Metonic cycle

The Metonic cycle in astronomy and calendar studies is an approximate common multiple of the orbital periods of the Earth and the Moon. 19 tropical years differ from 235 synodic months by just about 2 hours.

This approximation is used by the Hebrew calendar. It was known to the Greek astronomer Meton, who introduced it about 432 BC, and the Chaldean astronomer Kidinnu (4th cy. BC). It is also used in the computation of the date of Easter.

In a typical lunisolar calendar, most years are lunar years of 12 months, but in 7 of the 19 years have an extra month, known as an intercalary or embolismic month. Traditionally (in the ancient Babylonian and Hebrew calendars), the years: 3, 6, 8, 11, 14, 17, and 19, are the long (13-month) years of the Metonic cycle. This incorporates two less accurate subcycles, for which 8 years = 99 lunations (an Octaeteris), and 11 years = 135 lunations.

The 19-year cycle is also close (to somewhat more than half a day) to 255 draconic months, so it also is an eclipse cycle, which lasts only for about 4 or 5 recurrences of eclipses. The implicit 11-year cycle is close to 146.5 draconic months, and is a better eclipse cycle called tritos.