## Lunar-planetary links to the Lucas sequence – part 2

Posted: April 9, 2019 by oldbrew in Fibonacci, Lucas, solar system dynamics
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In Part 1 the period of time in question was 13 lunar tropical years (LTY). Here we show how this relates to the Jupiter-Saturn conjunction and other significant periods.

13 LTY = 169 * 27.321582 days (lunar orbit period) = 4617.3473 days
1 Jupiter-Saturn conjunction = 19.865036 years * 365.25636 days = 7255.8307 days
[planetary data source]

This gives a ratio of exactly 11:7 as follows:
11 * 4617.3473 = 50790.82 days
7 * 7255.8307 = 50790.814 days
7 and 11 are Lucas numbers.

Multiplying by 3 (which is both a Fibonacci and a Lucas number), the results from Part 1 can now be ‘plugged in’ to the chart on the right from a previous blog post, which is based on multiples of 21 (3 * 7) Jupiter-Saturn conjunctions, as the chart on the right shows.

Quoting from that post:
The synodic periods all occur in multiples of six, and one sixth of 2503 years is 417.1666 years which is 21 J-S, 382 J-E, 403 S-E and two de Vries cycles.

Updating that, the matching periods now are:
2 de Vries cycles
21 Jupiter-Saturn conjunctions (3 * 7)
382 Jupiter-Earth conjunctions
403 Saturn-Earth conjunctions (13 * 31)
352 Chandler wobbles (11 * 32)
429 Lunar tropical years (11 * 39 or 13 * 33)
627 Venus rotations (11 * 57 or 19 * 33)

Therefore: 31 Saturn-Earth = 33 Lunar tropical years.

Quoting from Part 1 of the post:
353 Earth tropical years (ETY) = 363 Lunar tropical years = 10 beats

363 LTY = 33 * 11
Therefore: 363 LTY = 31 * 11 (341) Saturn-Earth conjunctions (= synodic periods).

Quoting from another earlier post – Sidorenkov and the lunar or tidal year:
4719 LM = 128930.54 days  [note: 4719 = 363 * 13 i.e. 363 LTY]
4366 SM = 128930.55 days
4727 CR = 128930.34 days
5080 SSR = 128930.40 days
353 TY = 128930.49 days

(see post re. abbreviations).

NASA’s Saturn Fact Sheet says re. Saturn-Earth:
Synodic period (days) 378.09

TY = tropical years
128930.49 days / 341 S-E = 378.09527 days
This ties Saturn to Sidorenkov’s 353 year period, which is therefore 11/13ths of 21 J-S.
Also: 11/13ths of 429 LTY = 363 LTY.

Footnote:
In the graphic the full period is 126 J-S, described as 6 * 21.
It could also be described as 7 * 18, which are Lucas numbers.

1. oldbrew says: