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# What are the Metonic and Callipic Cycles?

What are the Metonic and Callipic Cycles?

The ‘Metonic Cycle’ is a particular approximation of relationship between the solar year and the lunar month. The ‘Callipic Cycle’ is an even better approximation.

The solar year, or ‘Tropical Year’ is the length of time that the Sun, as viewed from the Earth, takes to return to the same position, or equinox, in the sky. The ‘Sideral Month’, is the length of time that the Moon, as viewed from the Earth, takes to return to the same position relative to the stars on the celestial sphere. However, because both the orbit of the Moon around the Earth, and the Earth around the Sun are completely independent, this leads to some complications.

The cause of the phases of the moon is that from the Earth we see the part of the Moon that is illuminated by the Sun from different angles as the Moon traverses its orbit. So the appearance depends on the position of the Moon with respect to the Sun (as seen from the Earth). Because the Earth orbits the Sun, it takes the Moon extra time (after completing a Sidereal Month, i.e. a full circle) to catch up and return to the same position with respect to the Sun. This longer period is called the ‘Synodic Month’ or lunar month

A ‘year’ of 12 Synodic months is about 354 days on average, 11 days short of the 365 day solar year. So about every 3 years an extra 13th synodic month has to be inserted into the calendar. The Greek astronomer Meton of Athens introduced a formula for the relationship between Synodic months and the Topical year in 432 BC. It was his observation that a period of 19 solar years is almost exactly 235 lunar months, and rounded to full days equates 6940 days.

In the following century Callippus developed the Callippic cycle. This was a more accurate approximation, obtained by taking one day away from every fourth of Meton's cycles, so creating a 76-year cycle with a mean year of exactly 365.25 days.

The Metonic and Callipic cycles are key to modeling a long term lunar / solar calendar, but the 19 year cycle is also close to an eclipse cycle, and could potentially predict eclipses for about 4 or 5 recurrences of eclipses. However, the Ancient Greeks had knowledge of better eclipse cycles.

Further reading: [bib]487[/bib], [bib]489[/bib]

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### A simple explanation of the Metonic cycle

The current western (Gregorian) calendar corresponds to the return of the seasons. In other words, if you give a date of the year and a location, then you should have a good idea of the weather. For example, in Europe, July is hot and January is cold. However, our months do not represent any physical phenomenon, knowing the day of the month doesn't tell you anything about the natural surroundings.

However, there are calendars where the months keep track of the phases of the Moon, the first of the month is always a new Moon and the 15th of the month is always a full Moon. In particular, this is true for the Islamic and Jewish calendars.

A lunar month averages about 29.5 days, so in a lunar calendar months alternate between 29 and 30 days (instead of 30 and 31 in the western calendar). This means that 12 months give 354 days, so about 11 short of the calendar year. For this reason, the Islamic calendar is 11 days earlier every western year and this explains why Ramadan is shifted significantly after a few years. Therefore, given a date of the Islamic calendar, you don't know anything about the weather but you do know the phase of the Moon.

The Metonic cycle is the observation that 235 lunar months are almost exactly 19 solar years. In this way, adding a 13th month 7 times every 19 years allows a lunar calendar to synchronize with the return of the seasons. For such calendars both the date of the year and the date of the month have astronomical significance.

The Jewish calendar follows the Metonic cycle, so that the Jewish New Year on 1 Tishrei is always on the new Moon, and Pesah on 15 Nissan is always on a full Moon. This also explains why Jewish holidays can seem to shift by a month from one year to the next with respect to the western calendar. Due to the Metonic cycle, after exactly 19 years, a western calendar date and a Jewish calendar date should correspond to within very few days.