Archive for the ‘Lucas’ Category

Image credit: Wikipedia

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]

Jupiter-Saturn-Earth orbits chart

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.

 

The Lucas spiral, made with quarter-arcs, is a good approximation of the golden spiral when its terms are large [credit: Wikipedia]


Here we show numerical connections between the Moon, the Earth and Venus. These will be carried forward into part 2 of the post. The focus is on the smaller Lucas numbers (3-18).

Wikipedia says: The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values.

A look at the numbers:
19 Venus rotations = 169 (13²) lunar rotations
Lunar tropical year = 13 lunar rotations / orbits (1 rotation = 1 orbit)
So: 19 Venus rotations = 13 Lunar tropical years
(13 is a Fibonacci number. The Lunar tropical year is derived from the nearest whole number of lunar orbits to one Earth orbit.)

169 * 27.321582 = 4617.3473 days (Data source)
19 * 243.018 = 4617.342 days (Data source)

Now we bring in the Chandler wobble:
13*3 = 39
39 Lunar tropical years = 32 Chandler wobbles
19*3 = 57

Referring to the chart on the right:
7 and 18 are Lucas numbers.
This theme will continue in part 2 of the post.

(32 + 57 = 89 axial, and 89 is a Fibonacci number. In 1/89th of the period the sum of CW and Ve(r) occurrences is 1).

Re. the period of the Chandler wobble:
39 LTY / 32 CW = (169 * 3 * 27.321582) / 32 = 432.8763 days

Or, if we say 27 Chandler wobbles = 32 Earth tropical years:
(365.24219 * 32) / 27 = 432.8796 days

The two results are almost identical (Wikipedia rounds it to 433 days).

Note:
353 Earth tropical years (ETY) = 363 Lunar tropical years = 10 beats
1 beat = 35.3 ETY which is linked to the Chandler Wobble
See: Sidorenkov – THE CHANDLER WOBBLE OF THE POLES AND ITS AMPLITUDE MODULATION

These numbers also feed into part 2 of the post, with more planetary links.