For 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 during 330 BC. It is a period of 76 years, as an improvement of the 19-year Metonic cycle.

A century before Callippus, Meton had discovered the cycle in which 19 years equals 235 lunations. If we assume a year is about 365 ^{1}⁄_{4} days, 19 years total about 6940 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 ^{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.^{ [1] } Although the cycle's error has been computed as one full day in 553 years, or 4.95 parts per million.^{ [2] }

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 during the 47th year of the first Callippic cycle (283 BC), when on the eighth of Anthesterion, the Pleiades star cluster was occulted by the Moon.^{ [3] }

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. 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.^{ [3] }

One Callippic cycle corresponds to:

- 940.008 synodic months
- 1020.084 draconic months
- 80.084 eclipse years (160 eclipse seasons)
- 1007.410 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.

**Hipparchus of Nicaea** was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.

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

The **epact**, used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January. Its principal use is in determining the date of Easter by computistical methods. It varies from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.

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The Greek astronomer Hipparchus introduced two cycles that have been named after him in later literature.

**Callippus** was a Greek astronomer and mathematician.

**Babylonian mathematics** was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited. In respect of time they fall in two distinct groups: one from the Old Babylonian period, the other mainly Seleucid from the last three or four centuries BC. In respect of content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for nearly two millennia.

**Greek astronomy** is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as **Hellenistic astronomy**, while the pre-Hellenistic phase is known as **Classical Greek astronomy**. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.

**Babylonian astronomy** was the study or recording of celestial objects during early history Mesopotamia. These records can be found on Sumerian clay tablets, inscribed in cuneiform, dated to around 1000 BCE.

A **total lunar eclipse** will take place on March 3, 2026.

**Maya astronomy** is the study of the Moon, planets, Milky Way, Sun, and astronomical phenomena by the Precolumbian Maya Civilization of Mesoamerica. The Classic Maya in particular developed some of the most accurate pre-telescope astronomy in the world, aided by their fully developed writing system and their positional numeral system, both of which are fully indigenous to Mesoamerica. The Classic Maya understood many astronomical phenomena: for example, their estimate of the length of the synodic month was more accurate than Ptolemy's, and their calculation of the length of the tropical solar year was more accurate than that of the Spanish when the latter first arrived. As well as many temples from the Maya architecture have features orientated to celestial events.

In lunar calendars, a **lunar month** is the time between two successive syzygies. The precise definition varies, especially for the beginning of the month.

- ↑ Neugebauer, Otto (1975),
*A History of Ancient Mathematical Astronomy*,**1**, New York: Springer-Verlag, pp. 621–624, ISBN 0-387-06995-X - ↑
This article incorporates text from a publication now in the public domain : Chambers, Ephraim, ed. (1728). "Calippic Period". *Cyclopædia, or an Universal Dictionary of Arts and Sciences*.**1**(1st ed.). James and John Knapton, et al. p. 144. - 1 2 Evans, James (1998),
*The History & Practice of Ancient Astronomy*, New York / Oxford: Oxford University Press, pp. 186–187, ISBN 0-19-509539-1

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

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