The Callippic cycle (or Calippic) is a particular approximate
common multiple
In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers ''a'' and ''b'', usually denoted by lcm(''a'', ''b''), is the smallest positive integer that is divisible by bot ...
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,
Meton had described a cycle in which 19 years equals 235 lunations. If we assume a year is about days, 19 years total about 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 duration of = 365 + = 365 + + 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 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 cycle's error has been computed as one full day in 553 years, or 4.95
parts per million.
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
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canoni ...
'', for example, he cites (''Almagest'' VII 3, H25) observations by
Timocharis Timocharis of Alexandria ( grc-gre, Τιμόχαρις or Τιμοχάρης, ''gen.'' Τιμοχάρους; c. 320–260 BC) was a Greek astronomer and philosopher. Likely born in Alexandria, he was a contemporary of Euclid.
Work
What little is kn ...
during the 47th year of the first Callippic cycle (283 BC), when on the eighth of
Anthesterion
The Attic calendar or Athenian calendar is the lunisolar calendar beginning in midsummer with the lunar month of Hekatombaion, in use in ancient Attica, the ancestral territory of the ancient Athens, Athenian polis. It is sometimes called the Gre ...
, the
Pleiades star cluster was
occulted
An occultation is an event that occurs when one object is hidden from the observer by another object that passes between them. The term is often used in astronomy, but can also refer to any situation in which an object in the foreground blocks ...
by the
Moon.
The Callippic calendar originally used the names of months from the
Attic calendar. Later astronomers, such as
Hipparchus, preferred other calendars, including the ancient
Egyptian calendar
The ancient Egyptian calendar – a civil calendar – was a solar calendar with a 365-day year. The year consisted of three seasons of 120 days each, plus an intercalary month of five epagomenal days treated as outside of the year proper. Eac ...
. 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 of the month of
Athyr, during year 465 of
Nabonassar. However, the original, complete form of the Callippic calendar is no longer known.
Equivalents
One Callippic cycle corresponds to:
*940.008
synodic months
*1,020.084
draconic months
*80.084 eclipse years (160
eclipse seasons)
*1,007.410
anomalistic month
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations
In Shona, Middle Eastern, and Euro ...
s
The 80 eclipse years means that if there is a
solar eclipse
A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby obscuring the view of the Sun from a small part of the Earth, totally or partially. Such an alignment occurs during an eclipse season, approximately every six month ...
(or
lunar eclipse
A lunar eclipse occurs when the Moon moves into the Earth's shadow. Such alignment occurs during an eclipse season, approximately every six months, during the full moon phase, when the Moon's orbital plane is closest to the plane of the Earth ...
), 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
Jean Meeus (born 12 December 1928) is a Belgian meteorologist and amateur astronomer specializing in celestial mechanics, spherical astronomy, and mathematical astronomy.
Meeus studied mathematics at the University of Leuven in Belgium, wh ...
, ''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''
{{Greek astronomy
Ancient Greek astronomy
Calendars