In addition to the familiar month-long lunar cycle, the phases of the moon recur in even longer cycles, many of which were recognized by ancient astronomers. The following interesting calendrical facts were compiled by famed astronomical calculator Jean Meeus.

• The Metonic Cycle was discovered by the Greek astronomer Meton (born about 460 B.C.). This is a 19-year cycle, after which time the phases of the moon are repeated on the same days of the year, or approximately so. For instance, there was a full moon on March 18, 2003. Nineteen years hence, in 2022, there'll be another full moon on March 18.
• Counting forward from any given phase of the moon, the preceding phase will occur in two years, on—or very close to—the same calendar date. For example, in 2003, we had a full moon on March 18; and in 2005, the first-quarter moon will occur on March 17.
• After eight years, the same lunar phases repeat, but occur one or two days later in the year. The Greeks called this eight-year cycle the octaeteris. Indeed, in 2011, a full moon occurred on March 19.
• Finally, using our Gregorian calendar, 372 years provides an excellent long period cycle for the recurrence of a particular phase on a given date. Thus, we know with absolute certainty that the same full moon that shone down on us on March 18 of 2003 will be shining on March 18 in the year 2375.