Why Phi? – a lunar evection model, part 2

Posted: December 2, 2018 by oldbrew in Fibonacci, moon, Phi, solar system dynamics
Tags: ,

Image credit: interactivestars.com


It turns out that the previous post was only one half of the lunar evection story, so this post is the other half.

There are two variations to lunar evection, namely evection in longitude (the subject of the previous post) and evection in latitude, which ‘generates a perturbation in the lunar ecliptic latitude’ (source).

It’s found that the first is tied to the full moon cycle and the second to the draconic year.

The lunar evection in latitude is the beat period of the synodic month and the draconic year. The result is that it should average about 32.280777 days (46484.32 minutes).

Comparing synodic months (SM), draconic months (AM), and lunar evections in latitude (LE2) with the draconic year (DY) we find:
1 DY = 11.737662 SM
1 DY = 11.737662 + 1 = 12.737662 DM
1 DY = 11.737662 – 1 = 10.737662 LE2

Since 0.737662 * 385 = 283.99987 (284), we can say for our model:
3850 + 284 = 4134 LE2 (55*75, +9)
4235 + 284 = 4519 SM (55*82, +9)
4620 + 284 = 4904 DM (55*89, +9)
385 DY = 55*7 and 89-82 = 7 and 82-75 = 7

55 and 89 are Fibonacci numbers.

A very near-equivalent is: 61 DY = 655 LE2 = 716 SM = 777 DM.
That should be accurate enough (> 99.999%) for most purposes.

Analysis

The lunar evection in latitude is the beat period of the draconic year and the synodic month.
(Alternatively, DY = the beat period of LE2 and SM).

The difference between the the number of evections in longitude (LE) and evections in latitude in any given period = the difference between the number of draconic years and full moon cycles in the same period i.e.:
(Number of) LE – LE2 = (Number of) DY – FMC

The key period is the ‘lunar wobble’, approx. 2190.35 days, where both differences = 1.
This is the ‘axial’ period of the lunar nodal and apsidal cycles, i.e. the time taken for the sum of their occurrences to equal 1 (about 0.3222 nodal plus 0.6778 apsidal).

This model from an earlier post shows how some of these lunar periods fit together.
Note: ‘lunar wobble’ is shown as RLA in the chart.
The numbers of DY, FMC and RLA are divisible by 7, so:
297 DY – 250 FMC = 47 RLA.
LE – LE2 will also equal 47 in that period, as will draconic minus anomalistic months.

Source: Two long-term models of lunar cycles

Update 15/12/18

The ‘lunar wobble’ is a period where the number of:
Draconic months minus anomalistic months = 1
Draconic years minus full moon cycles = 1
Evections in longitude minus evections in latitude = 1
Apsidal cycle (portion of 1) plus nodal cycle (portion of 1) = 1

Apsidal: Anomalistic months, full moon cycle, evections in longitude, apsidal cycle
Nodal: Draconic months, draconic years, evections in latitude, nodal cycle

Comments
  1. oldbrew says:

    The Saros eclipse cycle = 6585.3212 days.

    After one saros, the Moon will have completed roughly an integer number of synodic, draconic, and anomalistic periods (223, 242, and 239) and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase and be at the same node and the same distance from the Earth.
    https://en.wikipedia.org/wiki/Saros_(astronomy)

    204 lunar evections in latitude = 6585.2785 days.

    The difference from the Saros is just over an hour.

  2. oldbrew says:

    5 lunar nodal cycles = 1053 evections (LE2) = 13 * 81 (81 = 3^4th power).
    3, 5, and 13 are Fibonacci numbers.

    The ratio of 81 evections (LE2) to half the lunar apsidal cycle (perigee to apogee, or vice versa) is:
    2614.7429 days (LE2) : 1615.7452 days = 1.6182891:1 (99.984% match to Phi, aka the golden ratio).

  3. oldbrew says:

    Equations (10) and (11) both indicate that there is a strong connection between the changing tilt and shape of the lunar orbit and the synodic period of Venus and the Earth.

    4 lunar wobbles = 5 V-E * 3 (within about 2.25 days in just under 24 years).
    The wobble is the key period here. It’s when the sum of nodal and apsidal cycles is 1.

  4. oldbrew says:

    Add to earlier list:

    LE1 – LE2 = LNC + LAC (sum of lunar nodal and apsidal cycles) in any period.
    E.g. in one tropical year both would be 0.1667~

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