Metonic cycle

Depiction of the 19 years of the Metonic cycle as a wheel, with the Julian date of the Easter New Moon, from a 9th-century computistic manuscript made in St. Emmeram's Abbey (Clm 14456, fol. 71r)
For example, by the 19-year Metonic cycle, the full moon repeats on or near Christmas day between 1711 and 2300.[1][2] A small horizontal libration is visible comparing their appearances. A red color shows full moons that are also lunar eclipses.

The Metonic cycle or enneadecaeteris (from Ancient Greek: 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 recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar.

A tropical year is longer than 12 lunar months and shorter than 13 of them. The arithmetic identity 12×12 + 7×13 = 235 allows it to be seen that a combination of 12 "short" years (12 months) and 7 "long" years (13 months) will be almost exactly equal to 19 solar years.

Application in traditional calendars

In the Babylonian and Hebrew lunisolar calendars, the years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the Metonic cycle. This cycle forms the basis of the Greek and Hebrew calendars, and is used for the computation of the date of Easter each year.

The Babylonians applied the 19-year cycle since the late sixth century BC.[3]

According to Livy, the second king of Rome, Numa Pompilius (reigned 715–673 BC), inserted intercalary months in such a way that "in the twentieth year the days should fall in with the same position of the sun from which they had started."[4] As "the twentieth year" takes place nineteen years after "the first year", this seems to indicate that the Metonic cycle was applied to Numa's calendar.

Diodorus Siculus reports that Apollo is said to have visited the Hyperboreans once every 19 years.[5]

The Metonic cycle has been implemented in the Antikythera mechanism which offers unexpected evidence for the popularity of the calendar based on it.[6]

The (19-year) Metonic cycle is a lunisolar cycle, as is the (76-year) Callippic cycle.[7] An important example of an application of the Metonic cycle in the Julian calendar is the 19-year lunar cycle insofar as provided with a Metonic structure.[8] In the following century, Callippus developed the Callippic cycle of four 19-year periods for a 76-year cycle with a mean year of exactly 365.25 days.

Around AD 260 the Alexandrian computist Anatolius, who became bishop of Laodicea in AD 268, was the first to devise a method for determining the date of Easter Sunday.[9] However, it was some later, somewhat different, version of the Metonic 19-year lunar cycle which, as the basic structure of Dionysius Exiguus’ and also of Bede’s Easter table, would ultimately prevail throughout Christendom,[10] at least until in the year 1582, when the Gregorian calendar was introduced.

The Celts knew the Metonic cycle thousands of years ago, as evidenced by artifacts such as the Knowth Calendar Stone.[11] It was almost certainly the basis for the 19-year so-called Celtic Great Year.

The Runic calendar is a perpetual calendar based on the 19-year-long Metonic cycle. It is also known as a Rune staff or Runic Almanac. This calendar does not rely on knowledge of the duration of the tropical year or of the occurrence of leap years. It is set at the beginning of each year by observing the first full moon after the winter solstice. The oldest one known, and the only one from the Middle Ages, is the Nyköping staff, which is believed to date from the 13th century.

The Bahá'í calendar, established during the middle of the 19th century, is also based on cycles of 19 solar years.

Hebrew calendar

A Small Mahzor (Hebrew מחזור, pronounced [maχˈzor], meaning "cycle") is a 19-year cycle in the lunisolar calendar system used by the Jewish people. It is similar to, but slightly different in usage with, the Greek Metonic cycle, and likely derived from or alongside the much earlier Babylonian calendar.[12]

Three ancient civilizations (Babylonia, China and Israel) used lunisolar calendars and knew of the rule of the intercalation from as early as 2000 BC. Whether or not the correlation indicates cause-and-effect relationship is an open question.[13][14]


It is possible that the Polynesian kilo-hoku (astronomers) discovered the Metonic cycle in the same way Meton had, by trying to make the month fit the year.[15]

Mathematical basis

The Metonic cycle is the most accurate cycle of time less than 100 years for synchronizing the tropical year and the lunar month, when the method of synchronizing is the intercalation of a thirteenth lunar month in a calendar year from time to time.[16]

Tropical year = 365.2422 days.[17]
365.2422 x 19 = 6,939.602 days (every 19 years)
Synodic month = 29.53059 days.[18]
29.53059 x 235 = 6,939.689 days (every 235 months)
19 years of 12 synodic months = 228 synodic months per cycle, 7 months short of the 235 months needed to achieve synchronization.

The traditional lunar year of 12 synodic months is about 354 days, approximately 11 days short of the solar year. Thus, every 2-3 years there is an accumulated discrepancy of approximately a full synodic month. In order to 'catch up' to this discrepancy, to maintain seasonal consistency and to prevent dramatic shifts over time, seven intercalary months are added (one at a time), at intervals of every 2-3 years during the course of 19 solar years.

The difference between 19 solar years and 235 synodic months is only about two hours, or 0.087 days.

See also


  1. ^ "Rare Full Moon on Christmas Day". NASA. 17 December 2015.
  2. ^ Skilling, Tom (20 December 2015). "Ask Tom: How unusual is a full moon on Christmas Day?". Chicago Tribune.
  3. ^ "The Babylonian Calendar". Mathematical Institute. Utrecht University. July 2021.
  4. ^ Livy, Ab Urbe Condita, I, XIX, 6.
  5. ^ Diodorus Siculus, Bibl. Hist. II.47.
  6. ^ Freeth, Tony; Jones, Alexander; Steele, John M.; Bitsakis, Yanis (31 July 2008). "Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism" (PDF). Nature. 454 (7204): 614–7. Bibcode:2008Natur.454..614F. doi:10.1038/nature07130. PMID 18668103. S2CID 4400693. Retrieved 20 May 2014.
  7. ^ Nothaft 2012, p. 168.
  8. ^ McCarthy & Breen 2003, p. 17.
  9. ^ Declercq 2000, pp. 65–66.
  10. ^ Declercq 2000, p. 66.
  11. ^ "Metonic Cycle: the 19-year cycle of the moon". Mythical Ireland. 30 October 2017.
  12. ^ "Jewish religious year | Cycle, Holidays, & Facts | Britannica". Retrieved 14 November 2021.
  13. ^ Watkins 1954.
  14. ^ Hannah 2005.
  15. ^ Johnson 2001, p. 238.
  16. ^ Richards 1998, pp. 94–96.
  17. ^ aaglossary 2020, s.v. year, tropical.
  18. ^ Richards 2013, p. 587.


  • Declercq, Georges (2000). Anno Domini: The Origins of the Christian Era. Turnhout. ISBN 9782503510507.
  • "Glossary". The Astronomical Almanac Online!. Washington, DC: United States Naval Observatory. 2020.
  • Hannah, Robert (2005). Greek & Roman Calendars: Construction of Time in the Classical World. London: Duckworth.
  • Johnson, Rubellite Kawena (2001). Essays in Hawaiian Literature Part 1 Origin Myths and Migration traditions. author.
  • McCarthy, Daniel P.; Breen, Aidan (2003). The ante-Nicene Christian Pasch | De ratione paschali: The Paschal tract of Anatolius, bishop of Laodicea. Dublin: Four Courts Press. ISBN 9781851826971. OCLC 367715096.
  • Nothaft, C Philipp E. (2012). Dating the Passion: The Life of Jesus and the Emergence of Scientific Chronology (200–1600. Leiden: BRILL. ISBN 9789004212190.
  • Richards, E. G. (1998). Mapping Time: The Calendar and its History. Oxford University Press. ISBN 978-0192862051.
  • Richards, E. G. (2013). "Calendars". In Urban, Sean E.; Seidelmann, P. Kenneth (eds.). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, CA: University Science Books. ISBN 978-1-891389-85-6.
  • Watkins, Harold (1954). Time Counts: The Story of the Calendars. New York: Philosophical Library.

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This is a mosaic image, one of the largest ever taken by NASA's Hubble Space Telescope, of the Crab Nebula, a six-light-year-wide expanding remnant of a star's supernova explosion. Japanese and Chinese astronomers recorded this violent event in 1054 CE, as did, almost certainly, Native Americans.

The orange filaments are the tattered remains of the star and consist mostly of hydrogen. The rapidly spinning neutron star embedded in the center of the nebula is the dynamo powering the nebula's eerie interior bluish glow. The blue light comes from electrons whirling at nearly the speed of light around magnetic field lines from the neutron star. The neutron star, like a lighthouse, ejects twin beams of radiation that appear to pulse 30 times a second due to the neutron star's rotation. A neutron star is the crushed ultra-dense core of the exploded star.

The Crab Nebula derived its name from its appearance in a drawing made by Irish astronomer Lord Rosse in 1844, using a 36-inch telescope. When viewed by Hubble, as well as by large ground-based telescopes such as the European Southern Observatory's Very Large Telescope, the Crab Nebula takes on a more detailed appearance that yields clues into the spectacular demise of a star, 6,500 light-years away.

The newly composed image was assembled from 24 individual Wide Field and Planetary Camera 2 exposures taken in October 1999, January 2000, and December 2000. The colors in the image indicate the different elements that were expelled during the explosion. Blue in the filaments in the outer part of the nebula represents neutral oxygen, green is singly-ionized sulfur, and red indicates doubly-ionized oxygen.
Author/Creator: Me, Licence: Copyrighted free use
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This view of the rising Earth greeted the Apollo 8 astronauts as they came from behind the Moon after the fourth nearside orbit. Earth is about five degrees above the horizon in the photo. The unnamed surface features in the foreground are near the eastern limb of the Moon as viewed from Earth. The lunar horizon is approximately 780 kilometers from the spacecraft. Width of the photographed area at the horizon is about 175 kilometers. On the Earth 240,000 miles away, the sunset terminator bisects Africa.
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This is a montage of planetary images taken by spacecraft managed by the Jet Propulsion Laboratory in Pasadena, CA. Included are (from top to bottom) images of Mercury, Venus, Earth (and Moon), Mars, Jupiter, Saturn, Uranus and Neptune. The spacecraft responsible for these images are as follows:
  • the Mercury image was taken by Mariner 10,
  • the Venus image by Magellan,
  • the Earth and Moon images by Galileo,
  • the Mars image by Mars Global Surveyor,
  • the Jupiter image by Cassini, and
  • the Saturn, Uranus and Neptune images by Voyager.
  • Pluto is not shown as it is no longer a planet, and no spacecraft has yet visited it when this montage was taken. The inner planets (Mercury, Venus, Earth, Moon, and Mars) are roughly to scale to each other; the outer planets (Jupiter, Saturn, Uranus, and Neptune) are roughly to scale to each other. PIA 00545 is the same montage with Neptune shown larger in the foreground. Actual diameters are given below:
  • Sun (to photosphere) 1,392,684 km
  • Mercury 4,879.4 km
  • Venus 12,103.7 km
  • Earth 12,756.28 km
  • Moon 3,476.2 km
  • Mars 6,804.9 km
  • Jupiter 142,984 km
  • Saturn 120,536 km
  • Uranus 51,118 km
  • Neptune 49,528 km
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Artist's impression of "the oldest star of our Galaxy": HE 1523-0901
  • About 13.2 billion years old
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CLM 14456 70v71r.jpg
Handschrift aus dem ehemaligen Benediktinerkloster St. Emmeram in Regensburg (Clm 14456, foll. 70v/71r).
fol. 70v oben: Kreisschema mit Lauf der Sonne
Hoc modo solis cursus hiemalis & equinoctialis & solstitium designatur
fol. 70v unten: Kreisschema mit den Mondphasen
hic solem invenit luna
fol. 71r oben: Kreisschema zum 19-jährigen Mondzyklus mit Angabe des julianischen Kalenderdatums des Osterneumonds (accensio lunae), etc.
fol. 71r unten: Berechnungen von Zeitmaßen für eine Woche (dies, puncta, minuta, momenta):
ebdomada habet dies vii h[orae] c lx viiii pu[nctae] dc lxxii min[utae] i dc lxxx mom[entae] vi dcc xx
"eine Woche hat sieben Tage, 169 (sic, statt 168) Stunden, 672 puncta, 1680 minuta, 6720 momenta."
Christmas full moons 1711-2300.gif
Author/Creator: Tomruen, Licence: CC BY-SA 4.0
A simulated timelapse of the full moon appearing on or near Christmas day from 1711-2300 CE, with one frame for every 19th year according to the periodicity of the Metonic cycle. The embedded graph shows the shifting timing of full moon with December 25 in the middle, December 24 below, and December 26 above in a secular drift due to the fact that the 19-year period approximating the Metonic cycle is not exact.