161 Coordinate System used in the Almagest

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The state of preservation of the Almagest is extraordinary, and it seems that in spite that it had been rewritten many times since the 2nd century, its observational data shows inexplicable accuracy. Notice that it is natural to expect that numerous typographical errors must have been made when the catalogue was copied. It is also strange that the star catalogue uses the spring equinox as the reference point for the measurements of the longitudes, which involved additional difficulties that were sorted out only during the period from the 10th to 16th century. In addition, Ptolemy chose the North Star as the first star of the catalogue, what was not substantiated by the astronomical observations in the 2nd century. At that time there was another star near the north galactic pole, but this choice is consistent with the observations that could be made in the 11th-16th century.

Let us point out that Ptolemy adopted in the Almagest the so-called ecliptical coordinate system, which was believed by the medieval astronomers to be perpetual, i.e. it was assumed that the ecliptical latitudes of stars were not subjected to any change in time, while the longitudes were increasing steadily, what was caused by the cyclic precession of the Earth's axis of rotation. However, the systematic and considerable latitudinal shift was discovered by the astronomer J. Bode (1747-1826), which puts the Almagest's traditional dating in doubt.

Let us point out that in the Middle Ages two star coordinate systems were known, namely, the ecliptical and equatorial systems. Beginning in the 17th century, only the equatorial coordinates have been used in astronomical catalogues. Ecliptical coordinates can only be found in the Almagest and in the 16th century catalogues, for

, , o 7-. • en n ,1 , example the star catalogue of Tycho Brahe (1546-1601). Figure 1.13: Precession of the Earth's

North Pole The reason for this is very simple — the equatorial coordi nates are much easier to measure than the ecliptical ones. At the time of Ptolemy and in the 15th-17th century period, astronomers believed that the ecliptical coordinates are "eternal," what turned out to be wrong. Ptolemy also believed that stars do not possess their own movements and that their configurations on the sky are invariable. But this claim also was not correct. In the mid-18th century it was discovered that the star Arcturus changes its position by 1o each 100 years (this value was later corrected to 1.4°).

The Almagest

Ptolemy declared in the Almagest that he had directly measured the ecliptical coordinates of all stars (more than 1000 of them) using an astrolabe, which was a rather complicated procedure. He also described the magnitude of stars using the integer scale from one (for the brightest stars) to six (for the faintest ones). If we compare the magnitudes 1 to 2 of Ptolemy's stars with the modern ones, we shall conclude that they were always determined correctly, while he often made mistakes in the interval of the magnitudes 3 to 6.

There are dozens of contemporary works devoted to dating of the Almagest. N.A. Morozov, for example, used the following simple method to determine the date of compilation of the Almagest star catalogue. Since we know that the stars' longitudes possess an annual precession of 50.2", therefore, if we divide the difference between today's longitudes and those listed by Ptolemy in the Almagest, we will be able to derive the date when the catalogue was compiled. The obtained by Morozov results were shocking: all the longitudes given in the first Latin edition indicated the 16th century, i.e. the time when this "ancient" book was published. We would like also to mention a very interesting book by English astronomer Robert Newton "The Crime of Claudius Ptolemy"40, in which he conducted a mathematical and statistical analysis of the astronomical data contained in the Almagest. The results of his research were unexpected. He arrived to the conclusion that the astronomical observations of the Almagest were falsified. These serious accusations put in doubt the validity of the Almagest's astronomical data for the history of science. By the way, R. Newton was not aware of the results obtained by Morozov and fully trusted Scaliger's chronology.

Figure 1.14: Locations of Alpha Ursae Minoris and Beta Ursae Minoris in the 2nd century A.D. (based on J.E. Bode's drawing).

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