On Tycho's Calculation of the Coordinates of Hamal, the Fundamental Star of Tycho's Catalog

Abstract

Tycho's star catalog enjoyed enormous prestige for centuries due to its accuracy. The entire catalog depends on the coordinates of one single star, Hamal (α Arietis), which explains why Tycho was so scrupulous in determining its coordinates using two different methods applied to more than 50 observations, as he described in his Progymnasmata. One of them proposed an ingenious way of dealing with refraction and parallax, two factors that he knew he could not control. Selecting particular observations, he was able to cancel out the effects of both refraction and parallax. Still, the entire calculation starts from the coordinates of the Sun calculated from his solar model. But Tycho's solar model assumes too large of an eccentricity, producing errors in the predictions of the solar longitude that can reach up to 8'. In this paper, I analyze Tycho's method for calculating the coordinates of α Arietis and explain how the method he proposed unintentionally avoided transferring the error of his solar model to his catalog.