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
8th 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.
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)
