Callippic cycle

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

Description

A century before Callippus,

had described a cycle in which 19 years equals 235 lunations, and judged it to be 6,940 days. This 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 duration of 6940⁄19 = 365 + 5⁄19 = 365 + 1⁄4 + 1⁄76 days = 365 d 6 h 18 min 56 s.

Callippus accepted the 19-year cycle, but held that the duration of the year was more closely 365+1⁄4 days (= 365 d 6 h), so he multiplied the 19-year cycle by 4 to obtain an integer number of days, and then omitted 1 day from the last 19-year cycle. Thus, he computed a cycle of 76 years that consists of 940 lunations and 27,759 days, which has been named the Callippic cycle after him.

The first year of the first Callippic cycle began at the summer

The Callippic calendar originally used the names of months from the

Equivalents

One Callippic cycle corresponds to:

• 940
  synodic months
• 1,020.084
  draconic months
• 80.084 eclipse years (160 eclipse seasons)
• 1,007.410
  anomalistic months

The 80 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one callippic cycle a New Moon (resp. Full Moon) will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur.

References

Further reading

• Jean Meeus, Mathematical Astronomy Morsels, Willmann-Bell, Inc., 1997 (Chapter 9, p. 51, Table 9A: Some eclipse periodicities)

External links

• Online Callippic calendar converter as used in Ptolemy's Almagest