The Metonic Cycle

In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Greek words for nineteen years) is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the tropical year and the synodic (lunar) month. The Greek astronomer Meton of Athens observed that a period of 19 tropical years is almost exactly equal to 235 synodic months, and rounded to full days counts 6940 days. The difference between the two periods (of 19 tropical years and 235 synodic months) is only 2 hours.
Taking a year to be 1/19th of this 6940-day cycle gives a year length of 365 + 1/4 + 1/76 days (the unrounded cycle is much more accurate), which is slightly more than 12 synodic months. To keep a 12-month lunar year in pace with the solar year, an intercalary 13th month would have to be added on seven occasions during the nineteen-year period. Meton introduced a formula for intercalation in circa 432 BC.
The cycle’s most significant contemporary use is to help in flight planning (trajectory calculations and launch window analysis) for lunar spacecraft missions[citation needed] as well as serving as the basis for the Hebrew calendar’s 19-year cycle. Other uses are in computus, the calculation of the date of Easter, and in tidal analysis.

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