The fateful error of Hipparchus
Hipparchos of Nicäa († ca
120 BC.):
The
most important astronomer of his time was the first to describe the
apparent motion of the stars due to the Earth's precession: The star
Spica had drifted by 2° since his predecessor Timocharis had described
its occultation by the moon. This had happened in the 36th year of the
Alexander era of Callippus.
Meanwhile this would go back about 200 years...
In fact 2° precession equal only 144 years. Hipparchus would therefore have dated the epoch 54 years too early:
When it comes to the orientation on the course of the moon, an error of
54 years easily goes unnoticed, since after this period of time solar
and lunar eclipses repeat at almost the same place and time of day -
something Hipparch himself had discovered and named 'Exeligmos'. The
error led to a triplication of Alexander's epoch:
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A. The Alexander Era after Callippos:
In the 32nd year of the 3rd Callippus cycle, the 178th year after
Alexander's death, Hipparchus had observed the autumnal equinox. If the
years were counted correctly, the 'year 1' was 183 years ago.
(Aristarch had observed the summer solstice in the 50th year of
Callippus, the 44th after Alexander's death → †Alx 6.CP1)
B. The alternative Alexander Era of Hipparchos:
The year 50.CP.3 minus 200 years minus 35 (i.e. 1.CP.1 -54 years)
Timocharis' observations referred to the Alexander Epoch, which was
established by Kallippos at the solstice at new moon before the
conquest of Babylon. As Hipparchus concluded, about 200 years would
have passed since then.
Timocharis' report states, the moon covered Spica at the beginning of
the third hour after sunset in Alexandria [~17:40ut] on the 15th
Elaphebolion|5th Tybi in the 36th year of Callippos (i.e. February 9th
60ce).
With a lunar diameter of 0.4°, moving within a band of ±5.1° from the
ecliptic, the chance of obscuring spica within any given month is about
1:25. Observation on Luna XV of a given month and within a given hour
further reduces the chance by 1:8500 (i.e. 1:29.5 x12 x24).
Furthermore: The visual placement of the contact at the moon's limb may
be accurate within ±2' (i.e. 1/12 of the moon's diameter): Timocharis'
observation was definitely unique throughout antiquity!
C. The Seleucid Era [Epoch 311bc]:
Since this epoch is not compatible with Alexander's biography, it was
attributed to Alexander's General: Seleukos Nicator the Great was said
to have conquered and 're-founded' Edessa 19 years (i.e. one lunar
cycle) after Alexander, then also Gaza and Babylon, before he started
another campaign to India. After all, a chronology of Alexander IV that
was irrelevant to him would have taken over?
According to Jewish tradition, the Seleucid era began in the sixth year
of Alexander the Great's reign [i.e. trad. 330bc]. Alexander was linked
to the Jewish chronology by a tax exemption in the Sabbatical year -
likewise Callippus' era by the beginning of the year for the Jews,
which was linked to the course of the moon; obsolescence by 54 years
would therefore have been contradictory. However, 19
years later (54j-19j=35j=5x7j), the cycles of the moon's course and the
Sabbatical year coincided with Hipparcho's calculation. Precession of
the celestial bodies 35 years before Timocharis would in fact have been
½° (which could possibly be verified by lore), and the precession
calculated by Hipparchus for 54 years likewise resulted in ½°.