Tycho Brahe

Tycho Ottesen Brahe
Tycho Brahe.JPG
Born 14 December 1546
Knutstorp Castle, Scania, then Denmark, today Sweden
Died 24 October 1601 (aged 54)
Prague
Nationality Danish
Education Private
Occupation Nobleman, Astronomer
Spouse(s) Kirstine Barbara Jørgensdatter
Children 8
Parents Otte Brahe and Beate Bille
Monument of Tycho Brahe and Johannes Kepler in Prague

Tycho Brahe, born Tyge Ottesen Brahe (14 December 1546 Knutstorp Castle – 24 October 1601 Prague), was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations. Coming from Scania, then part of Denmark, now part of modern-day Sweden, Brahe was well known in his lifetime as an astronomer and alchemist.

The Latinized name Tycho Brahe is usually pronounced /ˈtaɪkoʊ ˈbrɑː/ or /ˈbrɑːhi/ in English. The original Danish name Tyge Ottesen Brahe is pronounced in Modern Standard Danish as [ˈtˢyːə ˈʌd̥əsn̩ ˈb̥ʁɑː].

Tycho Brahe was granted an estate on the island of Hven and the funding to build the Uraniborg, an early research institute, where he built large astronomical instruments and took many careful measurements. After disagreements with the new king in 1597, he was invited by the Czech king and Holy Roman emperor Rudolph II to Prague, where he became the official imperial astronomer. He built the new observatory at Benátky nad Jizerou. Here, from 1600 until his death in 1601, he was assisted by Johannes Kepler. Kepler would later use Tycho's astronomical information to develop his own theories of astronomy.

As an astronomer, Tycho worked to combine what he saw as the geometrical benefits of the Copernican system with the philosophical benefits of the Ptolemaic system into his own model of the universe, the Tychonic system. He is universally referred to as "Tycho" rather than by his surname "Brahe", as was common in Scandinavia.

He is credited with the most accurate astronomical observations of his time, and the data was used by his assistant Kepler to derive the laws of planetary motion. No one before Tycho had attempted to make so many redundant observations, and the mathematical tools to take advantage of them had not yet been developed. He did what others before him were unable or unwilling to do—to catalogue the planets and stars with enough accuracy to determine whether the Ptolemaic or Copernican system was more valid in describing the heavens.

Contents

Life

Early years

Tycho Brahe was born on a farm in Roseau under the name Tyge Ottesen Brahe (de Knudstrup), adopting the Latinized form Tycho around age fifteen (sometimes written Tÿcho). He is often misnamed Tycho de Brahe. He was born at his family's ancestral seat of Knutstorp Castle (Danish: Knudstrup borg; Swedish: Knutstorps borg)[1] in then Danish Scania, now Swedish, to Otte Brahe and Beate Bille. His twin brother died before being baptized. (Tycho wrote a Latin ode (Wittendorf 1994, p. 68) to his dead twin which was printed as his first publication in 1572.) He also had two sisters, one older (Kirstine Brahe) and one younger (Sophia Brahe). Otte Brahe, Tycho's father, was a nobleman and an important figure at the court of the Danish King. His mother, Beate Bille, also came from an important family that had produced leading churchmen and politicians. Both parents are buried under the floor of Kågeröd Church, not far from Knutstorp. An epitaph, originally from Knutstorp, but now on a plaque near the church door, shows the whole family, including Tycho as a boy.

Tycho later wrote that when he was around two, his uncle, Danish nobleman Jørgen Brahe, "... without the knowledge of my parents took me away with him while I was in my earliest youth." Apparently this did not lead to any disputes nor did his parents attempt to get him back. According to one source,[2] Tycho's parents had promised to hand over a boy child to Jørgen and his wife, who were childless, but had not honoured this promise. Jørgen seems to have taken matters into his own hands and took the child away to his own residence, Tost(e)rup Castle. Jørgen Brahe inherited considerable wealth from his parents, which in terms of the social structure of the time made him eminently eligible for the post of County Sheriff, a royal appointment. He was successively County Sheriff to Tranekjær (1542-49), Odensegaard (1549-52), Vordingborg Castle(1552-57) and finally (1555 until his death in 1565) to Queen Dorothea at Nykøbing Castle on Falster[3]. It is hard to say exactly where Tycho was educated in his childhood years, and Tycho himself provides no information on this topic, but the sources quoted below agree that he took a Latin School education from the age of six until he was twelve years old.

On 19 April 1559, Tycho began his studies at the University of Copenhagen. There, following the wishes of his uncle, he studied law but also studied a variety of other subjects and became interested in astronomy. It was, however, the eclipse which occurred on 21 August 1560, particularly the fact that it had been predicted, that so impressed him that he began to make his own studies of astronomy, helped by some of the professors. He purchased an ephemeris and books such as Sacrobosco's Tractatus de Sphaera, Apianus's Cosmographia seu descriptio totius orbis and Regiomontanus's De triangulis omnimodis.

I've studied all available charts of the planets and stars and none of them match the others. There are just as many measurements and methods as there are astronomers and all of them disagree. What's needed is a long term project with the aim of mapping the heavens conducted from a single location over a period of several years. — Tycho Brahe, 1563 (age 17).

Tycho realized that progress in the science of astronomy could be achieved not by occasional haphazard observations, but only by systematic and rigorous observation, night after night, and by using instruments of the highest accuracy obtainable. He was able to improve and enlarge the existing instruments, and construct entirely new ones. Tycho's naked eye measurements of planetary parallax were unprecedented in their precision - accurate to the arcminute, or 1/30 the width of the full moon. His sister Sophia assisted Tycho in many of his measurements. These jealously guarded measurements were "usurped" by Kepler following Tycho's death.[4] Tycho was the last major astronomer to work without the aid of a telescope, soon to be turned skyward by Galileo.

Tycho's nose

While a student, Tycho lost part of his nose in a duel[5] with rapiers with Manderup Parsbjerg, a fellow Danish nobleman.[6] This occurred in the Christmas season of 1566, after a fair amount of drinking, while Tycho, just turned 20 years old, was studying at the University of Rostock in Germany.[6] Attending a dance at a professor's house, he quarreled with Parsbjerg. A subsequent duel (in the dark) resulted in Tycho losing the bridge of his nose. From this event Tycho became interested in medicine and alchemy.[5] For the rest of his life, he was said to have worn a realistic replacement made of silver and gold[5], using a paste to keep it attached.[6] Some people, such as Fredric Ihren and Cecil Adams have suggested that the false nose also had copper. Ihren wrote that when Tycho's tomb was opened in 24 June 1901 green marks were found on his skull, suggesting copper.[6] Cecil Adams also mentions a green colouring and that medical experts examined the remains.[7] Some historians have speculated that he wore a number of different prosthetics for different occasions, noting that a copper nose would have been more comfortable and less heavy than a precious metal one.[8]

Death of his father

His uncle and foster father, Jørgen Brahe, died in 1565 of pneumonia after rescuing Frederick II of Denmark from drowning. In April 1567, Tycho returned home from his travels and his father wanted him to take up law, but Tycho was allowed to make trips to Rostock, then on to Augsburg (where he built a great quadrant), Basel, and Freiburg. At the end of 1570 he was informed about his father's ill health, so he returned to Knudstrup, where his father died on 9 May 1571. Soon after, his other uncle, Steen Bille, helped him build an observatory and alchemical laboratory at Herrevad Abbey.[5]

Family life

In 1572, in Knudstrup, Tycho fell in love with Kirsten Jørgensdatter, a commoner whose father, Pastor Jørgen Hansen, was the Lutheran clergyman of Knudstrup's village church. Under Danish law, when a nobleman and a common woman lived together openly as husband and wife, and she wore the keys to the household at her belt like any true wife, their alliance became a binding morganatic marriage after three years. The husband retained his noble status and privileges; the wife remained a commoner. Their children were legitimate in the eyes of the law, but they were commoners like their mother and could not inherit their father's name, coat of arms, or land property. (Skautrup 1941, pp. 24-5)

Kirsten Jørgensdatter gave birth to their first daughter, Kirstine (named after Tycho's late sister, who died at 13) on 12 October 1573. Together they had eight children, six of whom lived to adulthood. In 1574, they moved to Copenhagen where their daughter Magdalene was born. Kirsten and Tycho lived together for almost thirty years until Tycho's death.

Tycho's elk and dwarf

Tycho was said to own one percent of the entire wealth of Denmark at one point in the 1580s and he often held large social gatherings in his castle. He kept a dwarf named Jepp (whom Tycho believed to be clairvoyant) as a court jester who sat under the table during dinner. Pierre Gassendi wrote[6] that Tycho also had a tame elk, and that his mentor the Landgrave Wilhelm of Hesse-Kassel (Hesse-Cassel) asked whether there was an animal faster than a deer. Tycho replied, writing that there was none, but he could send his tame elk. When Wilhelm replied he would accept one in exchange for a horse, Tycho replied with the sad news that the elk had just died on a visit to entertain a nobleman at Landskrona. Apparently during dinner[9] the elk had drunk a lot of beer, fallen down the stairs, and died.[10][6]

Death

Tycho Brahe's grave in Prague, new tomb stone from 1901

Tycho died on 24 October 1601 in Prague, eleven days after suddenly becoming very ill during a banquet. Toward the end of his illness he is said to have told Kepler "Ne frustra vixisse videar!", "Let me not seem to have lived in vain”.[11][12] For hundreds of years, the general belief was that he had strained his bladder. It had been said that to leave the banquet before it concluded would be the height of bad manners, and so he remained, and that his bladder, stretched to its limit, developed an infection which later killed him. This theory was supported by Kepler's first-hand account.

Recent investigations have suggested that Tycho did not die from urinary problems but instead from mercury poisoning: extremely toxic levels of it have been found in his hair and hair-roots. Tycho may have poisoned himself by imbibing some medicine containing unintentional mercuric chloride impurities, or may have been poisoned.[13] According to a 2005 book by Joshua Gilder and Anne-Lee Gilder, there is substantial circumstantial evidence that Kepler murdered Brahe; they argue that Kepler had the means, motive, and opportunity, and stole Tycho's data on his death.[14] According to the Gilders, they find it "unlikely"[14] Tycho could have poisoned himself since he was an alchemist known to be familiar with the toxicity of different mercury compounds.

Tycho Brahe's body is currently interred in a tomb in the Church of Our Lady in front of Týn near Old Town Square near the Astronomical Clock in Prague.

Career: observing the heavens

The 1572 supernova

The Calar Alto Observatory imaged Tycho's Supernova Remnant more than four centuries after its discovery

On 11 November 1572, Tycho observed (from Herrevad Abbey) a very bright star, now named SN 1572, which had unexpectedly appeared in the constellation Cassiopeia. Because it had been maintained since antiquity that the world beyond the Moon's orbit was eternally unchangeable (celestial immutability was a fundamental axiom of the Aristotelian world-view), other observers held that the phenomenon was something in the terrestrial sphere below the Moon. However, in the first instance Tycho observed that the object showed no daily parallax against the background of the fixed stars. This implied it was at least farther away than the Moon and those planets that do show such parallax. Moreover he also found the object did not even change its position relative to the fixed stars over several months as all planets did in their periodic orbital motions, even the outer planets for which no daily parallax was detectable. This suggested it was not even a planet, but a fixed star in the stellar sphere beyond all the planets. He published a small book, De Stella Nova (1573), thereby coining the term nova for a "new" star (we now classify this star as a supernova and we know that it is 7500 light-years from Earth). This discovery was decisive for his choice of astronomy as a profession. Tycho was strongly critical of those who dismissed the implications of the astronomical appearance, writing in the preface to De Stella Nova: "O crassa ingenia. O caecos coeli spectatores" ("Oh thick wits. Oh blind watchers of the sky").

Tycho's discovery was the inspiration for Edgar Allan Poe's poem, "Al Aaraaf."[15] In 1998, Sky & Telescope magazine published an article by Donald W. Olson, Marilynn S. Olson and Russell L. Doescher arguing, in part, that Tycho's supernova was also the same "star that's westward from the pole" in Shakespeare's Hamlet.

Tycho's observatories

Watercolor plan of Uraniborg

Tycho published the 1572 observations made from his first observatory at Herrevad Abbey in 1574. He then started lecturing on astronomy, but gave up and left Denmark in spring 1575 to tour abroad. He first visited William IV, Landgrave of Hesse-Kassel's observatory at Kassel, then went on to Frankfurt, Basel and Venice. Upon his return he had decided to relocate to Basel, but King Frederick II, King of Denmark and Norway, fearful of losing such a scientist, offered Tycho the island of Hven in Oresund with funding to set up an observatory. Tycho first built Uraniborg in 1576 (with a laboratory for his alchemical experiments in its cellar) and then Stjerneborg in 1581.[5]

When King Frederick II died in 1588 he was buried at Roskilde Cathedral, like other Danish monarchs, and his 11 year old son Christian IV, became the new king. Tycho's influence steadily declined and after several unpleasant disagreements, including neglecting to maintain the chapel where Christian's father was buried,[5] he left Hven in 1597 and moved to Prague in 1599. Sponsored by Rudolf II, the Holy Roman Emperor, he built a new observatory in a castle in Benátky nad Jizerou, 50 km from Prague, and he worked there for one year. The emperor then had him move back to Prague, where he stayed until his death. Besides the emperor himself, he was also financially supported by several nobles, including Oldrich Desiderius Pruskowsky von Pruskow, to whom he dedicated his famous volume, the "Mechanica."

In return for their support, Tycho's duties included preparing astrological charts and predictions for his patrons on events such as births, weather forecasting, and providing astrological interpretations of significant astronomical events such as the comet of 1577 and the supernova of 1572.[16]

Tycho's observational astronomy

Mural quadrant (Tycho Brahe 1598)

Tycho was the preeminent observational astronomer of the pre-telescopic period, and his observations of stellar and planetary positions achieved unparalleled accuracy for their time. His planetary observations were "consistently accurate to within about 1',"[17] the stellar observations as recorded in his observational logs were even more accurate, varying from 32.3" to 48.8" for different instruments,[18] although an error of as much as 3' was introduced into some of the stellar positions Tycho published in his star catalog due to his application of an erroneous ancient value of parallax and his neglect of refraction.[19] For example, Tycho measured Earth's axial tilt as 23 degrees and 31.5 minutes, which he claimed to be more accurate than Copernicus by 3.5 minutes. After his death, his records of the motion of the planet Mars enabled Kepler to discover the laws of planetary motion, which provided powerful support for the Copernican heliocentric theory of the solar system.

Tycho himself was not a Copernican, but proposed a system in which the Sun orbited the Earth while the other planets orbited the Sun. His system provided a safe position for astronomers who were dissatisfied with older models but were reluctant to accept the Earth's motion. It gained a considerable following after 1616 when Rome decided officially that the heliocentric model was contrary to both philosophy and Scripture, and could be discussed only as a computational convenience that had no connection to fact. His system also offered a major innovation: while both the geocentric model and the heliocentric model as set forth by Copernicus relied on the idea of transparent rotating crystalline spheres to carry the planets in their orbits, Tycho eliminated the spheres entirely.

He was aware that a star observed near the horizon appears with a greater altitude than the real one, due to atmospheric refraction, and he worked out tables for the correction of this source of error.

To perform the huge number of multiplications needed to produce much of his astronomical data, Tycho relied heavily on the then-new technique of prosthaphaeresis, an algorithm for approximating products based on trigonometric identities that predated logarithms.

Tycho's Geo-heliocentric Astronomy

In this depiction of the Tychonic system, the objects on blue orbits (the moon and the sun) revolve around the earth. The objects on orange orbits (Mercury, Venus, Mars, Jupiter, and Saturn) revolve around the sun. Around all is sphere of fixed stars.

Kepler tried, but was unable, to persuade Tycho to adopt the heliocentric model of the solar system. Tycho believed in geocentrism because he held the Earth was just too sluggish to be continually in motion and also believed that if the Earth orbited the Sun annually there should be an observable stellar parallax over any period of six months, during which the angular orientation of a given star would change. This parallax does exist, but is so small it was not detected until the 1830s, when Friedrich Bessel discovered a stellar parallax of 0.314 arcseconds of the star 61 Cygni in 1838.[20] Tycho advocated an alternative to the Ptolemaic geocentric system, a geo-heliocentric system now known as the Tychonic system. In such a system, first proposed by Heraclides in the 4th century BC, the Sun annually circles a central Earth (regarded as essentially different from the planets), while the five planets orbit the Sun. [21] In Tycho's model the Earth does not rotate daily, as Heraclides claimed, but is static.

Another crucial difference between Tycho's 1587 geo-heliocentric model and those of other geo-heliocentric astronomers, such as Paul Wittich, Reimarus Ursus, Roslin and Origanus, was that the orbits of Mars and the Sun intersected. [22] This was because Tycho had come to believe the distance of Mars from the Earth at opposition (that is, when Mars is on the opposite side of the sky from the Sun) was less than that of the Sun from the Earth. Tycho believed this because he came to believe Mars had a greater daily parallax than the Sun. But in 1584 in a letter to a fellow astronomer, Brucaeus, he had claimed that Mars had been further than the Sun at the opposition of 1582, because he had observed that Mars had little or no daily parallax. He said he had therefore rejected Copernicus's model because it predicted Mars would be at only two-thirds the distance of the Sun.[23] But he apparently later changed his mind to the opinion that Mars at opposition was indeed nearer the Earth than the Sun was, but apparently without any valid observational evidence in any discernible Martian parallax.[24] Such intersecting Martian and solar orbits meant that there could be no solid rotating celestial spheres, because they could not possibly interpenetrate. Arguably this conclusion was independently supported by the conclusion that the comet of 1577 was superlunary, because it showed less daily parallax than the Moon and thus must pass through any celestial spheres in its transit.

Tychonic astronomy after Tycho

Galileo's 1610 telescopic discovery that Venus shows a full set of phases refuted the pure geocentric Ptolemaic model. After that it seems 17th century astronomy then mostly converted to geo-heliocentric planetary models that could explain these phases just as well as the heliocentric model could, but without the latter's disadvantage of the failure to detect any annual stellar parallax that Tycho and others regarded as refuting it.[25] The three main geo-heliocentric models were the Tychonic, the Capellan with just Mercury and Venus orbiting the Sun such as favoured by Francis Bacon, for example, and the extended Capellan model of Riccioli with Mars also orbiting the sun whilst Saturn and Jupiter orbit the fixed Earth. But the Tychonic model was probably the most popular, albeit probably in what was known as 'the semi-Tychonic' version with a daily rotating Earth. This model was advocated by Tycho's ex-assistant and disciple Longomontanus in his 1622 Astronomia Danica that was the intended completion of Tycho's planetary model with his observational data, and which was regarded as the canonical statement of the complete Tychonic planetary system.

A conversion of astronomers to geo-rotational geo-heliocentric models with a daily rotating Earth such as that of Longomontanus may have been precipitated by Francesco Sizzi's 1613 discovery of annually periodic seasonal variations of sunspot trajectories across the sun's disc. They appear to oscillate above and below its apparent equator over the course of the four seasons. This seasonal variation is explained much better by the hypothesis of a daily rotating Earth together with that of the sun's axis being tilted throughout its supposed annual orbit than by that of a daily orbiting sun, if not even refuting the latter hypothesis because it predicts a daily vertical oscillation of a sunspot's position, contrary to observation. This discovery and its import for heliocentrism, but not for geo-heliocentrism, is discussed in the Third Day of Galileo's 1632 Dialogo. [26] However, prior to that discovery, in the late 16th century the geo-heliocentric models of Ursus and Roslin had featured a daily rotating Earth, unlike Tycho's geo-static model, as indeed had that of Heraclides in antiquity, for whatever reason.

The fact that Longomontanus's book was republished in two later editions in 1640 and 1663 no doubt reflected the popularity of Tychonic astronomy in the 17th century. Its adherents included John Donne, the atomist and astronomer Pierre Gassendi and also Ole Roemer, the great Danish astronomer who discovered the finite speed of light, and who died in 1710 still a Tychonic geocentrist.

Johannes Kepler published the Rudolphine Tables containing a star catalog and planetary tables using Tycho's measurements. Hven island appears west uppermost on the base.

The ardent anti-heliocentric French astronomer Jean-Baptiste Morin devised a Tychonic planetary model with elliptical orbits published in 1650 in a Tychonic simplified version of the Rudolphine Tables.[27]The tenacious longevity of the Tychonic model into the late 17th century and even the early 18th century was attested by Ignace Pardies who declared in 1691 that it was still the commonly accepted system and by Francesco Blanchinus who said it was still such in 1728.[28]

Indeed in possible support of this latter claim, it is especially notable that even the 1726 third edition of Newton's Principia was studiously no more than Tychonic geo-heliocentric in its declared six established astronomical phenomena in the preliminary 'Phenomena' section of Book 3, from which it sought to demonstrate its theory of universal mutual gravitational attraction. For example, Phenomenon 3 stated "The orbits of the five primary planets - Mercury, Venus, Mars, Jupiter and Saturn - encicle the sun.", thus notably excluding the Earth from primary planethood in agreement with Tycho's model.[29] But in fact even Newton's empirical reasoning for going beyond the extent of the partial degree of heliocentrism of the Capellan model to the Tychonic with Mars, Jupiter and Saturn also orbiting the Sun was strikingly invalid:

"Because Mars also shows a full face when near conjunction with the sun, and appears gibbous in the quadratures, it is certain that Mars goes around the sun. The same is proved also with respect to Jupiter and Saturn from their phases being always full;..."[30]

But of course these phenomena of these three outer planets are equally well explained by the Ptolemaic geocentric model.

It seems it was James Bradley's 1729 publication of his discovery of stellar aberration, three years after the Principia's third edition and two after Newton's death, that finally put paid to all forms of geocentrism. For this annual oscillation of stars was only satisfactorily explicable by the conjunction of the heliocentric hypothesis that the Earth annually orbited the Sun with that of the finite speed of light. The discovery of this novel phenomenon thus completed the heliocentric revolution with the complete conversion from all geo-heliocentrism to pure heliocentrism thereafter as now empirically established fact.

Named after Tycho

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Notes

  1. ↑ Dansk biografisk Lexikon / II. Bind. Beccau - Brandis (Danish)
  2. ↑ Godfred Hartmann (1989), Urania. Om mennesket Tyge Brahe (Urania. About Tyge Brahe, the Man)., Copenhagen: Gyldendal, ISBN 870062731 
  3. ↑ Dansk Biografisk Lexikon (Danish Biographical Lexicon). Copenhagen. Gyldendalske Boghandels Forlag, 1887-1905.
  4. ↑ Stephen Hawking (2004). The Illustrated On the Shoulders of Giants: The Great Works of Physics and Astronomy. Running Press. ISBN 0762418982. http://books.google.com/books?id=iNLqkbDGmiQC&pg=PA108&ots=KLcJ5zhIsa&dq=tycho+%22quickly+took+advantage+of+the+absence%22&as_brr=3&sig=3_FJFfbz8MbgLAJkh474uKNPcBg. 
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 J J O'Connor and E F Robertson. Brahe bography. April 2003. Retrieved 2008-09-28
  6. ↑ 6.0 6.1 6.2 6.3 6.4 6.5 Fredric Ihren. "Tycho Brahe's Nose And The Story Of His Pet Moose". www.nada.kth.se. Retrieved on 2008-10-13. from a translation from Gassendi
  7. ↑ Cecil Adams. Did astronomer Tycho Brahe really have a silver nose?. 1998-07-17. Retrieved 2008-10-06
  8. ↑ Henderson, Mark. "Tycho Brahe’s beloved pet was a drunken moose". Times of London. Retrieved on 2008-12-04.
  9. ↑ Ihren, from a translation
  10. ↑ J. L. E. Dreyer (1890). Tycho Brahe: A Picture of Scientific Life and Work in the Sixteenth Century. Adam and Charles Black, Edinburgh. unknown ISBN. . Page 210 of online version published 2004 covers the elk.
  11. ↑ Pierre Gassendi, "Tycho Brahe", 1654
  12. ↑ David L. Goodstein and Judith R. Goodstein (1999). Feynman's Lost Lecture: The Motion of Planets Around the Sun. W. W. Norton & Co. ISBN 0393039188. http://books.google.com/books?id=ysZI5NcksUcC&pg=PA28&ots=NJU2NTP1jT&dq=%22let+me+not+seem+to+have+lived+in+vain%22+Kepler&sig=0uK8JpIYDdfzefBUQCB1J8M22fo. 
  13. ↑ tychobrahe.com English
  14. ↑ 14.0 14.1 Joshua Gilder and Anne-Lee Gilder (2005). Heavenly Intrigue: Johannes Kepler, Tycho Brahe, and the Murder Behind One of History's Greatest Scientific Discoveries. Anchor. ISBN 978-1-4000-3176-4. 
  15. ↑ Hallqvist, Christoffer (February 7, 2006), Al Aaraaf and West Point, Qrisse's Edgar Allan Poe Pages, http://www.poedecoder.com/qrisse/bio/westpoint.php 
  16. ↑ Adam Mosley and the Department of History and Philosophy of Science of the University of Cambridge. Tycho Brahe and Astrology. 1999. Retrieved 2008-10-02
  17. ↑ Owen Gingerich and James R. Voelkel, "Tycho Brahe's Copernican Campaign," Journal for the History of Astronomy, 29(1998): 2-34, p. 30, n. 2.
  18. ↑ Walter G. Wesley, "The Accuracy of Tycho Brahe's Instruments," Journal for the History of Astronomy, 9(1978): 42-53, table 4.
  19. ↑ Dennis Rawlins, "Tycho's 1004 Star Catalog", DIO 3 (1993), p. 20, n. 70.
  20. ↑ J J O'Connor and E F Robertson. Bessel biography. University of St Andrews. Retrieved 2008-09-28
  21. ↑ See the three articles by Thoren, Jarell and Schofield in Wilson & Taton 'Planetary astronomy from the Renaissance to the rise of astrophysics' 1989 CUP for details
  22. ↑ Ibid
  23. ↑ See p178-80 of Dreyer's 1890 'Tycho Brahe'
  24. ↑ See p171 The Wittich Connection Gingerich and Westman 1988
  25. ↑ Taton & Wilson 1989
  26. ↑ See p345-56 of Stillman Drake's 1967 Dialogue concerning the two chief world systems. But see Drake's Sunspots, Sizzi and Scheiner' in his 1970 Galileo Studies for its critical discussion of Galileo's misleading presentation of this phenomenon.
  27. ↑ See pp.42, 50 & 166 of Taton & Wilson's 1989 The General History of Astronomy 2A.
  28. ↑ See p41 of Christine Schofield's article The Tychonic and Semi-Tychonic World Systems in Taton & Wilson (eds) 1989 'The General History of Astronomy Volume 2A'
  29. ↑ This interesting fact was apparently first pointed out in the 20th century by the philosopher of science Imre Lakatos in his Newton's effect on scientific standards posthumously published in his 1978 Philosophical Papers Volume 1. In addition to the many logical reasons that have been adduced by such as Duhem, Popper, Feyerabend, Lakatos and others, such as Leibniz and Roger Cotes, to show that Newton did not validly deduce his law of gravity from Kepler's three laws of planetary orbits, this fact also further scuppers the inductivist-positivist claim that he did, since Kepler's laws were heliocentric. Of course in the General Scholium added to its 1713 second edition Newton did endorse heliocentrism in stating "The six primary planets revolve about the sun in circles concentric with the sun..." (p940 Cohen & Whitman Principia) But the Principia never gave any proof that the Earth orbited the sun, not even an invalid one such as were his Phenomenon 3 proofs that Mars, Jupiter and Saturn did.
  30. ↑ p799 Principia Cohen & Whitman 1999

References

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