Planetary periods in Hipparchus (1)

Text
Some fundamental empirical data of Hipparchus theories were taken from Babylonian astronomy. Hipparchus’ planetary periods are quoted by Ptolemy in the Almagest 9.3. One group of the cuneiform astronomical texts of the Seleucid period contains observational data and can be divided into four major sub-groups. The planetary periods play a particular role in one of these sub-groups, the so-called “goal-year texts.” These texts combine, for a given year (the “goal year”), planetary phenomena which happened a planetary period earlier. These fixed periods are:
for Saturn 59 years
for Jupiter 71 and 83 years
for Mars 79 and 47 years
for Venus 8 years
for Mercury 46 years

The duplicity in the case of Mars and Jupiter is explained by the observation that the first mentioned year number is associated with the synodic period, the second with the sidereal period of these planets. It is exactly these five periods which Ptolemy quotes as used by Hipparchus for his determination of the planetary mean motions, values which then were slightly refined by the application of Ptolemy’s own theory over much longer intervals of time. The fact that Hipparchus chose the periods used in Babylonian goal-year texts as the basis for his investigations is in all probability not accidental. It was well known to the Babylonian astronomers that the above-quoted periods were not exact. The mathematical astronomical texts consider as accurate the following periods:
for Saturn 265 years
for Jupiter 427 years
for Mars 284 years
for Venus 1151 years
for Mercury 480 years

The occurrence of exactly these numbers in astrological literature leaves no doubt that this part of the Babylonian theory was familiar to the Greeks as well. The reason for Hipparchus’ not using these larger and and supposedly exact periods undoubtedly lies in the fact that he was aware of their fictitious accuracy. It is clear that they were not the result of direct observations over so long intervals of time but resulted from the combination of smaller, slightly inaccurate periods, such that the corrections were eliminated as nearly as possible in the combined period. For the Babylonian theoretical texts these resulting larger periods were naturally chosen as the basis of further computation. Hipparchus remained as close as possible to the primary empirical material of which the goal-year texts are the reflection. The Babylonian goal-year texts also appear in mediaeval astrological treatises.

Source (list of abbreviations)
Ptolemy, Almagest 9.3

Bibliography

Amar Annus

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