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JOHANNES KEPLER

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Bianca
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« Reply #15 on: October 25, 2008, 10:48:08 am »



Diagram of the geocentric trajectory of Mars through several periods of retrograde motion.
Astronomia nova, Chapter 1, (1609).
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« Reply #16 on: October 25, 2008, 10:54:03 am »









Dioptrice, the Somnium manuscript, and other work



In the years following the completion of Astronomia Nova, most of Kepler's research was focused on preparations for the Rudolphine Tables and a comprehensive set of ephemerides (specific predictions of planet and star positions) based on the table (though neither would be completed for many years). He also attempted (unsuccessfully) to begin a collaboration with Italian astronomer Giovanni Antonio Magini. Some of his other work dealt with chronology, especially the dating of events in the life of Jesus, and with astrology, especially criticism of dramatic predictions of catastrophe such as those of Helisaeus Roeslin.

Kepler and Roeslin engaged in series of published attacks and counter-attacks, while physician Philip Feselius published a work dismissing astrology altogether (and Roeslin's work in particular). In response to what Kepler saw as the excesses of astrology on the one hand and overzealous rejection of it on the other, Kepler prepared Tertius Interveniens (Third-party Interventions). Nominally this work — presented to the common patron of Roeslin and Feselius — was a neutral mediation between the feuding scholars, but it also set out Kepler's general views on the value of astrology, including some hypothesized mechanisms of interaction between planets and individual souls. While Kepler considered most traditional rules and methods of astrology to be the "evil-smelling dung" in which "an industrious hen" scrapes, there was "also perhaps a good little grain" to be found by the conscientious scientific astrologer.

In the first months of 1610, Galileo Galilei — using his powerful new telescope — discovered four satellites orbiting Jupiter. Upon publishing his account as Sidereus Nuncius (Starry Messenger), Galileo sought the opinion of Kepler, in part to bolster the credibility of his observations. Kepler responded enthusiastically with a short published reply, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger). He endorsed Galileo's observations and offered a range of speculations about the meaning and implications of Galileo's discoveries and telescopic methods, for astronomy and optics as well as cosmology and astrology. Later that year, Kepler published his own telescopic observations of the moons in Narratio de Jovis Satellitibus, providing further support of Galileo. To Kepler's disappointment, however, Galileo never published his reactions (if any) to Astronomia Nova.

After hearing of Galileo's telescopic discoveries, Kepler also started a theoretical and experimental investigation of telescopic optics using a telescope borrowed from Duke Ernest of Cologne.  The resulting manuscript was completed in September of 1610 and published as Dioptrice in 1611. In it, Kepler set out the theoretical basis of double-convex converging lenses and double-concave diverging lenses — and how they are combined to produce a Galilean telescope — as well as the concepts of real vs. virtual images, upright vs. inverted images, and the effects of focal length on magnification and reduction. He also described an improved telescope — now known as the astronomical or Keplerian telescope — in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.
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« Reply #17 on: October 25, 2008, 10:55:12 am »



One of the diagrams from Strena Seu de Nive Sexangula,
illustrating the Kepler conjecture








Around 1611, Kepler circulated a manuscript of what would eventually be published (posthumously) as Somnium (The Dream). Part of the purpose of Somnium was to describe what practicing astronomy would be like from the perspective of another planet, to show the feasibility of a non-geocentric system. The manuscript, which disappeared after changing hands several times, described a fantastic trip to the moon; it was part allegory, part autobiography, and part treatise on interplanetary travel (and is sometimes described as the first work of science fiction).

Years later, a distorted version of the story may have instigated the witchcraft trial against his mother,
as the mother of the narrator consults a demon to learn the means of space travel. Following her eventual acquittal, Kepler composed 223 footnotes to the story — several times longer than the actual text — which explained the allegorical aspects as well as the considerable scientific content (particularly regarding lunar geography) hidden within the text.

As a New Year's gift that year, he also composed for his friend and some-time patron Baron Wackher von Wackhenfels a short pamphlet entitled Strena Seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow). In this treatise, he investigated the hexagonal symmetry of snowflakes and, extending the discussion into a hypothetical atomistic physical basis for the symmetry, posed what later became known as the Kepler conjecture, a statement about the most efficient arrangement for packing spheres.
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« Reply #18 on: October 25, 2008, 11:00:27 am »










Personal and political troubles



In 1611, the growing political-religious tension in Prague came to a head. Emperor Rudolph — whose health was failing — was forced to abdicate as King of Bohemia by his brother Matthias. Both sides sought Kepler's astrological advice, an opportunity he used to deliver conciliatory political advice (with little reference to the stars, except in general statements to discourage drastic action). However, it was clear that Kepler's future prospects in the court of Matthias were dim.

Also in that year, Barbara Kepler contracted Hungarian spotted fever, then began having seizures. As Barbara was recovering, Kepler's three children all fell sick with smallpox; Friedrich, 6, died. Following
his son's death, Kepler sent letters to potential patrons in Württemberg and Padua. At the University
of Tübingen in Württemberg, concerns over Kepler's perceived Calvinist heresies in violation of the Augsburg Confession and the Formula of Concord prevented his return.

The University of Padua — on the recommendation of the departing Galileo — sought Kepler to fill
the mathematics professorship, but Kepler, preferring to keep his family in German territory, instead travelled to Austria to arrange a position as teacher and district mathematician in Linz. However, Barbara relapsed into illness and died shortly after Kepler's return.

Kepler postponed the move to Linz and remained in Prague until Rudolph's death in early 1612, though between political upheaval, religious tension, and family tragedy (along with the legal dispute over his wife's estate), Kepler could do no research. Instead, he pieced together a chronology manuscript, Eclogae Chronicae, from correspondence and earlier work. Upon succession as Holy Roman Emperor, Matthias re-affirmed Kepler's position (and salary) as imperial mathematician but allowed him to move
to Linz.
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« Reply #19 on: October 25, 2008, 11:04:07 am »









Linz and elsewhere (1612–1630)



In Linz, Kepler's primary responsibilities (beyond completing the Rudolphine Tables) were teaching
at the district school and providing astrological and astronomical services. In his first years there,
he enjoyed financial security and religious freedom relative to his life in Prague — though he was excluded from Eucharist by his Lutheran church over his theological scruples. His first publication
in Linz was De vero Anno (1613), an expanded treatise on the year of Christ's birth; he also parti-
cipated in deliberations on whether to introduce Pope Gregory's reformed calendar to Protestant German lands; that year he also wrote the influential mathematical treatise Nova stereometria
doliorum vinariorum, on measuring the volume of containers such as wine barrels (though it would
not be published until 1615).






Second marriage



On October 30, 1613, Kepler married the twenty-four-year-old Susanna Reuttinger.

Following Barbara's death, Kepler had considered eleven different matches.

He eventually returned to Reuttinger (the fifth match) who, he wrote, "won me over with love,
humble loyalty, economy of household, diligence, and the love she gave the stepchildren."

The first three children of this marriage (Margareta Regina, Katharina, and Sebald) died in childhood.

Three more survived into adulthood: Cordula (b. 1621); Fridmar (b. 1623); and Hildebert (b. 1625).

According to Kepler's biographers, this was a much happier marriage than his first.
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« Reply #20 on: October 25, 2008, 11:06:59 am »









Epitome of Copernican Astronomy, calendars, and the witch trial of Kepler's mother



Since completing the Astronomia nova, Kepler had intended to compose an astronomy textbook.

In 1615, he completed the first of three volumes of Epitome astronomia Copernicanae (Epitome of Copernican Astronomy); the first volume (books I-III) was printed in 1617, the second (book IV) in 1620, and the third (books V-VII) in 1621. Despite the title, which referred simply to heliocentrism, Kepler's textbook culminated in his own ellipse-based system. Epitome became Kepler's most influential work. It contained all three laws of planetary motion and attempted to explain heavenly motions through physical causes.  Though it explicitly extended the first two laws of planetary motion (applied to Mars in Astronomia nova) to all the planets as well as the Moon and the Medicean satellites of Jupiter, it did not explain how elliptical orbits could be derived from observational data.

As a spin-off from the Rudolphine Tables and the related Ephemerides, Kepler published astrological calendars, which were very popular and helped offset the costs of producing his other work — especially when support from the Imperial treasury was withheld. In his calendars — six between 1617 and 1624 — Kepler forecast planetary positions and weather as well as political events; the latter were often cannily accurate, thanks to his keen grasp of contemporary political and theological tensions. By 1624, however, the escalation of those tensions and the ambiguity of the prophecies meant political trouble for Kepler himself; his final calendar was publicly burned in Graz.

 




Geometrical harmonies in the regular polygons from Harmonices Mundi (1619).



The iconic frontispiece to the Rudolphine Tables celebrates the great astronomers of the past:

Hipparchus, Ptolemy, Copernicus, and most prominently, Tycho Brahe.


In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Cristoph, claimed Kepler's mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617, Katharina was accused of witchcraft; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620 she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler. The accusers had no stronger evidence than rumors, along with a distorted, second-hand version of Kepler's Somnium, in which a woman mixes potions and enlists the aid of a demon. However, Katharina 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 to focus on his "harmonic theory". The result, published in 1619, was Harmonices Mundi ("Harmony of the Worlds").
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« Reply #21 on: October 25, 2008, 11:08:18 am »



A hand-annotated illustration plate from Johannes Kepler's
Harmonice mundi (1619), showing the perfect solids.

source:
http://hsci.cas.ou.edu/digitized/16thCentury/Kepler/1619/Kepler-1619-pl-3-image/
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« Reply #22 on: October 25, 2008, 11:11:38 am »










Harmonices Mundi



Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world."[54] In Harmony, he attempted to explain the proportions of the natural world — particularly the astronomical and astrological aspects — in terms of music. The central set of "harmonies" was the musica universalis or "music of the spheres," which had been studied by Pythagoras, Ptolemy and many others before Kepler; in fact, soon after publishing Harmonices Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.

Kepler began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler's solids. From there, he extended his harmonic analysis to music, meteorology and astrology; harmony resulted from the tones made by the souls of heavenly bodies — and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler — with Tycho's data and his own astronomical theories — treated them much more precisely and attached
new physical significance to them.

Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion. He then tried many combinations until he discovered that (approximately) "The square of the periodic times are to each other as the cubes of the mean distances." However, the wider significance for planetary dynamics of this purely kinematical law was not realized until the 1660s. For when conjoined with Christian Huygens' newly discovered law of centrifugal force it enabled Isaac Newton, Edmund Halley and perhaps Christopher Wren and Robert Hooke to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them.  This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall
is uniformly accelerated, and also by Galileo's student Borrelli in his 1666 celestial mechanics.
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« Reply #23 on: October 25, 2008, 11:12:49 am »



The iconic frontispiece to the Rudolphine Tables
celebrates the great astronomers of the past:


Hipparchus,

Ptolemy,

Copernicus, and most prominently,

Tycho Brahe.
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« Reply #24 on: October 25, 2008, 11:15:29 am »



Kepler's horoscope for General WallensteinIn 1628, following the military successes of the Emperor Ferdinand's armies under General Wallenstein, Kepler became an official adviser to Wallenstein.








Rudolphine Tables and Kepler's last years



In 1623, Kepler at last completed the Rudolphine Tables, which at the time was considered his major work. However, due to the publishing requirements of the emperor and negotiations with Tycho Brahe's heir, it would not be printed until 1627. In the meantime religious tension — the root of the ongoing Thirty Years' War — once again put Kepler and his family in jeopardy. In 1625, agents of the Catholic Counter-Reformation placed most of Kepler's library under seal, and in 1626 the city of Linz was besieged. Kepler moved to Ulm, where he arranged for the printing of the Tables at his own expense.

 

Though not the general's court astrologer per se, Kepler provided astronomical calculations for Wallenstein's astrologers and occasionally wrote horoscopes himself. In his final years, Kepler spent much of his time traveling, from court in Prague to Linz and Ulm to a temporary home in Sagan, and finally to Regensburg.

Soon after arriving in Regensburg, Kepler fell ill. He died on November 15, 1630, and was buried there; his burial site was lost after the army of Gustavus Adolphus destroyed the churchyard.
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« Reply #25 on: October 25, 2008, 11:21:00 am »









Reception of Kepler's astronomy



Kepler's laws were not immediately accepted. Several major figures such as Galileo and René Descartes completely ignored Kepler's Astronomia nova. Many astronomers, including Kepler's teacher, Michael Maestlin, objected to Kepler's introduction of physics into his astronomy. Some adopted compromise positions. Ismael Boulliau accepted elliptical orbits but replaced Kepler's area law with uniform motion in respect to the empty focus of the ellipse while Seth Ward used an elliptical orbit with motions defined by an equant.

Several astronomers tested Kepler's theory, and its various modifications, against astronomical observations. Two transits of Venus and Mercury across the face of the sun provided sensitive tests
of the theory, under circumstances when these planets could not normally be observed. In the case of the transit of Mercury in 1631, Kepler had been extremely uncertain of the parameters for Mercury, and advised observers to look for the transit the day before and after the predicted date. Pierre Gassendi observed the transit on the date predicted, a confirmation of Kepler's prediction.[64] This was the first observation of a transit of Mercury. However, his attempt to observe the transit of Venus just one month later, was unsuccessful due to inaccuracies in the Rudolphine Tables. Gassendi did not realize that it was not visible from most of Europe, including Paris.[65] Jeremiah Horrocks, who observed the 1639 Venus transit, had used his own observations to adjust the parameters of the Keplerian model, predicted the transit, and then built apparatus to observe the transit. He remained a firm advocate of the Keplerian model.

Epitome of Copernican Astronomy was read by astronomers throughout Europe, and following Kepler's death it was the main vehicle for spreading Kepler's ideas. Between 1630 and 1650, it was the most widely used astronomy textbook, winning many converts to ellipse-based astronomy.  However, few adopted his ideas on the physical basis for celestial motions. In the late seventeenth century, a number of physical astronomy theories drawing from Kepler's work — notably those of Giovanni Alfonso Borelli and Robert Hooke — began to incorporate attractive forces (though not the quasi-spiritual motive species postulated by Kepler) and the Cartesian concept of inertia. This culminated in Isaac Newton's Principia Mathematica (1687), in which Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation.
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« Reply #26 on: October 25, 2008, 11:28:18 am »



PRAGUE
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« Reply #27 on: October 25, 2008, 11:32:37 am »



The GDR stamp featuring Johannes Kepler.









Kepler's historical and cultural legacy
 


Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the philosophy and historiography of science. Kepler and his laws of motion were central to early histories of astronomy such as Jean Etienne Montucla’s 1758 Histoire des mathématiques and Jean-Baptiste Delambre's 1821 Histoire de l’astronomie moderne. These and other histories written
from an Enlightenment perspective treated Kepler's metaphysical and religious arguments with skepticism and disapproval, but later Romantic-era natural philosophers viewed these elements as central to his success. William Whewell, in his influential History of the Inductive Sciences of 1837, found Kepler to be the archetype of the inductive scientific genius; in his Philosophy of the Inductive Sciences of 1840, Whewell held Kepler up as the embodiment of the most advanced forms of scientific method. Similarly, Ernst Friedrich Apelt — the first to extensively study Kepler's manuscripts, after their purchase by Catherine the Great — identified Kepler as a key to the "Revolution of the sciences".
Apelt, who saw Kepler's mathematics, aesthetic sensibility, physical ideas, and theology as part of a unified system of thought, produced the first extended analysis of Kepler's life and work.

Modern translations of a number of Kepler's books appeared in the late-nineteenth and early-twentieth centuries, the systematic publication of his collected works began in 1937 (and is nearing completion in the early twenty-first century), and Max Caspar's seminal Kepler biography was published in 1948. However, Alexandre Koyré's work on Kepler was, after Apelt, the first major milestone in historical interpretations of Kepler's cosmology and its influence. In the 1930s and 1940s Koyré, and a number of others in the first generation of professional historians of science, described the "Scientific Revolution" as the central event in the history of science, and Kepler as a (perhaps the) central figure in the revolution. Koyré placed Kepler's theorization, rather than his empirical work, at the center of the intellectual transformation from ancient to modern world-views. Since the 1960s, the volume of historical Kepler scholarship has expanded greatly, including studies of his astrology and meteorology, his geometrical methods, the role of his religious views in his work, his literary and rhetorical methods, his interaction with the broader cultural and philosophical currents of his time, and even his role as an historian of science.
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« Reply #28 on: October 25, 2008, 11:36:44 am »



10 euro Johannes Kepler silver coin.








The debate over Kepler's place in the Scientific Revolution has also spawned a wide variety of philosophical and popular treatments. One of the most influential is Arthur Koestler's 1959 The Sleepwalkers, in which Kepler is unambiguously the hero (morally and theologically as well as intellectually) of the revolution.

Influential philosophers of science — such as Charles Sanders Peirce, Norwood Russell Hanson, Stephen Toulmin, and Karl Popper — have repeatedly turned to Kepler: examples of incommensurability, analogical reasoning, falsification, and many other philosophical concepts have been found in Kepler's work.

Physicist Wolfgang Pauli even used Kepler's priority dispute with Robert Fludd to explore the implications of analytical psychology on scientific investigation.

A well-received, if fanciful, historical novel by John Banville, Kepler (1981), explored many of the themes developed in Koestler's non-fiction narrative and in the philosophy of science.

Somewhat more fanciful is a recent work of nonfiction, Heavenly Intrigue (2004), suggesting that Kepler murdered Tycho Brahe to gain access to his data. 

Kepler has acquired a popular image as an icon of scientific modernity and a man before his time; science popularizer Carl Sagan described him as "the first astrophysicist and the last scientific astrologer."

In Austria, Johannes Kepler has left behind such a historical legacy that he was one of the motifs of one of the most famous silver collector's coins: the 10-euro Johannes Kepler silver coin, minted in September 10, 2002. The reverse side of the coin has a portrait of Kepler, who spent some time teaching in Graz and the surrounding areas. Kepler was acquainted with Hans Ulrich von Eggenberg personally, and he probably influenced the construction of Eggenberg Castle (the motif of the obverse of the coin). In front of him on
the coin is the model of nested spheres and polyhedra from Mysterium Cosmographicum.
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« Reply #29 on: October 25, 2008, 11:43:16 am »









Works



Mysterium cosmographicum (The Sacred Mystery of the Cosmos) (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)

Tertius Interveniens (Third-party Interventions) (1610)

Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610)
 
Dioptrice (1611)
 
De nive sexangula (On the Six-Cornered Snowflake) (1611)

De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit (1613)

Eclogae Chronicae (1615, published with Dissertatio cum Nuncio Sidereo)

Nova stereometria doliorum vinariorum (New Stereometry of Wine Barrels) (1615)

Epitome astronomiae Copernicanae (Epitome of Copernican Astronomy) (published in three parts from 1618–1621)

Harmonice Mundi (Harmony of the Worlds) (1619)
 
Mysterium cosmographicum (The Sacred Mystery of the Cosmos) 2nd Edition (1621)
 
Tabulae Rudolphinae (Rudolphine Tables) (1627)

Somnium (The Dream) (1634)







See also



Heliocentrism

History of astronomy

History of physics

Kepler conjecture

Kepler-Poinsot polyhedra

Kepler's laws of planetary motion

Kepler triangle

Keplerian problem

Scientific Revolution
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