Tycho Brahe

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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 — 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.

Tycho's observations of stellar and planetary positions were noteworthy both for their accuracy and quantity. With an accuracy approaching one arcminute, his celestial positions were much more accurate than those of any predecessor or contemporary — about five times as accurate as the observations of Wilhelm of Hesse. Rawlins (1993:§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, & 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 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'. Although the stellar observations as recorded in his observational logs were more accurate, varying from 32.3" to 48.8" for different instruments, systematic errors of as much as 3' were introduced into some of the stellar positions Tycho published in his star catalog — due, for instance, to his application of an erroneous ancient value of parallax and his neglect of polestar refraction. 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.

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.

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.

Much 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 were 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 notebook. 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. 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, 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. This and other instruments were placed in the two observatories attached to the manor.

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, that he considered to be foundational. He was also critical of the observational data that Copernicus built his theory on, which he correctly considered to have a high margin of error. Instead, Tycho proposed a "geo-heliocentric" system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun. Tycho's system had many of the same observational and computational advantages that Copernicus' system had, and both systems also could accommodate the phases of Venus, although Galilei had yet to discover them. Tycho's system provided a safe position for astronomers who were dissatisfied with older models but were reluctant to accept the heliocentrism and the Earth's motion. It gained a considerable following after 1616 when Rome declared 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. Tycho's system also offered a major innovation: while both the purely 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. Kepler, as well as other Copernican astronomers, tried to persuade Tycho to adopt the heliocentric model of the Solar System, but he was not persuaded. According to Tycho, the idea of a rotating and revolving Earth would be "in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount."

With respect to physics, Tycho held that the Earth was just too sluggish and heavy 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" or "Quintessence"; this substance, not found on Earth, was light, strong, unchanging, and its natural state was circular motion. By contrast, the Earth (where objects seem to have motion only when moved) and things on it were composed of substances that were heavy and whose natural state was rest. Accordingly, Tycho said the Earth was a "lazy" body that was not readily moved. Thus while Tycho acknowledged that the daily rising and setting of the Sun and stars could be explained by the Earth's rotation, as Copernicus had said, still

With respect to the stars, Tycho 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 thanks to Earth's changing position. (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.) The Copernican explanation for this lack of parallax was that the stars were such a great distance from Earth that Earth's orbit was almost insignificant by comparison. However, Tycho noted that this explanation introduced another problem: Stars as seen by the naked eye appear small, but of some size, with more prominent stars such as Vega appearing larger than lesser stars such as Polaris, which in turn appear larger than many others. Tycho had determined that a typical star measured approximately a minute of arc in size, with more prominent ones being two or three times as large. In writing to Rothmann, Tycho used basic geometry to show that, assuming a small parallax that just escaped detection, the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the Sun to Saturn. Moreover, the only way the stars could be so distant and still appear the sizes they do in the sky would be if even average stars were gigantic — at least as big as the orbit of the Earth, and of course vastly larger than the Sun. And, Tycho said, the more prominent stars would have to be even larger still. And what if the parallax was even smaller than anyone thought, so the stars were yet more distant? Then they would all have to be even larger still. Tycho said

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. In fact, Rothmann responded to this argument of Tycho's by saying:

Religion played a role in Tycho's geocentrism also – 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.

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. 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. 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. 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.

Tycho's distinctive contributions to lunar theory include his discovery of the 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 Kepler in 1602, and Kepler's own derivative form appears in Kepler's Rudolphine Tables of 1627.

Kepler used Tycho's records of the motion of Mars to deduce laws of planetary motion, enabling calculation of astronomical tables with unprecedented accuracy (the Rudolphine Tables) and providing powerful support for a heliocentric model of the Solar System.

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. 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. Longomontanus' work was published in several editions and used by many subsequent astronomers, and through him the Tychonic system was adopted by astronomers as far away as China.

The ardent anti-heliocentric French astronomer Jean-Baptiste Morin devised a Tychonic planetary model with elliptical orbits published in 1650 in a simplified, Tychonic version of the Rudolphine Tables. 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. 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. 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. But in Germany, the Netherlands, and England, the Tychonic system "vanished from the literature much earlier".

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.

Tycho also worked in medicine and alchemy. He was strongly influenced by Paracelsus, who considered the human body to be directly influenced by celestial bodies. The paracelsian view of man as a microcosm, and astrology as the science tying together the celestial and bodily universes was also shared by Philip Melanchthon, and was precisely one of the points of contention between Melanchthon and Luther, and hence between the philippists and the gnesio-Lutherans. For Tycho there was a close connection between empiricism and natural science on one hand and religion and astrology on the other. Using his large herbal garden at Uraniborg, Tycho produced several recipes for herbal medicines, using them to treat illnesses such as fever and plague. In his own time, Tycho was also famous for his contributions to medicine; his herbal medicines were in use as late as the 1900s. The expression Tycho Brahe days, in Scandinavian folklore, refers to a number of "unlucky days" that were featured in many almanacs beginning in the 1700s, but which have no direct connection to Tycho or his work. Whether because he realized that astrology was not an empirical science or because he feared religious repercussions Tycho seems to have had a somewhat ambiguous relation to 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, 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.

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