Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002ahes...56..435d&link_type=abstract
Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 56, No. 5, p. 435 - 450 (2002)
Astronomy and Astrophysics
Astronomy
2
History Of Astronomy, Star Catalogues
Scientific paper
There are just two substantial sources of star coordinates preserved for us from antiquity: the star catalogue of Ptolemy's Almagest, and the rising, setting, and culmination phenomena, along with some star declinations and right ascensions, from Hipparchus' Commentary to Aratus. Given the controversy associated with the idea that Ptolemy's catalogue is, in whole or in substantial part, a copy of an earlier but now lost catalogue of Hipparchus, it is of interest to try to establish clear and significant associations, or the lack thereof, between the two sets of ancient star data. There have been two complementary efforts to clarify the possible associations. Vogt used the phenomena and declinations to reconstruct the ecliptical coordinates of some 122 stars in Hipparchus' Commentary that also appear in the Almagest catalogue. Vogt's conclusion was that since his reconstructed coordinates and the Almagest coordinates were, in general, different, Ptolemy did not obtain his data from Hipparchus. Vogt did notice five stars with very similar errors and concluded that Ptolemy probably did copy those from Hipparchus. More recently, however, Grasshoff has pointed out that there are several reasons to doubt Vogt's conclusion. Further, Grasshoff worked in the opposite direction, using the Almagest coordinates to compute the Hipparchan phenomena, and concluded, for two reasons, that the Almagest data and the Commentary data share a common origin. First, there are a number of stars that share large common errors, and it is highly unlikely that these agreements could be coincidental. Second, the correlation coefficients between the various error sets are typically large and statistically significant, and this also suggests a common origin of the two data sets. However, Grasshoff provided no analysis of the correlations to support this second conclusion. In this paper I will (1) analyze the correlations between the errors of the phenomena and the predictions of these phenomena following from the Almagest coordinates using extensive Monte Carlo simulations to show directly that it is highly improbable that the Almagest coordinates are substantially independent of the Commentary data; (2) determine the systematic errors in the Hipparchan phenomena, and show that they are strongly related to the known systematic errors in the Almagest coordinates. In both cases the comparisons point to a common origin of the Commentary data and the Almagest data.
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