Editing Tycho Brahe (section)

==Career: observing the heavens==

===Observational astronomy===
[[File:Fotothek df tg 0005915 Astronomie ^ Messinstrument.jpg|thumb|Brahe's illustration of his [[sextant]], from his [[star catalogue]] ''Astronomiae instauratae mechanica'', 1602]]
Tycho's view of science was driven by his passion for accurate observations, and the quest for improved instruments of measurement drove his life's work. Tycho was the last major astronomer to work without the aid of a [[telescope]], soon to be turned skyward by [[Galileo Galilei]] and others. Given the limitations of the naked eye for making accurate observations, he devoted many of his efforts to improving the accuracy of the existing types of instrument{{snd}}the [[sextant]] and the quadrant. He designed larger versions of these instruments, which allowed him to achieve much higher accuracy. Because of the accuracy of his instruments, he quickly realized the influence of wind and the movement of buildings, and instead opted to mount his instruments underground directly on the bedrock.{{sfn|Christianson|2000|p=83}}

Tycho's observations of [[star|stellar]] and [[planet]]ary positions were noteworthy both for their accuracy and quantity.{{sfn|Swerdlow|1996|pp=207{{ndash}}210}} With an accuracy approaching one arcminute, his celestial positions were much more accurate than those of any predecessor or contemporary{{snd}}about five times as accurate as the observations of Wilhelm of Hesse.{{sfn|Høg|2009}} {{harvcoltxt|Rawlins|1993|p=§B2}} asserts of Tycho's Star Catalog D, "In it, Tycho achieved, on a mass scale, a precision far beyond that of earlier catalogers. Cat D represents an unprecedented confluence of skills: instrumental, observational, and computational, all of which combined to enable Tycho to place most of his hundreds of recorded stars to an accuracy of ordermag 1'!"

He aspired to a level of accuracy in his estimated positions of celestial bodies of being consistently within an [[minute of arc|arcminute]] of their real celestial locations, and also claimed to have achieved this level. But, in fact, many of the stellar positions in his star catalogues were less accurate than that. The median errors for the stellar positions in his final published catalog were about 1.5', indicating that only half of the entries were more accurate than that, with an overall mean error in each coordinate of around 2'.{{sfn|Rawlins|1993|p=12}} 

Although the stellar observations as recorded in his observational logs were more accurate, varying from 32.3" to 48.8" for different instruments,{{sfn|Wesley|1978|pp=42{{ndash}}53, table 4}} systematic errors of as much as 3' were introduced into some of the stellar positions Tycho published in his star catalog{{snd}}due, for instance, to his application of an erroneous ancient value of parallax and his neglect of polestar refraction.{{sfn|Rawlins|1993|p=20, n. 70}} Incorrect transcription in the final published star catalogue, by scribes in Tycho's employ, was the source of even larger errors, sometimes by many degrees.{{refn|1=Victor Thoren{{sfn|Taton|Wilson|1989}} says: "[the accuracy of the 777 star catalogue C] falls below the standards Tycho maintained for his other activities&nbsp;... the catalogue left the best qualified appraiser of it (Tycho's eminent biographer J. L. E. Dreyer) manifestly disappointed. Some 6% of its final 777 positions have errors in one or both co-ordinates that can only have arisen from 'handling' problems of one kind or another. And while the brightest stars were generally placed with the minute-of-arc accuracy Tycho expected to achieve in every aspect of his work, the fainter stars (for which the slits on his sights had to be widened, and the sharpness of their alignment reduced) were considerably less well located." (ii) Michael Hoskin{{sfn|Hoskin|1997|p=101}} concurs with Thoren's finding "Yet although the places of the brightest of the non-reference stars [in the 777 star catalogue] are mostly correct to around the minute of arc that was his standard, the fainter stars are less accurately located, and there are many errors." (iii) The greatest max errors are given by Dennis Rawlins.<ref>{{harvcoltxt|Rawlins|1993}}, p. 42</ref> They are in descending order a 238° scribal error in the right ascension of star D723; a 36° scribal error in the right ascension of D811; a 23° latitude error in all 188 southern stars by virtue of a scribal error; a 20° scribal error in longitude of D429; and a 13.5° error in the latitude of D811.|group=note}}

Celestial objects observed near the horizon and above appear with a greater [[altitude]] than the real one, due to atmospheric [[refraction]], and one of Tycho's most important innovations was that he worked out and published the very first tables for the systematic correction of this possible source of error. But, as advanced as they were, they attributed no refraction whatever above 45° altitude for solar refraction, and none for starlight above 20° altitude.{{sfn|Taton|Wilson|1989|pp=14{{ndash}}15}}

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 [[List of trigonometric identities|trigonometric identities]] that predated logarithms.{{sfn|Thoren|1988}}

===Instruments===

Many of Tycho's observations and discoveries were done with the aid of various instruments, many of which he himself made. The process that went into creating and refining his devices was haphazard at first, but was critical in the advancement of his observations. He pioneered an early example while he was a student in Leipzig. While he was gazing at the stars he realized that he needed a better way to write down not just his observations but also the angles and descriptions as well. So, he pioneered the use of the observational.{{sfn|Christianson|2017}} In this notebook, he made his observations and asked himself questions to try and answer later on. Tycho also made sketches of what he saw as well from comets to the motions of planets.

His astronomical instrument innovation continued after his schooling.  When he gained access to his inheritance, he went straight to work creating brand new instruments to replace the ones he used as a student. Tycho created a quadrant that was thirty-nine centimeters in diameter and added a new type of sight to it called a ''pinnacidia'', or light cutters as it is translated.{{sfn|Christianson|2020|p=60}} This brand-new sight meant that the old pinhole style sight was rendered obsolete. When the sights of the pinnacidia were aligned in the correct manner the object that it is lined up with it will look exactly the same from both ends. This instrument was kept still on a heavy-duty base and adjusted via a brass plumb line and thumb screws, all of which helped give Tycho Brahe more accurate measurements of the heavens.

There were times that the instruments Tycho made were for a specific purpose or an event that he was witness to. Such was the case in 1577 when he first started construction of what would be called Uraniborg. In that year a comet was spotted moving across the sky. During this period of time Tycho made many observations, and one of the instruments that he used to make his observations was called a brass azimuthal quadrant. At sixty-five centimeters in radius it was a large instrument built either in 1576 or 1577,<ref name="NCA">{{cite web |title=Tycho Brahe (1546–1601) |url=https://www2.hao.ucar.edu/Education/FamousSolarPhysicists/tycho-brahes-observations-instruments |website=NCAR High Altitude Observatory |publisher=UCAR |access-date=27 November 2021}}</ref> just in time for Tycho to use it to observe the path and distance of the 1577 comet. This instrument helped him to accurately track the comet's path as it crossed the orbits of the [[Solar System]].

A great many more instruments were constructed at Tycho Brahe's new manor on Hven called Uraniborg. It was a combination of a home, observatories and laboratory where he made some of his discoveries along with many of his instruments. Several of these instruments were very large, such as a steel azimuth quadrant equipped with a brass arc that was six feet (or 194 centimeters) in diameter.{{sfn|Christianson|2000|p=72}} This and other instruments were placed in the two observatories attached to the manor.

=== The Tychonic cosmological model ===
{{Main|Tychonic system}}
[[File:Tychonian system.svg|thumb|The Tychonic system, surrounded by a sphere of fixed stars. The Moon and the Sun are shown orbiting the Earth, and five planets orbit the Sun.]]

Although Tycho admired Copernicus and was the first to teach his theory in Denmark, he was unable to reconcile Copernican theory with the basic laws of Aristotelian physics, which he believed to be foundational. He was critical of the observational data that Copernicus built his theory on, which he correctly considered to be inaccurate. Instead, Tycho proposed a "geo-heliocentric" system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun. His system had many of the observational and computational advantages of Copernicus' system. It provided a safe position for those astronomers who were dissatisfied with older models, but reluctant to accept heliocentrism.{{sfn|Hetherington|Hetherington|2009|p=134}} 

It gained a following after 1616, when the Catholic Church declared the heliocentric model to be contrary to philosophy and Christian [[Religious text|scripture]], and only able to be discussed as a computational convenience.{{sfn|Russell|1989}} Tycho's system offered a major innovation in that it eliminated the idea of [[Celestial spheres|transparent rotating crystalline spheres]] to carry the planets in their orbits. Kepler and other Copernican astronomers, tried unsuccessfully to persuade Tycho to adopt the heliocentric model of the [[Solar System]]. To Tycho, the idea of a moving Earth was "in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount."{{sfn|Repcheck|2008|p=187}}

Tycho held that the Earth was too sluggish and massive to be continuously in motion. According to the accepted Aristotelian physics of the time, the heavens, whose motions and cycles were continuous and unending, were made of [[Aether (classical element)|aether]], a substance not found on Earth, that caused objects to move in a circle. By contrast, objects on Earth seem to have motion only when moved, and the natural state of objects on its surface was rest. Tycho said the Earth was an inert body, not readily moved.{{sfn|Blair|1990|pp=361{{ndash}}362}}{{sfn|Moesgaard|1972|p=40}}{{sfn|Gingerich|1973|p=87}} He acknowledged that the rising and setting of the Sun and stars could be explained by a rotating Earth, as Copernicus had said, still:

<blockquote>such a fast motion could not belong to the earth, a body very heavy and dense and opaque, but rather belongs to the sky itself whose form and subtle and constant matter are better suited to a perpetual motion, however fast.{{sfn|Blair|1990|p=361}}</blockquote>

Tycho believed that, if the Earth did orbit the Sun, there should be an observable [[stellar parallax]] every six months (the stars' positions would change thanks to Earth's changing position).{{refn|1=This parallax does exist, but is so small it was not detected until 1838, when [[Friedrich Bessel]] discovered a parallax of 0.314 arcseconds of the star [[61 Cygni]].<ref name="OCoRob">{{cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |title=Friedrich Wilhelm Bessel |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Bessel.html |website=MacTutor |publisher=[[University of St Andrews]] |access-date=28 September 2008}}</ref>|group=note}} The lack of any stellar parallax was explained by the Copernican theory as being due to the stars' enormous distances from Earth. Tycho noted and attempted to measure the apparent relative sizes of the stars in the sky. He used [[geometry]] to show that the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the Sun to Saturn and to be seen at these distances the stars  would have to be gigantic, at least as big as the orbit of the Earth, and of course vastly larger than the Sun.{{sfn|Blair|1990|p=364}}{{sfn|Moesgaard|1972|p=51}} Tycho said:

<blockquote>Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference.{{sfn|Blair|1990|p=364}}</blockquote>

Copernicans offered a religious response to Tycho's geometry: titanic, distant stars might seem unreasonable, but they were not, for the Creator could make his creations that large if He wanted.{{sfn|Moesgaard|1972|p=52}}{{sfn|Vermij|2007|pp=124{{ndash}}125}} In fact, Rothmann responded to this argument of Tycho's by saying:

<blockquote>[W]hat is so absurd about [an average star] having size equal to the whole [orbit of the Earth]? What of this is contrary to divine will, or is impossible by divine Nature, or is inadmissible by infinite Nature? These things must be entirely demonstrated by you, if you will wish to infer from here anything of the absurd. These things that vulgar sorts see as absurd at first glance are not easily charged with absurdity, for in fact divine Sapience and Majesty is far greater than they understand. Grant the vastness of the Universe and the sizes of the stars to be as great as you like{{snd}}these will still bear no proportion to the infinite Creator. It reckons that the greater the king, so much greater and larger the palace befitting his majesty. So how great a palace do you reckon is fitting to GOD?{{sfn|Graney|2012|p=217}}</blockquote>

Religion played a role in Tycho's geocentrism{{snd}}he cited the authority of scripture in portraying the Earth as being at rest. He rarely used Biblical arguments alone. To him they were a secondary objection to the idea of Earth's motion, and over time he came to focus on scientific arguments, but he did take Biblical arguments seriously.{{sfn|Blair|1990|pp=362{{ndash}}364}}

Tycho's 1587 geo-heliocentric model differed from those of other geo-heliocentric astronomers, such as Wittich, [[Reimarus Ursus]], [[Helisaeus Roeslin]] and [[David Origanus]], in that the orbits of Mars and the Sun intersected. 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. 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.{{sfn|Dreyer|1890|pp=178{{ndash}}180}} 

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.{{sfn|Gingerich|Westman|1988|p=171}} 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. While Tycho Brahe and his contemporaries lacked a fully developed alternative to Aristotelian physics, Brahe's comet observations cast significant doubt on its validity. <ref name=":0" />

===Lunar theory===
Tycho's distinctive contributions to [[lunar theory]] include his discovery of the [[variation (astronomy)|variation]] of the Moon's longitude. This represents the largest inequality of longitude after the [[equation of the center]] and the [[evection]]. He also discovered librations in the inclination of the plane of the lunar orbit, relative to the ecliptic (which is not a constant of about 5° as had been believed before him, but fluctuates through a range of over a quarter of a degree), and accompanying oscillations in the longitude of the [[lunar node]]. These represent perturbations in the Moon's ecliptic latitude. Tycho's lunar theory doubled the number of distinct lunar inequalities, relative to those anciently known, and reduced the discrepancies of lunar theory to about a fifth of their previous amounts. It was published posthumously by [[Johannes Kepler|Kepler]] in 1602, and Kepler's own derivative form appears in Kepler's ''Rudolphine Tables'' of 1627.{{sfn|Thoren|1967}}

=== Subsequent developments in astronomy ===
Kepler used Tycho's records of the motion of Mars to deduce [[Kepler's laws of planetary motion|laws of planetary motion]],{{sfn|Stephenson|1987|pp=22, 39, 51, 204}} enabling calculation of astronomical tables with unprecedented accuracy (the ''Rudolphine Tables''){{refn|1=According to Owen Gingerich{{sfn|Taton|Wilson|1989|p=77}} and Christopher Linton,{{sfn|Linton|2004|p=224}} these tables were some 30 times more accurate than other astronomical tables then available.|group=note}} and providing powerful support for a [[heliocentric]] model of the Solar System.{{sfn|Swerdlow|2004|p=96}}{{sfn|Stephenson|1987|pp=67{{ndash}}68}}
[[File:Naboth Capella.JPG|thumb|[[Valentin Naboth]]'s drawing of [[Martianus Capella]]'s geo-heliocentric astronomical model (1573)]]

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 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.{{sfn|Taton|Wilson|1989}}{{page needed|date=December 2022}} 

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. 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. Longomontanus' work was published in several editions and used by many subsequent astronomers. Through him, the Tychonic system was adopted by astronomers as far away as China.{{sfn|Hashimoto|1987}}

[[File:Libr0309.jpg|thumb|upright=1.7|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 (mathematician)|Jean-Baptiste Morin]] devised a Tychonic planetary model with elliptical orbits published in 1650 in a simplified, Tychonic version of the ''Rudolphine Tables''.{{sfn|Taton|Wilson|1989|pp=42, 50, 166}} Another geocentric French astronomer, [[Jacques du Chevreul]], rejected Tycho's observations including his description of the heavens and the theory that Mars was below the Sun.{{sfn|Feingold|Navarro-Brotons|2006}}{{page needed|date=December 2022}} Some acceptance of the Tychonic system persisted through the 17th century and in places until the early 18th century. It was supported after a 1633 decree about the Copernican controversy, by "a flood of pro-Tycho literature" of Jesuit origin. Among pro-Tycho Jesuits, Ignace Pardies declared in 1691 that it was still the commonly accepted system, and Francesco Blanchinus reiterated that as late as 1728.{{sfn|Taton|Wilson|1989|p=41}} 

Persistence of the Tychonic system, especially in Catholic countries, has been attributed to its satisfaction of a need, relative to Catholic doctrine, for "a safe synthesis of ancient and modern". After 1670, even many Jesuit writers only thinly disguised their Copernicanism. In Germany, the Netherlands, and England, the Tychonic system "vanished from the literature much earlier".{{sfn|Taton|Wilson|1989|p=43}}

[[James Bradley]]'s discovery of [[stellar aberration]], published in 1729, eventually gave direct evidence excluding the possibility of all forms of geocentrism including Tycho's. Stellar aberration could only be satisfactorily explained on the basis that the Earth is in annual orbit around the Sun, with an orbital velocity that combines with the finite speed of the light coming from an observed star or planet, to affect the apparent direction of the body observed.{{sfn|Taton|Wilson|1989|p=205}}

===Work in medicine, alchemy and astrology===
Tycho worked in medicine and alchemy. He was influenced by the Swiss physician [[Paracelsus]], who considered the human body to be directly affected by celestial bodies.{{sfn|Christianson|1979}} Tycho used Paracelsus's ideas to connect empiricism and natural science, and religion and astrology.{{sfn|Almási|2013}} Using his [[Kitchen_garden#Herb_garden|herbal garden]] at Uraniborg, Tycho produced recipes for herbal medicines, and used them to treat fever and plague.{{sfn|Figala|1972}} His herbal medicines were in use until the end of the 19th century.{{sfn|Kragh|2005|p=243}} 

The expression ''[[Tycho Brahe days]]'' referred to "unlucky days" that were featured in almanacs from the 1700s onwards, but which have no direct connection to Tycho or his work.{{sfn|Thoren|Christianson|1990|p=215}} Whether because Tycho realized that astrology was not an empirical science, or because he feared religious repercussions, he did not publicise his own astrological work. For example, two of his more astrological treatises, one on weather predictions and an almanac, were published in the names of his assistants, in spite of the fact that he worked on them personally. Some scholars have argued that he lost faith in horoscope astrology over the course of his career,{{sfn|Thoren|Christianson|1990|pp=215–216}} and others that he simply changed his public communication on the topic as he realized that connections with astrology could influence the reception of his empirical astronomical work.{{sfn|Almási|2013}}