The Callippic cycle (or Calippic) is a particular approximate common multiple of the

tropical year A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time fro ...

and the

synodic 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 ...

, proposed by

Callippus Callippus (; grc, Κάλλιππος; c. 370 BC – c. 300 BC) was a Greek astronomer and mathematician. Biography Callippus was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato. He also worked with Aristotle at the ...

in 330 BC. It is a period of 76 years, as an improvement of the 19-year

Metonic cycle The Metonic cycle or enneadecaeteris (from grc, ἐννεακαιδεκαετηρίς, from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recu ...

Description

A century before Callippus,

Meton Meton of Athens ( el, Μέτων ὁ Ἀθηναῖος; ''gen''.: Μέτωνος) was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the 5th century BC. He is best known for calculations involving the eponymou ...

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 In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they ...

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

solstice A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around June 21 and December 21. In many countrie ...

of 330 BC (28 June in the

proleptic Julian calendar The proleptic Julian calendar is produced by extending the Julian calendar backwards to dates preceding AD 8 when the quadrennial leap year stabilized. The leap years that were actually observed between the implementation of the Julian calendar i ...

), and was subsequently used by later astronomers. In

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...

'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 canon ...

'', for example, he cites (''Almagest'' VII 3, H25) observations by Timocharis 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 Athenian polis. It is sometimes called the Greek calendar be ...

, the

Pleiades The Pleiades (), also known as The Seven Sisters, Messier 45 and other names by different cultures, is an asterism and an open star cluster containing middle-aged, hot B-type stars in the north-west of the constellation Taurus. At a distance o ...

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 Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

. The Callippic calendar originally used the names of months from the

Attic calendar 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 Athenian polis. It is sometimes called the Greek calendar be ...

. Later astronomers, such as

Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equi ...

, 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. Ea ...

. 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 Nabû-nāṣir was the king of Babylon from 747 to 734 BC. He deposed a foreign Chaldean usurper named Nabu-shuma-ishkun, bringing native rule back to Babylon after twenty-three years of Chaldean rule. His reign saw the beginning of a new era c ...

. However, the original, complete form of the Callippic calendar is no longer known.

Equivalents

One Callippic cycle corresponds to: *940.008

s *1,020.084

draconic 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 *80.084 eclipse years (160

eclipse season An eclipse season is the period, roughly every six months, when eclipses occur. Eclipse seasons are the result of the axial parallelism of the Moon's tilted orbital plane ( tilted five degrees to the Earth's orbital plane), just as Earth's wea ...

s) *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 In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, ...

of the

orbit of the Moon The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days (a tropical month and sidereal month) and one revolution relative to the Sun in about 29.53 days (a ...

, and under these circumstances another eclipse can occur.

References

External links

Online Callippic calendar converter as used in Ptolemy's ''Almagest''
{{Greek astronomy Ancient Greek astronomy Calendars

Description

Equivalents

References

Further reading

External links