Tycho Brahe 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. 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
Tycho Brahe 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 Christoph Rothmann, a Copernican astronomer, 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