Ancient Declinations and Precession (original) (raw)

In Almagest 7.3 Ptolemy lists the declinations of 18 stars from the time of Timocharis and Aristyllos, from the time of Hipparchus, and from his own time. 1 For six of the stars he says that the change in declination over the period of 265 years between his time and Hipparchus' time corresponds closely to the change in declination of the endpoints of various segments of the ecliptic that are 2 2/3° in length. Ptolemy uses these correspondences to claim that the sphere of the fixed stars is rotating eastward about the poles of the ecliptic 1° every 100 years, in agreement with several alternative determinations of the rate of precession that he offers nearby in the Almagest (and, of course, in disagreement with the correct value of 72 years per degree). However, Ptolemy gave the positions of these segments only roughly, within signs of the zodiac, e.g. "near the middle of Taurus." If the positions are ecliptic longitudes, as most previous commentators have assumed, 2 then some are grossly inaccurate. For example, for η Ursae Majoris he puts the segment near the beginning of Libra, or 180°, while the longitude of the star at his time was actually close to the beginning of Virgo, or 150°. Manitius assumed that they were polar longitudes, 3 while Rawlins more recently speculated that they might refer to right ascensions. 4 Polar longitudes and right ascensions cannot be distinguished conclusively in this case, since Ptolemy tells us only roughly where the segments lie-at the end of Aries, near the middle of Taurus, etc. However, the fact that Ptolemy did not mention the ecliptical longitudes of the stars in question suggests that he probably did not analyze the changes in declination in the same way that modern commentators have, and raises the question of exactly how he did analyze them. The following discussion suggests one approach, admittedly speculative, to answering that question.