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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Almagest | 2/4 | https://en.wikipedia.org/wiki/Almagest | reference | science, encyclopedia | 2026-05-05T08:32:30.906530+00:00 | kb-cron |
The layout of the catalogue has always been tabular. Ptolemy writes explicitly that the coordinates are given as (ecliptical) "longitudes" and "latitudes", which are given in columns, so this has probably always been the case. It is significant that Ptolemy chooses the ecliptical coordinate system because of his knowledge of precession, which distinguishes him from all his predecessors. Hipparchus' celestial globe had an ecliptic drawn in, but the coordinates were equatorial. Since Hipparchus' star catalogue has not survived in its original form, but was absorbed into the Almagest star catalogue (and heavily revised in the 265 years in between), the Almagest star catalogue is the oldest one in which complete tables of coordinates and magnitudes have come down to us. As mentioned, Ptolemy includes a star catalog containing 1022 stars. He says that he "observed as many stars as it was possible to perceive, even to the sixth magnitude". The ecliptic longitudes are given in terms of a zodiac sign and a number of degrees and fractions of a degree. The zodiac signs each represent exactly 30°, starting with Aries representing longitude 0° to 30°. The degrees are added to the lower limit of the 30-degree range to obtain the longitude. Unlike the situation with the zodiac of modern-day astrology, most of the stars of a given zodiac constellation in the catalog fall in the 30-degree range designated by the same name (the so-called 'zodiac sign'). The ecliptic longitudes are about 26° lower than those of AD 2000 (the J2000 epoch). Ptolemy says that the ecliptic longitudes are for the beginning of the reign of Antoninus Pius (138 AD) and that he found that the longitudes had increased by 2° 40′ since the time of Hipparchus which was 265 years earlier (Alm. VII, 2). But calculations show that his ecliptic longitudes correspond more closely to around the middle of the first century CE (+48 to +58). Since Tycho Brahe found this offset, astronomers and historians investigated this problem and suggested several causes:
that all coordinates were calculated from Hipparchus' observations, whereby the precession constant, which was known too inaccurately at the time, led to a summation error (Delambre 1817); that the data had in fact been observed a century earlier by Menelaus of Alexandria (Björnbo 1901); that the difference is a sum of individual errors of various kinds, including calibration with outdated solar data; that Ptolemy's instrument was wrongly calibrated and had a systematic offset.
Subtracting the systematic error leaves other errors that cannot be explained by precession. Of these errors, about 18 to 20 are also found in Hipparchus' star catalogue (which can only be reconstructed incompletely). From this it can be concluded that a subset of star coordinates in the Almagest can indeed be traced back to Hipparchus, but not that the complete star catalogue was simply "copied". Rather, Hipparchus' major errors are no longer present in the Almagest and, on the other hand, Hipparchus' star catalogue had some stars that are entirely absent from the Almagest. It can be concluded that Hipparchus' star catalogue, while forming the basis, has been reobserved and revised.
==== Errors in the coordinates ==== The figure he used is based on Hipparchus' own estimate for precession, which was 1° in 100 years, instead of the correct 1° in 72 years. Dating attempts through proper motion of the stars also appear to date the actual observation to Hipparchus' time instead of Ptolemy. Many of the longitudes and latitudes have been corrupted in the various manuscripts. Most of these errors can be explained by similarities in the symbols used for different numbers. For example, the Greek letters Α and Δ were used to mean 1 and 4 respectively, but because these look similar copyists sometimes wrote the wrong one. In Arabic manuscripts, there was confusion between for example 3 and 8 (ج and ح). (At least one translator also introduced errors. Gerard of Cremona, who translated an Arabic manuscript into Latin around 1175, put 300° for the latitude of several stars. He had apparently learned from Moors, who used the letter س (sin) for 300 (like the Hebrew ש (shin)), but the manuscript he was translating came from the East, where س was used for 60, like the Hebrew ס (samekh).) Even without the errors introduced by copyists, and even accounting for the fact that the longitudes are more appropriate for 58 AD than for 137 AD, the latitudes and longitudes are not fully accurate, with errors as great as large fractions of a degree. Some errors may be due to atmospheric refraction causing stars that are low in the sky to appear higher than where they really are. A series of stars in Centaurus are off by a couple of degrees, including the star we call Alpha Centauri. These were probably measured by a different person or persons from the others, and in an inaccurate way.