Lunar-planetary links to the Lucas sequence – part 1

Posted: April 5, 2019 by oldbrew in Fibonacci, Lucas, moon, solar system dynamics
Tags: ,

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.

Comments
  1. tallbloke says:

    The Chandler wobble is a type of spin precession. The links OB is finding between rotation and orbit speak of physical mechanisms hitherto not perceived. Very intriguing stuff. Well done OB.

  2. oldbrew says:

    Thanks Rog. This is just the warm-up act for part 2 😉

    Part 3 can’t be ruled out either.
    – – –
    If 27 CW = 32 TY and 32 CW = 39 LTY then:
    144 * 3 CW = 8³ TY
    144 * 2 CW = 13 * 3³ ETY
    (Derived from: 27 * 32 CW = 144 * 3 * 2 CW)

    2,3,8,13 and 144 are Fibonacci numbers.

  3. […] Lunar-planetary links to the Lucas sequence – part 1 […]

  4. […] Part 1 showed that 7 Jupiter-Saturn conjunctions (J-S) = 11 * 13 lunar tropical years (LTY), and from Part […]

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