Callippic cycle

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In astronomy and calendar studies, the Callippic cycle (or Calippic) is a particular approximate common multiple of the year (specifically the tropical year) and the synodic month, that was proposed by Callippus in 330 BC. It is a period of 76 years, as an improvement on the 19-year Metonic cycle.

A century before Callippus, Meton invented the cycle of 19 years that counted 6,940 days, which exceeds 235 lunations by almost a third of a day, and 19 tropical years by four tenths of a day. It implicitly gave the solar year a length of 6940/19 = 365 + 1/4 + 1/76 days = 365 d 6 h 18 min 56 s. But Callippus knew that the length of the year was more closely 365 + 1/4 day (= 365d 6h 00m 00s), so he multiplied the 19-year cycle by 4 to reach an integer number of days, and then dropped 1 day from the last 19-year cycle. Thus he constructed a cycle of 76 years which contains 940 lunations and 27,759 days, and has been called the Callippic after him. The cycle's error is one full day in 553 years, or 4.95 parts per million.[1]

The first year of the first Callippic cycle began at the summer solstice of 330 BC (28 June in the proleptic Julian calendar), and was subsequently used by later astronomers. In Ptolemy's Almagest, for example, he cites (Almagest VII 3, H25) observations by Timocharis in the 47th year of the first Callippic cycle (283 BC), when on the eighth of Anthesterion, the Pleiades were occulted by the Moon.[2]

The Callippic calendar originally used the names of months from the Attic calendar, although later astronomers, such as Hipparchus, preferred other calendars, including the Egyptian calendar. Also Hipparchus invented his own Hipparchic calendar cycle as an improvement upon the Callippic cycle. Ptolemy's Almagest provided some conversions between the Callippic and Egyptian calendars, such as that Anthesterion 8, 47th year of the first Callippic period was equivalent to day 29 in the month of Athyr, in year 465 of Nabonassar. However, the original, complete form of the Callippic calendar is no longer known.[2]


[edit] References

  1. ^ This article incorporates content from the 1728 Cyclopaedia, a publication in the public domain.
  2. ^ a b Evans, James. "The Callippic Cycle." The History & Practice of Ancient Astronomy. Oxford University Press US. 1998. ISBN 0-19-509539-1. 186–7.
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