The accuracy of the measurements in Ulugh Beg's star catalogue

The star catalogue compiled by Ulugh Beg and his collaborators in Samarkand (ca. 1437) is the only catalogue primarily based on original observations between the times of Ptolemy and Tycho Brahe. Evans (1987) has given convincing evidence that Ulugh Beg's star catalogue was based on measurements made with a zodiacal armillary sphere graduated to 15(') , with interpolation to 0.2 units. He and Shevchenko (1990) were primarily interested in the systematic errors in ecliptic longitude. Shevchenko's analysis of the random errors was limited to the twelve zodiacal constellations. We have analyzed all 843 ecliptic longitudes and latitudes attributed to Ulugh Beg by Knobel (1917). This required multiplying all the longitude errors by the respective values of the cosine of the celestial latitudes. We find a random error of +/- 17minp 7 for ecliptic longitude and +/- 16minp 5 for ecliptic latitude. On the whole, the random errors are largest near the ecliptic, decreasing towards the ecliptic poles. For all of Ulugh Beg's measurements (excluding outliers) the mean systematic error is -10minp 8 +/- 0minp 8 for ecliptic longitude and 7minp 5 +/- 0minp 7 for ecliptic latitude, with the errors in the sense ``computed minus Ulugh Beg''. For the brighter stars (those designated alpha , beta , and gamma in the respective constellations), the mean systematic errors are -11minp 3 +/- 1minp 9 for ecliptic longitude and 9minp 4 +/- 1minp 5 for ecliptic latitude. Within the errors this matches the systematic error in both coordinates for alpha Vir. With greater confidence we may conclude that alpha Vir was the principal reference star in the catalogues of Ulugh Beg and Ptolemy. Evans, J. 1987, J. Hist. Astr. 18, 155. Knobel, E. B. 1917, Ulugh Beg's Catalogue of Stars, Washington, D. C.: Carnegie Institution. Shevchenko, M. 1990, J. Hist. Astr. 21, 187.