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Science & Technology => History of Science => Topic started by: Bianca on October 25, 2008, 09:38:56 am

Post by: Bianca on October 25, 2008, 09:38:56 am

A 1610 portrait of Johannes Kepler by an unknown artist


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


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


Styria; Bohemia;
Upper Austria


Mathematics and
Natural Philosophy


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

Religious stance


Post by: Bianca 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.

Post by: Bianca 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.



Post by: Bianca on October 25, 2008, 09:51:25 am

Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum

Post by: Bianca on October 25, 2008, 09:53:11 am


                          CLOSE UP OF THE INNER SECTION

Post by: Bianca 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.

Post by: Bianca 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).

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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).

Post by: Bianca on October 25, 2008, 10:25:49 am

Remnant of Kepler's Supernova SN 1604

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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).

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca 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").

Post by: Bianca on October 25, 2008, 11:08:18 am

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


Post by: Bianca 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.

Post by: Bianca on October 25, 2008, 11:12:49 am

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



Copernicus, and most prominently,

Tycho Brahe.

Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca on October 25, 2008, 11:28:18 am


Post by: Bianca 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.

Post by: Bianca 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.

Post by: Bianca on October 25, 2008, 11:43:16 am


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


History of astronomy

History of physics

Kepler conjecture

Kepler-Poinsot polyhedra

Kepler's laws of planetary motion

Kepler triangle

Keplerian problem

Scientific Revolution

Post by: Bianca on October 25, 2008, 11:45:09 am


Named in Kepler's honour

Kepler Space Observatory, a solar-orbiting, planet-hunting telescope due to be launched by NASA in 2009

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, a crater on the moon

Kepler, a crater on Mars

1134 Kepler, 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.

Kepler College, Seattle, Washington

Keplerstraße in Hanau near Frankfurt am Main

Keplerstraße and Keplerbrücke in Graz, Austria

Kepler Launch Site

Keplerplatz, a station on the U1 line of the Vienna U-Bahn rapid transit (Metro) system

Johannes Kepler Grammar School , Prague, Czech Republic near the place Kepler lived while in Prague

Two rockets, the Kepler and the Kepler II, appear in Kim Possible episodes Car Alarm and Graduation respectively.

Kepler Mission, a NASA mission to observe extra-solar planets from space.

Post by: Bianca on October 25, 2008, 11:47:36 am


Post by: Bianca on October 25, 2008, 12:48:50 pm

"The heavenly motions...

are nothing but a continuous song for several voices,

perceived not by the ear but by the intellect,

a figured music which sets landmarks

in the immeasurable flow of time."

John Banville:


(Minerva 1990)

Post by: Bianca on October 25, 2008, 12:52:57 pm

Kepler's Background

Johannes Kepler was born on 6th January 1572 (NS) at Weil-der-Stadt in the German province of Swabia. His grandfather had been mayor of the town but the Kepler family fortunes were in decline. His father was a bullying adventurer who earned a precarious living as a mercenary soldier and deserted the family when Johannes was 17. His mother, an inn-keeper's daughter, had a reputation for witchcraft.

Born prematurely, Johannes was weak and sickly. He spent a solitary, unhappy childhood, but at least he was fortunate in that the ruling Dukes of Württemburg had created a relatively enlightened system of education in Swabia. With a view to recruiting the brightest minds for the Protestant clergy, a system of grants and scholarships was available to promising (male) children of poor families, and despite his ill health, Johannes was precociously brilliant.

His schooldays, though academically successful, were thoroughly miserable. His know-all cleverness irritated his classmates, who frequently beat him up. He considered himself physically repulsive (admitting to 'a dog-like horror of baths'), thoroughly unlikeable, an outsider. He turned to the world of ideas for escape and found solace in an abiding religious conviction.

In 1587 Kepler went to Tübingen University where he proved to be an excellent mathematician. He also became an advocate of the controversial Copernican theory of the solar system, which he often defended in public debates. At that time Kepler was not particularly interested in astronomy. The idea of a Sun-centred universe had a mystical appeal. He intended to become a clergyman and when he graduated in 1591 he entered the Tübingen faculty of theology. Before taking his final examinations, however, he was recommended for the vacant post of teacher of mathematics and astronomy at the Protestant school at Graz in Austria, which he took up in April 1594, aged 23. There were no clear distinctions between astronomy and astrology; amongst his duties as 'mathematicus' Kepler was expected to issue an annual almanac of astrological predictions. In his first almanac he predicted an exceptionally cold winter and a Turkish incursion into Austria. When both predictions proved correct, he unexpectedly gained a reputation as a prophet.

Post by: Bianca on October 25, 2008, 12:54:08 pm

The Cosmic Mystery


On 19th July 1595 (NS), a sudden revelation changed the course of Kepler's life. In preparation for a geometry class he had drawn a figure on the blackboard of an equilateral triangle within a circle with a second circle inscribed within it. He realised that the ratio of the two circles replicated the ratio of the orbits of Jupiter and Saturn. In a flash of inspiration, he saw the orbits of all the planets around the Sun arranged so that regular geometric figures would fit neatly between them. He tested this intuition using two-dimensional plane figures — the triangle, square, pentagon, etc. — but this didn't work. As space is three-dimensional, he went on to experiment with three-dimensional geometric solids.

Ancient Greek geometers knew that the number of solids that can be constructed from regular geometric figures is limited to five. They are known variously as the 'perfect', 'Pythagorean' or 'Platonic' solids. Kepler speculated that one of the five solids could be inserted between each concentric planetary sphere. This seemed to explain why there were just six planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn) with five intervals separating them, and why the intervals were so irregular. Convinced that he had discovered a subtle geometric relationship between the diameters of the planetary orbits and their distances from the Sun, Kepler wrote Mysterium Cosmographicum ('the cosmic mystery'), published in 1596. The scheme worked reasonably well with the planetary distances then accepted, but even Kepler could see that it wasn't perfect. Assuming that better data on planetary orbits would bear out his theory, he devoted the rest of his life to justifying his vision through scientific observation and hard mathematical proofs.

Post by: Bianca on October 25, 2008, 12:56:41 pm


The five 'Platonic' solids:

the tetrahedron (comprising four triangles);

the cube (six squares);

octohedron (eight triangles);

dodecahedron (twelve pentagons)

and isosahedron

(twenty triangles)

Post by: Bianca on October 25, 2008, 12:58:45 pm

In pursuing his quest to pin down the cosmic mystery, Kepler transcended formidable obstacles in his personal and professional life and rose to become one of the immortal names in European astronomy. [1]

His greatest achievement was the formulation of the Laws of Planetary Motion which made a fundamental break with astronomical tradition in describing the orbits of the planets as elliptical rather than circular and in recognising that a planet's speed is not uniform but varies at different stages of its orbit. The first two Laws were announced in l609 in Astronomia Nova ('the new astronomy'). It took a further nine years to formulate the Third Law which established a relationship between a planet's distance from the Sun and the time it takes to complete an orbit. This was announced in Harmonice Mundi ('harmony of the world'), published 16l8. Collectively Kepler's Laws superseded the ancient Ptolemaic concept of a spherical universe with epicyclic motion. They provided the foundation upon which Isaac Newton was to build his epoch-making theory of universal gravitation towards the end of the 17th century.

To Kepler himself, however, the planetary laws represented far more than the description of a physical mechanism. In the tradition of the legendary Greek philosopher Pythagoras (6th century BC), Kepler did not view science and spirituality as mutually exclusive. The deeper significance of Kepler's Laws is that they reconcile the emerging vision of a Sun-centred planetary system with the ancient Pythagorean concept of armonia, or universal harmony.

Post by: Bianca on October 25, 2008, 12:59:42 pm

Celestial Harmony

Pythagoras discovered that the pitch of a musical note depends upon the length of the string which produces it. This allowed him to correlate the intervals of the musical scale with simple numerical ratios. When a musician plays a string stopped exactly half-way along its length an octave is produced. The octave has the same quality of sound as the note produced by the unstopped string but, as it vibrates at twice the frequency, it is heard at a higher pitch. The mathematical relationship between the keynote and its octave is expressed as a 'frequency ratio' of 1:2. In every type of musical scale, the notes progress in a series of intervals from a keynote to the octave above or below. Notes separated by intervals of a perfect fifth (ratio 2:3) and a perfect fourth (3:4) have always been the most important 'consonances' in western music. In recognising these ratios, Pythagoras had discovered the mathematical basis of musical harmony.

In one sense Pythagoras had also invented western science. By associating measurements of length with musical tones he made the first known reduction of a quality (sound) into a quantity (length and ratio). The understanding of nature through mathematics remains a primary objective of science today. But Pythagoras also recognised that the musical octave is the simplest and most profound expression of the relationship between spirit and matter. The 'miracle of the octave' is that it divides wholeness into two audibly distinguishable parts, yet remains recognisable as the same musical note — a tangible manifestation of the hermetic maxim 'as above, so below'. The short-lived but profoundly influential Pythagorean Brotherhood sought to unite "religion and science, mathematics and music, medicine and cosmology, body, mind and spirit in an inspired and luminous synthesis". [2]

The Pythagoreans used music to heal the body and to elevate the soul, yet they believed that earthly music was no more than a faint echo of the universal 'harmony of the spheres'. In ancient cosmology, the planetary spheres ascended from Earth to Heaven like the rungs of a ladder. Each sphere was said to correspond to a different note of a grand musical scale. The particular tones emitted by the planets depended upon the ratios of their respective orbits, just as the tone of a lyre-string depended upon its length. Another type of celestial scale related the planetary tones to their apparent rates of rotation around the Earth. The music of the spheres was never a fixed system of correspondences. Many variant schemes existed because each philosopher would necessarily approach it from a slightly different perspective.

The musicologist Joscelyn Godwin comments,

"...the celestial harmony of the solar system... is of a scope and harmonic complexity that no single approach can

exhaust. The nearest one can come to understanding it as a whole is to consider some great musical work and think

 of the variety of analytical approaches that could be made to it, none of them embracing anything like the whole."


Post by: Bianca on October 25, 2008, 01:02:04 pm


Plato, Pliny, Cicero and Ptolemy are amongst the philosophers of the ancient world who contemplated the music of the spheres. The doctrine was transmitted to medieval Europe where it found its most glorious expression in the architecture of great abbeys and cathedrals consciously designed to conform to the proportions of musical and geometric harmony. The English hermeticist Robert Fludd (1574-1637) visualised grand celestial scales spanning three octaves and linking levels of existence from the sub-planetary elemental worlds to exultant choirs of angelic intelligences beyond the stars. The beautiful engravings which illustrate Fludd's encyclopaedic works are amongst the most comprehensive descriptions of pre-Copernican cosmology ever devised. [4]

The ideals of Pythagorean harmony inspired Copernicus himself. Nicholas Copernicus (1473-1543) spent most of his life in the fortified city of Frauenburg in Prussia fulfilling administrative duties as a canon of the cathedral chapter and devoting the rest of his time to contemplation of the cosmic harmonies. The cumbersome mathematics of the Ptolemaic system, with its maze of epicycles grafted on to reconcile various observational discrepancies, offended his Pythagorean sense of proportion. He realised that a Sun-centred planetary system not only gave better predictions of celestial motion but could also he expressed through more elegant geometry — to the greater glory of God the Creator.

Kepler's early enthusiasm for the Copernican system was inspired by the same sense of idealism. He could readily accept the Sun as the centre of the planetary system, but the necessity of rejecting circular orbits came as something of a shock. The circle is an archetypal symbol of harmony and perfection; Kepler recoiled with disgust when an unsightly bulge began to emerge from his analysis of the orbit of Mars. Yet the elliptical orbits eventually revealed a scheme of celestial harmony more subtle and profound than any that had gone before.

Kepler's, First Law states that the planets move in ellipses and that the Sun is not at the exact centre of their orbits. Each planet moves between a 'perihelion' point nearest the Sun and an 'aphelion' point furthest away. The Second Law states that the planets move faster at perihelion than at aphelion. Kepler measured their angular velocities at these extremes (i.e. how far they travel in 24 hours in minutes and seconds of arc as viewed from the Sun) and expressed this ratio as a musical interval. Saturn, for instance, moves at a rate of 106" per day at aphelion and l35" at perihelion. Cancelled down, the ratio 106:135 differs by only two seconds from 4:5 — equivalent to the interval of a major third. Kepler found that the angular velocities of all the planets closely correspond to musical intervals. When he compared the extremes for combined pairs of planets the results were even more marvellous, yielding the intervals of a complete scale. Thus, the ratio between Jupiter's maximum and Mars' minimum speed corresponds, to a minor third; the interval between Earth and Venus to a minor sixth. Rather than the fixed-tone planetary scales of earlier schemes, Kepler's measurements revealed ever-changing polyphonic chords and harmonies as the planets move between perihelion and aphelion. Furthermore, he had shifted the focus of celestial harmony from the Earth to the Sun: "Henceforth it is no longer a harmony made for the benefit of our planet, but the song which the cosmos sings to its lord and centre, the Solar Logos". [5]

Scientific materialists have tended to dismiss the spiritual dimension to Kepler's work as either the remnants of a deeply-ingrained 'medievalism' which he was unable to shake off or, even less charitably, as the fantasies of an over-worked mind. His vision of the music of the spheres, however, is based upon the hard facts of astronomical measurement. The astronomer Fred Hoyle agrees that the correspondence between musical ratios and planetary velocities as described by Kepler is "frighteningly good". [6] The Kepler scholar Francis Warrain extended Kepler's researches and found that the angular velocities of Uranus, Neptune and Pluto, which were unknown during Kepler's lifetime, also correspond to harmonic ratios. The music of the spheres is more than a beautiful poetic intuition. The dynamics of the solar system, first laid bare by Kepler's mathematical genius, are directly analogous to the laws of musical harmony.

Post by: Bianca on October 25, 2008, 01:04:23 pm

                                                      Kepler and Astrology

Although he first became famous for the accuracy of his predictions and scored an impressive number of 'hits' during his career, Kepler's attitude to conventional astrology was ambivalent and complex. In attempting to disentangle it, we can at least begin by dismissing the notion that he rejected astrology out-of-hand. In the official history of scientific progress, the values of the Age of Reason and Industrial Revolution were projected onto the brilliant mathematician who had unravelled the laws of planetary motion. It seemed inconceivable that he could be tainted with the medieval superstition of astrology. Like Isaac Newton's passion for alchemy and theology, this aberration was best glossed over or, as actually happened in Kepler's case, twisted into a distortion of the truth.

Kepler's famous metaphor comparing astrology to the 'foolish daughter' of the 'wise mother' (astronomy) has often been cited as evidence of his disbelief. Seen in context, however, the foolish daughter represents a particular style of astrology — popular astrology — which was not to Kepler's taste. He was always careful to distinguish his reverential vision of the celestial harmonies from the practices of the backstreet astrologers and almanac-makers "who prefer to engage in mad ravings with the uneducated masses".[7] Kepler's astrology was on another plane altogether. Before condemning him for his blatant intellectual snobbery, however, consider how many 'serious' astrologers today feel exactly the same way about Sun-sign columns. Kepler was neither the first nor the last astrologer to pour scorn on those who practise apparently inferior forms of the art. His disapproval stems from his conviction that astrology is nothing less than a divine revelation, "...a testimony of God's works and... by no means a frivolous thing". Unfortunately, Kepler's salary as Imperial Mathematicus was rarely paid (the Imperial treasury owed him 20,000 florins by the end of his career) so he was obliged to scratch out a living by giving astrological advice to wealthy clients and composing astrological almanacs for the 'uneducated masses' he so despised. Reluctantly, Kepler conceded that "the mother would starve if the daughter did not earn anything". In another famous turn of phrase, he warned those learned professors who had grown sceptical of astrology that they were likely to "throw the baby out together with the bathwater" if they rejected it entirely.

So Kepler was undoubtedly an astrologer — but he was no respecter of astrological tradition. His ideas seem radical even by the standards of mainstream astrology today. For a start, he dismissed the use of the 12 houses as 'Arabic sorcery'. While accepting that the angles were important, he could see no justification for conventional house division. "Demonstrate the old houses to me," he wrote to one of his correspondents, "Explain their number; prove that there can be neither fewer nor more... show me undoubted and striking examples of their influence." [8] He even went so far as to question the validity of the signs of the zodiac, arguing that they were derived from human reasoning and arithmetical convenience rather than any natural division of the heavens.[9] He had no time for elaborate schemes of planetary sign rulership and saw no reason why some planets should be classed as benefic and others as malefic.

Kepler left no astrological convention unchallenged. His rigorous questioning hints at a massive reformation of astrology, on a scale which Ken Negus has compared to the reformation that Martin Luther brought about in the Church. Kepler's great attempt to purge astrology seems to echo the Pythagorean katharsis — a frenzied purification of the soul undertaken in order to restore divine harmony. More prosaically, it should be seen in the context of the monumental changes taking place in theoretical astronomy during the 16th and 17th centuries. The ancient Aristotelian doctrines that had given astrology some measure of scientific credibility were crumbling fast. Copernicus had displaced the Earth from the centre of the universe; Tycho had proved that the 'immutable' heavens were subject to change as new stars blazed in the sky; Galileo's telescope had opened up dimensions undreamt of by Ptolemy; Kepler himself had shattered the serene, circular motions of the planetary orbits forever. He sensed that astrology would have to adjust to the new astronomy if it were to keep pace with the march of science.

Post by: Bianca on October 25, 2008, 01:05:31 pm

The New Aspects

The key to Kepler's proposed reform is his approach to the aspects. Traditional astrology recognises five significant relationships, based upon the twelvefold division of the zodiac signs. Ptolemy taught that their significance was derived by analogy with the ratios of the musical scale.[10] The conjunction is equivalent to the same two notes played in unison. The opposition divides the circle in the ratio 1:2, which corresponds to the octave. The sextile (5:6) corresponds to a minor third, the square (3:4) to a perfect fourth and the trine (2:3) to a perfect fifth. By placing less emphasis upon the zodiac signs, however, Kepler was free to explore additional aspect relationships in his pursuit of the Pythagorean synthesis of music, geometry and astronomy.

Kepler's new aspects were based upon harmonic theory and grounded in empirical observation of astrological effects. From his long-term study of weather conditions correlated with planetary angles and from detailed analysis of his collection of 800 birth charts, Kepler concluded that when planets formed angles equivalent to particular harmonic ratios a resonance was set up, both in the archetypal 'Earth-soul' and in the souls of individuals born under those configurations. [11] He considered this 'celestial imprint' more important than the traditional emphasis on signs and houses: "in the vital power of the human being that is ignited at birth there glows that remembered image..." The geometric-harmonic imprint constitutes "the music that impels the listener to dance" as the movements of the planets, by transit and direction, echo and re-echo the natal theme. In addition to the Ptolemaic aspects, Kepler proposed the quintile (72°), bi-quintile (144°) and sesqui-quadrate (135°). Extending the analogy of the musical scale, the quintile is equivalent to an interval of a major third (4:5), the sesqui-quadrate to a minor sixth (5:8) and the bi-quintile to a major sixth (3:5).

Kepler realised that many more aspect configurations are possible, but rejected them on aesthetic grounds. The Ptolemaic aspects and his three new ones gave a pleasing correspondence with the consonances of the musical scale, other aspect ratios produced only discord. The mathematical principles of musical harmony are directly related to geometry — which Goethe described as 'frozen music'. Kepler rejected aspects based upon geometric figures like the 7-sided septagon and 9-sided nonagon because they cannot be constructed with straight-edge and compasses — the only instruments permissible in classical geometry. He regarded such figures as 'unknowable' and declared that "God did not employ the septagon and other figures of this species to embellish the world."[12]

The new aspects were soon adopted by astrologers, though perhaps not in quite the spirit that Kepler would have wished. William Lilly wrote Christian Astrology in 1647, less than 20 years after Kepler's death. In the section on the 'Effects of Directions', Lilly gives instructions for finding not only the quintile, bi-quintile and sesqui-quadrate, but also the semi-sextile (30°), semi-quintile (36°), semi-quadrate (45°) and sesqui-quintile (108°). His lengthy analysis of the directions in the chart of 'an English merchant' gives some early examples of the new aspects in practical interpretation.[13] The direction of the Midheaven to sesqui-quadrate Mars, for instance, "may endanger, in some small measure, our Native's repute with false aspersions". The Ascendant to quintile Mercury suggests that he "should now have rectified his books of accounts and receive much benefit from Mercurial men". The quintile-based aspects emerge as 'mildly beneficial' in their effects; the quadrate-based as 'slightly harmful' — which became the standard textbook interpretation of the 'minor aspects' from Lilly's time to the present.

More in line with Kepler's radical approach are the teachings of the 20th century Hamburg School which originated in l913 when the amateur astrologer Alfred Witte (1878-1941) was invited to give a talk to the Hamburg Kepler Circle.[14] Witte's system of 'planetary pictures', based upon midpoint combinations, was developed by Rheinhold Ebertin (1901-88), author of the indispensable Combination of Stellar Influences. The spirit of Kepler can also be glimpsed in harmonic astrology as developed by John Addey (1920—82), though with the interesting distinction that where Kepler looked to musical scales and harmonies, Addey's harmonic wave-forms are more suggestive of rhythm and tempo.

Though rarely articulated, the concept of universal harmony flows like an underground current through the philosophy of astrology down the ages. In this sense Johannes Kepler, the first 'modern' astrologer, belongs to a broader tradition which links such apparently diverse thinkers as Pythagoras and Ptolemy, Robert Fludd and John Addey, Gurdjieff and Rudolph Steiner. No-one can claim a monopoly on truth. Every astrologer, regardless of style or technique, is attuned to their own unique variation on the 'song of the angels', the all-pervading music of the spheres.

Post by: Bianca on October 25, 2008, 01:06:36 pm


Please note:

Larry Ely argues that the above chart is incorrect. In a message left in the guestbook he writes:

"He was born in Weil der Stadt, whose coordinates are 48n45; 8e53. Kepler gave his birth time as 2:30 pm

in Arthur Koestler, The Watershed. That time is Sun Time, or Local Apparent Time. The corresponding UT

is aproximately 14:01. The Mideaven is 21Aq54 and the Ascendant is 24Ge19. Kepler said his MC was in

the 22nd degree of Aquarius, and his AS was in the 25th degree of Gemini, so his given time of 2:30 pm

checks out. His angles may be need to be rectified by perhaps up to 15' arc, but judging from some

events and from a time composite to my chart, the angles above are accurate to about 5' arc, I think."

Post by: Bianca on October 25, 2008, 01:09:27 pm

Notes & References:

  1 ] The standard biography is Kepler by Max Caspar, translated by C. Doris Hellman (Collier-Mac, 1962). Try your local library. More readily available is Arthur Koestler's The Sleepwalkers (Peregrine Books, 1988) which contains a detailed study of Kepler' s troubled life and the development of his ideas. Also recommended is John Banville' s historical novel Kepler cited above.
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  2 ] Koestler, op cit. p. 27
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  3 ] Joscelyn Godwin: Harmonies of Heaven and Earth (Thames and Hudson 1987), p.130
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  4 ] For an annotated collection of Fludd's most important plates, see Robert Fludd: Hermetic Philosopher and Surveyor of Two Worlds by Joscelyn Godwin (Thames and Hudson 1979). Kepler and Fludd corresponded with one another, but Fludd regarded Kepler's mathematical approach to cosmology as superficial, while Kepler regarded Fludd's magical approach as superstitious.
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  5 ] Harmonies of Heaven and Earth p.145
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  6 ] Quoted in 'Kepler's Belief in Astrology' by Nick Kollerstrom. History and Astrology edited by A. Kitson (Unwin 1989), p.167.
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  7 ] Quoted in Kepler's Astrology: Excerpts, selected, translated and edited by Ken Negus (Eucopia Publications 1987). Unless otherwise stated, all quotes by Kepler himself are from this compilation.
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  8 ] From a letter to the astronomer David Fabricius quoted in Neo-Astrology: a Copernican Revolution by Michel Gauquelin (Arkana 1991), p.92
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  9 ] Kepler later qualified his criticism of the zodiac signs by remarking that, "...the human race has envisioned this partition from the time of the Chaldeans down to our own time". This being so, he wondered whether "God himself does not conform to it... and whether He does not wish to speak to human beings therewith in a language or method of communication that they understand".
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  10 ] Ptolemy: Tetrabiblos (Loeb) p.73-5. In Ptolemy's unfinished Harmonics, he proposed the earliest known 'tone-zodiac', linking the 12 signs to musical intervals. This idea has been explored by other astro-musical theorists, notably Rudolph Steiner.
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  11 ] Kepler' s belief in the ancient doctrine that the Earth as a whole may be regarded as a living entity is echoed in the 'Gaia principle' popularised by James Lovelock during the 1980s.
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  12 ] Koestler op. cit. p.396
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  13 ] William Lilly: Christian Astrology (1647, Regulus reprint 1984), p.785 et seq.
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  14 ] M. Harding and C. Harvey: Working with Astrology (Arkana 1990), p.11.
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Post by: Bianca on October 25, 2008, 01:11:20 pm

David Plant

is a respected scholar of the history and traditional practice of astrology.

He is also an expert on the English Civil War period and the life and work of the 17th century
astrologer William Lilly. He runs two very reputable websites:

the English Merlin site, which is devoted to all aspects of the life and times of William Lilly and his contemporaries; and

the British Civil Wars and Commonwealth site, which explores the turmoil of the Civil Wars and Interregnum, and the constitutional experiments of the Commonwealth and Protectorate period of
the 1650s.

Both sites are leading points of reference for their fields and a visit is strongly recommended.

© David Plant

Post by: Bianca on October 25, 2008, 01:16:04 pm

Post by: Bianca on October 25, 2008, 01:31:46 pm


Kepler’s house

Johannes Kepler came to join Tycho in Prague.

With Tycho’s observations Kepler was able to work out the laws of planetary motion.

He published the first two in Astronomia Nova in 1609 while he was living in a house in Karlova St.

Above is the plaque on the house.

Post by: Bianca on October 25, 2008, 01:39:34 pm


Johannes Kepler's Residence

This early Gothic house dates from 1250, making it the oldest completely preserved wooden house in Germany.

The small middle-class house at the corner of the lane named Am Schallern was the residence of mathematician and astronomer Johannes Kepler and his family in the years 1626 to 1628.

It was restored according to scientific rules in 1976 and 1977, and most of its substance has been preserved:

an early Gothic building and a treasured monument due to its architectural details, its location, and its historical significance.

Post by: Bianca on October 25, 2008, 01:40:07 pm


                              Mediating the Public’s Encounter with Science: The Kepler Salon


Astronomer Johannes Kepler lived in Linz from 1612 to 1627. His former residence at Rathausgasse 5—immediately adjacent to Linz’s Main Square—is now being revived in the spirit of science.

Kepler’s former apartment in downtown Linz is currently undergoing renovation.

A space on the 1st Upper Level will provide a setting for a Linz09 project entitled Kepler Salon, where the focus will be on science.

Research approaches and findings from the natural sciences and engineering, social sciences and cultural studies, as well as the field of medicine will be presented in entertaining fashion.

The Kepler Salon is designed as a showcase of work being done at Linz universities and research facilities, and as a site for up-close-and-personal encounters with the world of science on the part of the general public.

Taking up the tradition of the 18th-century literary salon, the accent will be on dialog and the exchange of ideas. The forms that these encounters will take range from disputations among experts, public experiments and Q&A sessions all the way to readings and discussions dealing with other Linz09 projects.

The Kepler Salon series of events will kick off in January 2009 and continue throughout the Capital of Culture year.

Post by: Bianca on October 25, 2008, 01:45:16 pm


LINZ - Kepler Haus

It was in this house between 1621 and 1626 that Johannes Kepler completed his work on the Tabulae Rudolfinae (a table of exacting measurements of the motions of the plantets). 

Kepler's laws of plantary motion have come to form the basis for all modern plantary astronomy and led Newton to his discovery of the law of gravitation.

His son, Hildebert, was baptised here 6 April 1625.

Post by: Bianca on October 25, 2008, 01:49:56 pm



Post by: Bianca on October 25, 2008, 01:57:17 pm