Why Phi? – a lunar evection model

Apogee = position furthest away from Earth. Earth. Perihelion = position closest to the sun. Moon. Perigee = position closest to Earth. Sun. Aphelion = position furthest away from the sun. (Eccentricities greatly exaggerated!)

Lunar evection has been described as the solar perturbation of the lunar orbit.

One lunar evection is the beat period of the synodic month and the full moon cycle. The result is that it should average about 31.811938 days (45809.19 minutes).

Comparing synodic months (SM), anomalistic months (AM), and lunar evections (LE) with the full moon cycle (FMC) we find:
1 FMC = 13.944335 SM
1 FMC = 13.944335 + 1 = 14.944335 AM
1 FMC = 13.944335 – 1 = 12.944335 LE

Since 0.944335 * 18 = 16.9983 = 99.99% of 17, and 18 – 17 = 1, we can say for our model:
18 FMC = 233 LE (18*13, -1) = 251 SM (18*14, -1) = 269 AM (18*15, -1)

Noting that 233 is a Fibonacci number, if we multiply by 8:
144 FMC (18*8) = 233*8 LE (for model purposes)

8, 144 and 233 are all Fibonacci (F) numbers, and 144 and 233 are consecutive F numbers i.e.:
233 / 144 = Phi
Therefore: FMC / 8 LE = Phi, or the golden ratio
Cross-check: 12.944335 / 8 = 1.6180418 (Phi = 1.618034)

This means that for any Fibonacci number (F1) of full moon cycles, the number of lunar evections in that period will be F2 * 8, where F2 is the next number in the Fibonacci series. The accuracy of the result increases as the numbers increase, which is the nature of the Fibonacci series.

An example would be the period of 55 full moon cycles, which is close to both 62 tropical years and 7 lunar apsidal cycles (55 + 7 = 62). Using F1 = F2 * 8:

55 FMC = 22648.143 days
The next Fibonacci number after 55 is 89.
89 * 8 LE = 22650.1 days
Accuracy of match is > 99.991%.

Related: Predicting the Start of the Next El Niño Event — by Ian Wilson.