The Lunar Cycle Calendar & Moon Phases
Our moon does not emit light. It merely reflects it. The Lunar Cycle Calendar tracks the orbit of the moon about the earth as it fluctuates between two extremes of visibility:
Near invisible - The New Moon
Fully visible - The Full Moon
In general the moon is near invisible when it is between the earth and the sun, with sunlight just reflecting a slight crescent of the moon. By contrast it is fully visible when the earth is between the sun and the moon. Earthbound viewers here see the full face of the moon bathed in reflected sunlight:
The Synodic Month & Moon Phases
It is important to realise that the length of each successive month of this type is not constant. It fluctuates roughly between 29 and 31 days. Our calendar months do the same - though here of course established through human design.
The most exacting average for the Synodic Month cycle is [1]: 29.5305891 days
Now the reason why the cycle is not constant is primarily due to the fact that the moon orbit is elliptical about the earth, whilst also the earth orbit is elliptical about the sun. Any celestial body in an elliptical orbit is continuously changing its speed whilst moving about its primary body. The complexities of the earth-moon orbital relations cause each successive Synodic month to be slightly different to the preceding one. The Lunar Cycle Calendar takes account of such variations from month to month.
In addition, the plane of the moon's orbit is offset from that of the earth's about the sun by some 5.145396 degrees [2]. This very fact explains why we do not have an eclipse every single month. With most months the 'disc of the moon' from the viewpoint of the earth, moves either over or under the 'disc of the sun' in passing. Only when there is a direct crossing do we have an eclipse.
The Metonic Cycle
It is a simple fact that there is no harmonious fit between the Lunar Cycle Calendar and the Earth year (365.2421897) [3]. A precise whole number of months do not fit within the length of the year. One can see with a simple division sum that there is a sizable remainder:
365.2421897 / 29.5305891 = 12.3682662 months per year
At the completion of one Earth year, we find ourselves already over 1/3 of the way into the 13th Synodic Month. Confronted with this, we might well inquire if there is some basic time cycle that captures a harmonious re-synchronisation, between both years and months.
Indeed there is. It is known as the Metonic Cycle, named after the ancient Greek astronomer Meton, who lived in 5th century BC Athens.
Now Meton was not the first to discover the cycle. It was known to the more ancient Sumerians and Babylonians a few thousand years earlier. That said however, historically speaking, the cycle is most commonly associated with Meton. It is his name therefore that 'takes the glory' in referring to the cycle.
What Meton identified, like the Sumerians and Babylonians before him, was that there was a close match between 19 Earth Years, and 235 Synodic Months:
19 x 365.2421897 = 6939.601604 days
235 x 29.5305891 = 6939.688443 days
The discrepancy between both time values is only some 2 hours 5 minutes.
Now what this means, is that from any given earth-moon starting arrangement, after 19 years, there will be a very close return to the starting pattern. There will be a resynchronisation of the Lunar Cycle Calendar with respect to a whole number of Earth years. The pattern and duration of successive months will therefore closely match that of the preceding 19 years.
The Metonic cycle is by definition a period of precisely 235 Synodic Months, being only some 2 hours 5 minutes greater in length than 19 full years.
Next: Mayan Mythology & the Popol Vuh
Notes
[1] The Astronomical Almanac 2003.
Nautical Almanac Office, United States Naval Observatory, and H. M. Nautical Almanac Office, Rutherford Appleton Laboratory. (2001), Page D2
[2] Explanatory Supplement to the Astronomical Almanac.
University Science Books. (1992), Page 698
[3] Ibid. (1992), Page 701