The Metonic Cycle is the Moon’s 19-year cycle where the Moon returns to exactly the same place (at the same longitude and against the same constellation) in the sky with the same phase. The Metonic Cycle is a period of about 6939.6 days, the approximate length of both 235 consecutive lunations and 19 solar years. Knowledge of this cycle is important in determining when to assign intercalate months to lunisolar calendars. Meton, an Athenian who lived in the middle of the fifth century B. C. is the cycle's namesake. Meton himself referred to it in a publication as the nineteen-year cycle. There is some question as to whether Meton discovered it on his own or whether he learned of it from Babylonian sources, because it was discovered there about fifty years before Meton's time. Lunisolar calendars have twelve lunar cycles in their common years. That's about eleven days short of a solar year. Each month starts on the day of a new Moon, or on the day a new lunar crescent is first sighted. Without intercalation, months start eleven days later in relation to seasons each successive year. An ordinary calendar is a solar (Sun) calendar. It keeps the dates in sync with the Sun. For instance, the Sun is at its highest point as we view it around the 21st of June – the summer solstice. The solar cycle (a year) takes 365 and a quarter days to complete. Every four years is a leap year when an extra day is added to the year. This accounts for the quarter day and keeps the date nearly in sync with the seasons. The cycle is not quite 365 and a quarter days. The error is 3 days in 400 years. A lunar (Moon) calendar keeps the lunar dates in sync with the Moon. For example, the 1st of the month could be on the new Moon. Then the 7th of the month would fall at the waxing half Moon. The dates vary for different types of lunar calendars, Muslim, Chinese, Buddhist, Jewish etc. Some have the 1st on the full Moon. However, all follow the Metonic Cycle that keeps the lunar dates in sync with the Moon.
# Tropical Lunar Month: The Moon returns to the same spot in the sky (against the backdrop of the same constellation) every 27.322 days, which is called the Tropical Lunar month. However, the Moon's phase is not the same for two days.
# Synodic Lunar Month: The Moon returns to the same phase every 29.5306 days and is called the Synodic Lunar month. There are 12 synodic months and 13 tropical months (returns) in one year. Therefore, it takes 19 years (or 6939 days) for the Moon to return to the same spot in the sky at same phase. This can be seen as: 19 tropical years - 365.24 days x 19 = 6939.56 days,
235 synodic months = 29.5306 days x 235 = 6939.691 days,
254 tropical months = 27.322 days x 254 = 6939.788 days.
# Lunar Leap Year (LLY): To keep the Moon's cycles as close to the Sun's cycle, an extra synodic month and an extra tropical month are added. So instead of 12 synodic months and 13 tropical months in a year, it is 13 synodic months and 14 tropical months.
