Callippic cycle

Encyclopedia

In astronomy

and calendar

studies, the

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 discovered 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 that contains 940 lunations and 27,759 days, and has been called the

Although the cycle's error has been calculated as one full day in 553 years, or 4.95 parts per million., in actuality 27,759 days in 76 years has a mean year of exactly 365 + 1/4 days, which relative to the mean northward equinoctial year is about 11 minutes too long per year, in other words the cycle drifts another day late per 130 + 10/11 years, which is considerably worse than the drift of the unrounded Metonic cycle

. If the Callippic cycle is considered as closer to its unrounded length of 27,758 + 3/4 days (based on 940 lunations) then its accuracy is essentially the same as the unrounded Metonic cycle (within a few seconds per year). If it is taken as 940 lunations less one day then the Callippic mean year will be shortened by 1/76 day (18 minutes 57 seconds), making it grossly too short, and it will also grossly drift ahead with respect to the mean lunar cycle at the rate of 1/940 of a day (1 minute 31 seconds) per lunar month. If the cycle length is truncated to 27,758 days then the mean year is 365 days 5 hours 41 minutes 3 seconds, or almost 8 minutes too short per year, and it will drift ahead of the mean lunar cycle by about (3/4)/940 day (1 minute 9 seconds) per lunar month. Altogether, the purported accuracy of this cycle is not impressive, but it is of historical interest.

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

in the 47th year of the first Callippic cycle (283 BC

), when on the eighth of Anthesterion, the Pleiades

were occulted

by the Moon

.

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

, in year 465 of Nabonassar

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

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

and calendar

Calendar

A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...

studies, the

**Callippic cycle**(or Calippic) is a particular approximate common multipleLeast common multiple

In arithmetic and number theory, the least common multiple of two integers a and b, usually denoted by LCM, is the smallest positive integer that is a multiple of both a and b...

of the year

Year

A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic....

(specifically the tropical year

Tropical year

A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...

) and the synodic month, that was proposed by Callippus

Callippus

Callippus or Calippus was a Greek astronomer and mathematician.Callippus was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato. He also worked with Aristotle at the Lyceum, which means that he was active in Athens prior to Aristotle's death in 322...

in 330 BC

330 BC

Year 330 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Year of the Consulship of Crassus and Venno...

. It is a period of 76 years, as an improvement on the 19-year Metonic cycle

Metonic cycle

In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...

.

A century before Callippus, Meton discovered 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 that contains 940 lunations and 27,759 days, and has been called the

*Callippic*after him.Although the cycle's error has been calculated as one full day in 553 years, or 4.95 parts per million., in actuality 27,759 days in 76 years has a mean year of exactly 365 + 1/4 days, which relative to the mean northward equinoctial year is about 11 minutes too long per year, in other words the cycle drifts another day late per 130 + 10/11 years, which is considerably worse than the drift of the unrounded Metonic cycle

Metonic cycle

In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...

. If the Callippic cycle is considered as closer to its unrounded length of 27,758 + 3/4 days (based on 940 lunations) then its accuracy is essentially the same as the unrounded Metonic cycle (within a few seconds per year). If it is taken as 940 lunations less one day then the Callippic mean year will be shortened by 1/76 day (18 minutes 57 seconds), making it grossly too short, and it will also grossly drift ahead with respect to the mean lunar cycle at the rate of 1/940 of a day (1 minute 31 seconds) per lunar month. If the cycle length is truncated to 27,758 days then the mean year is 365 days 5 hours 41 minutes 3 seconds, or almost 8 minutes too short per year, and it will drift ahead of the mean lunar cycle by about (3/4)/940 day (1 minute 9 seconds) per lunar month. Altogether, the purported accuracy of this cycle is not impressive, but it is of historical interest.

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

Solstice

A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...

of 330 BC

330 BC

Year 330 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Year of the Consulship of Crassus and Venno...

(28 June in the proleptic Julian calendar

Proleptic Julian calendar

The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding AD 4 when its quadrennial leap year stabilized. The leap years actually observed between its official implementation in 45 BC and AD 4 were erratic, see the Julian calendar article for details.A calendar...

), and was subsequently used by later astronomers. In Ptolemy

Ptolemy

Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

's

*Almagest*

, for example, he cites (Almagest

The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...

*Almagest*VII 3, H25) observations by TimocharisTimocharis

Timocharis of Alexandria was a Greek astronomer and philosopher. Likely born in Alexandria, he was a contemporary of Euclid....

in the 47th year of the first Callippic cycle (283 BC

283 BC

Year 283 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Dolabella and Maximus...

), when on the eighth of Anthesterion, the Pleiades

Pleiades (star cluster)

In astronomy, the Pleiades, or Seven Sisters , is an open star cluster containing middle-aged hot B-type stars located in the constellation of Taurus. It is among the nearest star clusters to Earth and is the cluster most obvious to the naked eye in the night sky...

were occulted

Occultation

An occultation is an event that occurs when one object is hidden by another object that passes between it and the observer. The word is used in astronomy . It can also refer to any situation wherein an object in the foreground blocks from view an object in the background...

by the Moon

Moon

The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

.

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

Attic calendar

The Attic calendar is a hellenic calendar that was in use in ancient Attica, the ancestral territory of the Athenian polis. This article focuses on the 5th and 4th centuries BC, the classical period that produced some of the most significant works of ancient Greek literature. Because of the...

, although later astronomers, such as Hipparchus

Hipparchus

Hipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...

, preferred other calendars, including the Egyptian calendar

Egyptian calendar

The ancient civil Egyptian calendar had a year that was 360 days long and was divided into 12 months of 30 days each, plus five extra days at the end of the year. The months were divided into three weeks of ten days each...

. Also Hipparchus invented his own Hipparchic calendar cycle

Hipparchic cycle

The Greek astronomer Hipparchus introduced two cycles that have been named after him in later literature.The first is described in Ptolemy's Almagest IV.2...

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 AthyrMonth of Hathor

Hathor , also known as Hatour, is the third month of the Coptic calendar. It lies between November 10 and December 9 of the Gregorian calendar...

, in year 465 of Nabonassar

Nabonassar

Nabonassar founded a kingdom in Babylon in 747 BC. This is now considered as the start of the Neo-Babylonian Dynasty. At the time the Assyrian Empire was in disarray through civil war and the ascendancy of other kingdoms such as Urartu...

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