Full moon cycle
fumocy is an abbreviation for "Full Moon Cycle". It was introduced by Karl Palmen in the CALNDR-L mailing list in October 2002.
It refers to the observation that full moons vary in apparent size, in a cycle of about 14 lunations. The variation in apparent size of the Moon is due to the fact that the orbit of the Moon is distinctly elliptic, and as a consequence at one time it is nearer to the Earth (perigeum) than half an orbit later (apogeum). The orbit period of the Moon from perigeum to apogeum and back to perigeum is called the anomalistic month, and its average duration is:
- AM = 27.55455 days
Full Moons repeat in a cycle called synodic month, and it has an average duration of:
- SM = 29.53059 days
The Full Moon Cycle is the beat period of these two, and has a duration of:
This is slightly less than 14 synodic months, and slightly less than 15 anomalistic months. Its significance is that when you start with a large Full Moon at the perigeum, then subsequent Full Moons will occur ever later after the passage of the perigeum; after 1 fumocy, the accumulated difference between the number of completed anomalistic months and the number of completed synodic months is exactly 1.
When tracking fumocy's by counting cycles of 14 synodic months, a correction of 1 synodic month should take place after 18 fumocy's:
- 18*FC = 251*SM =269*AM , not:
- 18*14 = 252*SM
A good longer period spans 55 fumocies or rather 767 synodic months, which is close to an integer number of anomalistic months as well as an integer number of days:
- 767*SM = 822*AM = 22650 days = 55*FC + 2 days
Besides predicting when a Full Moon will be large, the fumocy cycle can be used to more accurately predict the exact time of the Full Moon or New Moon. The Moon's phases do not repeat very regularly: the time between two similar phases may vary between 29.272 and 29.833 days (see new moon for a detailed account). The reason is that the orbit of the Moon is elliptic, its velocity is not constant, so the time of the true phase will differ from the mean phase. The deviations can be expressed as a series expansion of sine terms. The major terms depend on the mean anomaly at the time of (mean) New or Full Moon, that is: the distance along its orbit from the perigeum, which is the phase of the Moon in its anomalistic cycle. As we have seen, this anomalistic cycle coincides with the synodic cycle again after 1 fumocy.