Why Phi? – Jupiter and the Full Moon Cycle

Posted: December 28, 2015 by oldbrew in moon, solar system dynamics

Jupiter and the Moon - not to scale of course [image credit: IBNLive]

Jupiter and the Moon – not to scale of course
[image credit: IBNLive]

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.

  1. vuurklip says:

    Phiscinating! Here in Cape Town we recently experienced proxigean high tides at the same time as we had a lunar eclipse. How can we determine when super tides occur as a result of a) the moon closest to earth, b) Earth closest to Sun, c) Lunar eclipse, all occurring at the same time.

    Are there any other significant cycles adding to exceptional high tides? I.E when all the ducks are in a row?

  2. oldbrew says:

    vuurklip: try the NASA Eclipse website.

    Or Wikipedia: http://en.wikipedia.org/wiki/Eclipse_cycle

    Tides can work differently in different locations, e.g. diurnal or semi-diurnal.
    Earth perihelion is currently in early January.

  3. Curious George says:

    2015 = 5 x (377 + 2 x 13)
    2016 = 2 x 2 x 3 x 8 x 21, all Fibonacci numbers on the right hand side.

  4. oldbrew says:

    George: for a bonus point, give the relationship of the two numbers 😉

  5. Curious George says:

    I claim my bonus: 2015 is this year, 2016 is the next year.

    You can express any integer in terms of Fibonacci numbers, if you allow addition. That 2016 can be expressed without using any additions is just a sheer luck.

    Happy New Year 2016 to you and your (occasionally skeptical) followers.

  6. oldbrew says:

    CG: ‘You can express any integer in terms of Fibonacci numbers, if you allow addition.’

    True, but we normally only allow +/- 1, which shows how close the numbers are to an exact match.

    Phi ratios and planetary alignments are nearly always about near-resonance or near-commensurability, Phi being the most irrational number.

    Anyway, I reckon 2016 is 144 x 3². HNY.

    Correction! 144 x 14 thanks TB – too many numbers today 😦

  7. oldbrew says:

    ‘The KAM theorem states that if the system is subjected to a weak non-linear perturbation, some of the invariant tori are deformed and survive, while others are destroyed. The ones that survive are those that have “sufficiently irrational frequencies” (the non-resonance condition, so they do not interfere with one another). The golden ratio being the most irrational number is often evident in such systems of oscillators. It is also physically significant in that circles with golden mean frequencies are the last to break up in a perturbed dynamical system, so the motion continues to be quasi-periodic, i.e., recurrent but not strictly periodic or predictable.’


    ‘According to the KAM theorem (Kolmogorov, Arnold, Moser), the most stable periodic orbit of a dynamic system is that which has the Golden Ratio as a winding number. The more irrational the winding number is (the ratio of the resonance frequencies) the more stable is the periodic orbit. Since the Golden Ratio is the most irrational number, it follows that the orbit with the Golden Ratio as a winding number is the most stable.’

  8. tallbloke says:

    144 x 3² was always 1296 when I was a lad at school. 🙂

  9. This phi relation is a bit complex and might need to be seen another way.

    However the two Jupiter orbits being equal to twenty five eclipse years is a very good “observation”: accurate and direct. This is to be expected since Jupiter dominates the Moon, having a synodic period of 13.5 lunar months, 9/8 of the lunar year of 12 months, that is a Pythagorean tone.

    My own work, and that of my brother, is full of this sort of material which can then only move forward through developing some theory for their explanation. Also, one can talk about whether early astronomers could have used such shortcuts to make their calendars easier to organise.

  10. oldbrew says:

    Richard H: If we said Jupiter:FMC was 2:21 that would be 99.79% true (136 x (21/2)) = 1428).

  11. oldbrew: You are absolutely right, the FMC is one of a number of parameters in the Jupiter Moon system.

  12. tallbloke says:

    Richard H, welcome here. I have a copy of your brother’s 1993 book ‘A Key to Stonehenge’ which is a fascinating read, we’ve had a couple of discussions about it here on the talkshop. I certainly don’t think we should underestimate the capabilities of the people who built stonehenge.

  13. I have this disease (of thinking the megalithic was highly intelligent) as you can see at my megalithicscience.org and https://independent.academia.edu/HeathRichard, which you may enjoy. Robin has been sharing your posts by email for some time, mainly on climate change. It is a great achievement to get such wide ranging involvement of competent people in a blog.

  14. oldbrew says:

    The full moon cycle is closely linked to the lunar nodal cycle.

    A ratio of 2 LNC:33 FMC is almost true, with one ‘extra’ full moon cycle over the period of 106 lunar nodal cycles (so 1750 FMC per 106 LNC) – which is not far short of 2000 years.

  15. oldmanK says:

    Re Richard Heath’s comment above I can confirm his disease is real and chronic, and shared by others eg myself. If he wishes to confirm he may have a look at this link:


    We can still learn a lot from our ancestors.

  16. ulriclyons says:

    1431 is a triangular number with n=53 and a hexagonal number with n=27, 136 is a triangular number with n=16.

    [Reply] OK Ulric, Happy New Year amnesty, let’s see how it goes. Rog

  17. Lucy Skywalker says:

    A nice surprise, on a rare visit here these days, finding Richard Heath commenting on phi linked to Jupiter/fullmoon-cycle. I immediately thought of one of my favourite books, A Little Book of Coincidences, where I find this lovely quote on page 46:

    “Richard Heath recently revealed that the Golden Ration is defined here [ie by looking at the relative speeds of orbit of Earth, Jupiter and Saturn – shown in drawing] in time and space to a stunning 99.99% accuracy! The two giants of our solar system thus reinforce life on Earth.”

    Happy New Year to many old friends!

  18. tallbloke says:

    What a nice surprise on a New Years Eve to hear from you Lucy. Hope you’re enjoying yourself. We’re making interesting progress with our theory, see also the Why Phi orbital parameters thread. Cheers, Rog.

  19. tallbloke says:

    OB: The more irrational the winding number is (the ratio of the resonance frequencies) the more stable is the periodic orbit.

    Yes, I already demonstrated this geometrically in this post: