Credit: NASA

I found out there’s an easy way to simplify one of the lunar charts published on the Talkshop in 2015 on this post:

Why Phi? – some Moon-Earth interactions

In the chart, synodic months (SM) and apsidal cycles (LAC) are multiples of 104:

79664 / 104 = 766

728/104 = 7

The other numbers are not multiples of 104, but if 7 is added to each we get this:

86105 + 7 = 86112 = 828 * 104 (TM)

85377 + 7 = 85384 = 821 * 104 (AM)

5713 + 7 = 5720 = 55 * 104 (FMC)

6441 + 7 = 6448 = 62 * 104 (TY)

TM = tropical months

AM = anomalistic months

SM = synodic months

LAC = lunar apsidal cycles

FMC = full moon cycles

TY = tropical years

Here’s an imaginary alternative chart based on these multiples of

104. [Cross-check: 828 – 766 = 62]

In reality, 55 FMC = just over 62 TY and 7 LAC = just short of 62 TY.

For every 7 apsidal cycles (LAC), there are 766 synodic months (both chart versions).

In the real chart:

For every 104 apsidal cycles, all numbers except SM slip by -1 from being multiples of 104. So after 7*104 LAC all the other totals except SM are ‘reduced’ by 7 each.

In the case of tropical years, 6448 – 7 = 6441 = 19 * 339

19 tropical years = 1 Metonic cycle

If the period had been 6448 TY it would not have been a whole number of Metonic cycles.

Also 6441 * 4 TY (25764) is exactly one year more than 25763 synodic years i.e. the precession cycle, by definition.

Fibonacci: 104 is 13*8, and the modified FMC number is 55 (all Fibonacci numbers).

Phi: we’ve explained elsewhere that the number of full moon cycles in one lunar apsidal cycle is very close to 3*Phi².

We can see from the modified chart that the FMC:LAC ratio of 55:7 is 3 times greater than 55:21 (55/21 = ~Phi²)

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Note – for more discussion of the ~62 year period, try this search:

site:tallbloke.wordpress.com 62 year

[see Google site search box in grey zone on left of this web page]