematician with the responsibility to complete his unfinished work. He illegally appropriated Tycho's observations, the property of his heirs, which subsequently led to four year delays each to the publications of two of his works whilst he negotiated copyright permissions for the use of Tycho's data. The next 11 years as imperial mathematician would be the most productive of his life.
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« Reply #9 on: October 25, 2008, 10:19:36 am »












Advisor to Emperor Rudolph II



Kepler's primary obligation as imperial mathematician was to provide astrological advice to the emperor. Though Kepler took a dim view of the attempts of contemporary astrologers to precisely predict the future or divine specific events, he had been casting detailed horoscopes for friends, family and patrons since his time as a student in Tübingen. In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler's advice in times of political trouble (though Kepler's recommendations were based more on common sense than the stars). Rudolph was actively interested in the work of many of his court scholars (including numerous alchemists) and kept up with Kepler's work in physical astronomy as well.

Officially, the only acceptable religious doctrines in Prague were Catholic and Utraquist, but Kepler's position in the imperial court allowed him to practice his Lutheran faith unhindered. The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle. Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness. Court life, however, brought Kepler into contact with other prominent scholars (Johannes Matthäus Wackher von Wackhenfels, Jost Bürgi, David Fabricius, Martin Bachazek, and Johannes Brengger, among others) and astronomical work proceeded rapidly.
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« Reply #10 on: October 25, 2008, 10:21:37 am »



            KEPLER OPTICA








Astronomiae Pars Optica
 


As he continued analyzing Tycho's Mars observations — now available to him in their entirety — and began
the slow process of tabulating the Rudolphine Tables, Kepler also picked up the investigation of the laws of optics from his lunar essay of 1600.

Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction applied to all astronomical observations.

Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, 1604, was published as 'Astronomiae Pars Optica' (The Optical Part
of Astronomy). In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies.

He also extended his study of optics to the human eye, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the eye's lens onto the retina. The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected "in the hollows of the brain" due to the "activity of the Soul."

Today, Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).
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« Reply #11 on: October 25, 2008, 10:25:49 am »



Remnant of Kepler's Supernova SN 1604
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« Reply #12 on: October 25, 2008, 10:29:06 am »










The Supernova of 1604
 


On October 1604, a bright new evening star (SN 1604) appeared, but Kepler did not believe the
rumors until he saw it himself. Kepler began systematically observing the star.

Astrologically, the end of 1603 marked the beginning of a fiery trigon, the start of the ca. 800-year cycle of great conjunctions; astrologers associated the two previous such periods with the rise of Charlemagne (ca. 800 years earlier) and the birth of Christ (ca. 1600 years earlier), and thus
expected events of great portent, especially regarding the emperor.

It was in this context, as the imperial mathematician and astrologer to the emperor, that Kepler described the new star two years later in his De Stella Nova. In it, Kepler addressed the star's astronomical properties while taking a skeptical approach to the many astrological interpretations
then circulating. He noted its fading luminosity, speculated about its origin, and used the lack of observed parallax to argue that it was in the sphere of fixed stars, further undermining the doctrine of the immutability of the heavens (the idea accepted since Aristotle that the celestial spheres were perfect and unchanging).

The birth of a new star implied the variability of the heavens.

In an appendix, Kepler also discussed the recent chronology work of Laurentius Suslyga; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem — analogous to the present new star — would have coincided with the first great conjunction of the earlier 800-year cycle.
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« Reply #13 on: October 25, 2008, 10:32:48 am »





                       

Illustration by Kepler from his book De Stella Nova in Pede Serpentarii (On the New Star in Ophiuchus's Foot) indicating the location of the 1604 supernova. The supernova, also know as Kepler's Supernova, is the star marked with a 'N' on the right foot of the Ophiuchus (Serpent Bearer) constellation.

It is the last supernova in the Milky Way observed with certainty by mankind.
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« Reply #14 on: October 25, 2008, 10:42:39 am »









Astronomia nova



The extended line of research that culminated in Astronomia nova (A New Astronomy) — including the first two laws of planetary motion — began with the analysis, under Tycho's direction, of Mars' orbit.

Kepler calculated and recalculated various approximations of Mars' orbit using an equant (the mathematical tool that Copernicus had eliminated with his system), eventually creating a model that generally agreed with Tycho's observations to within two arcminutes (the average measurement error). But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data.[30]

Within Kepler's religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert's theory of the magnetic soul of the Earth from De Magnete (1600) and on his own work on optics. Kepler supposed that the motive power (or motive species) radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it.

Perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle, however, required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times — the second law of planetary motion.

 
He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After approximately 40 failed attempts, in early 1605 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fit the Mars data, he immediately concluded that all planets move in ellipses, with the sun at one focus — the first law of planetary motion. Because he employed no calculating assistants, however, he did not extend the mathematical analysis beyond Mars.

By the end of the year, he completed the manuscript for Astronomia Nova, though it would not be published until 1609 due to legal disputes over the use of Tycho's observations, the property of his heirs.
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