Tycho Brahe
Observational astronomy

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.
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