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 current observational data was a day off. He realized that more accurate observations would be the key to making more exact predictions. He purchased an ephemeris and books on astronomy, including Johannes de Sacrobosco's "De sphaera mundi", Petrus Apianus's "Cosmographia seu descriptio totius orbis" and Regiomontanus's "De triangulis omnimodis". Jørgen Thygesen Brahe, however, wanted Tycho to educate himself in order to become a civil servant, and sent him on a study tour of Europe in early 1562. 15-year old Tycho was given as mentor the 19-year-old Anders Sørensen Vedel, whom he eventually talked into allowing the pursuit of astronomy during