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.
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 which 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.
Click here to see diagram showing how
the Metonic Cycle is calculated:
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.
TY = TM – SM
Tropical year = tropical month MINUS synodic month
To calculate large numbers of cycles, metonic intervals
can be added (eg. III + VIII = XI)
