A very good Phi-related correlation can easily be found between the period of Jupiter’s orbit and the length of the full moon cycle, as we’ll describe in a moment.
First, what exactly is the full moon cycle?
One of several definitions given by Wikipedia says:
‘the full moon cycle is the period that it takes the Sun to return to the perigee of the Moon’s orbit (as seen from the Earth). So it is a kind of “perigee year”.’
It’s also the beat period of the Moon’s synodic (SM) and anomalistic (AM) months:
(SM x AM / SM – AM) = 411.78443 days (figure from Wikipedia).
NASA JPL gives the orbit period of Jupiter as 4332.82 days (converted from calendar years)
4332.82 x 136 = 589263.52 days
411.78443 x 1431 = 589263.51 days
Analysing the match:
34 x 2 x 2 Jupiter orbits = 55 x 13 x 2, +1 full moon cycles (FMC)
1,2,13,34 and 55 are Fibonacci numbers.
As a not-so-rough guide we could solve like this:
55/34 = Phi
cancel a common ‘x 2’ from each side of the equation
ignore the ‘+1’
1 Jupiter orbit = Phi (1.618034~) x 13/2 FMC [approx.]
which would be about 2 days short, or 0.00046~%.
Note: Jupiter also links to the lunar eclipse cycle.
2 Jupiter orbits = 25 draconic (or eclipse) years, accurate to within a few hours.