Why Phi? – some Moon-Earth interactions

Posted: November 9, 2015 by oldbrew in Celestial Mechanics, Fibonacci, moon, Phi
Tags: , ,

lunar_TYTallbloke writes: Stuart ‘Oldbrew’ has been getting his calculator warm to discover the congruences in various aspects of the Lunar orbit around Earth, and its relationship to Earth-Moon orbit around the Sun. Emerging from this study are some useful insights into longer periods, such as the ‘precession of the equinoxes‘.

Some matching periods of lunar numbers:
86105 tropical months (TM) @ 27.321582 days = 2352524.8 days
85377 anomalistic months (AM) @ 27.55455 days = 2352524.8 days
79664 synodic months (SM) @ 29.530589 days = 2352524.8 days

These identical values are used in the chart on the right (top row). The second row numbers are the difference between the numbers in the first row (TM – AM and AM – SM).
The derivation of the third row number (6441) is shown on the chart itself [click on the chart to enlarge it].

The period of 6441 tropical years (6440.75 sidereal years) is one quarter of the Earth’s ‘precession of the equinox’.
Multiplying by 4: 25764 tropical years = 25763 sidereal years.
The difference of 1 is due to precession.

Comments:
1) the familiar equation of 235 lunations = 254 lunar orbits = 19 years is present (with a very slight adjustment), by cancelling the multiplication by 339: see notes below.

2) the number of full moon cycles is one more than a Fibonacci multiple (34,21 and 8 are Fibonacci numbers)

3) the ratio of lunar apsidal cycles (LAC) to full moon cycles (FMC) is almost 1:3 x phi² (or 34/13, x 3 in Fibonacci terms) – one ‘extra’ full moon cycle per 6441 tropical years (TY). This is also seen at the shorter period of 115 tropical years, which is about 13 LAC and 102 FMC (34 x 3): 13 + 102 = 115. [6441 = 115 x 56, +1]

This 115-year period was identified in a study by Dr. Nicola Scafetta:
‘The major beat periods occur at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years.’

Scafetta also says: ‘The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium such as the Oort, Wolf, Spörer, Maunder and Dalton minima, as well as the 17 115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years.’ [bold added]

4) 6441 TY x 4 = 25764 TY, around the commonly accepted Earth precession period.
Wikipedia says ‘about’ 25770 years.

5) 25764 TY = 25763 sidereal years (365.25636 days) exactly, so the difference of 1 indicates a full equinoctial precession period from the lunar perspective.

6) the period is very close to 144 Jose cycles or 144 x 9 Jupiter-Saturn conjunctions, or 144 ‘solar inertial motion’ cycles. Again, one more is needed.
144 x 9, +1 J-S = 25765 years (144 is a Fibonacci number).

7) 6441 TY is 339 x 19 TY, or 339 Metonic cycles = quarter precession period = 6440.75 sidereal years.
339 = 34 x 5 x 2, -1 (340 – 1) – Fibonacci numbers 2,5, and 34.

NB if the number WAS 340, the full precession period would be 340 x 19 x 4 = 25840y.
25840 = 2584 x 5 x 2
(2584 is the first Fibonacci number that is a multiple of 19 i.e. 34 x 19 x 4).

These numerical ‘near-misses’ seem to be the norm in planetary motions.

79664 synodic months (SM) = 339 x 235, -1
86105 tropical months (TM) = 339 x 254, -1
This deduction of 1 in ~80,000 from each of these numbers explains the 19-year Metonic cycle (254 – 235 = 19):
6441 TY = 339 x 19 TY

79664 SM = 13 x 8 x 766 (so an exact multiple of 13 synodic months)
766 SM = 7 lunar apsidal cycles

The lunar nodal cycle

1 lunar nodal cycle = 18.5992 sidereal years = 19.5992 draconic years
The difference of 1 (19.5992 – 18.5992) defines the cycle.
In whole numbers: 185992 sid. years = 195992 drac. years = 10000 full moon cycles.
185992 / 10000 = 18.5992, 195992 / 10000 = 19.5992

Calculations tell us the number of precessions (period = 6441 TY x 4) needed to get a whole number of lunar nodal cycles (LNC) is 54 (6441 TY x 4 x 54).

In that period there will be 74799 LNC.
That’s 55 x 34 x 8 x 5, -1 (all Fibonacci numbers).
Period = 1,391,256 tropical years (6441 x 4 x 54) or 54 precession cycles.
The ‘-1’ indicates that’s the full repeating period of LNC.

Since there are 728 apsidal cycles in the 1/4 precession period, the number in 54 precessions is:
728 x 4 x 54 = 157248 = 144 x 21 x 13 x 4 (144,21 and 13 are Fibonacci numbers)

———————-
Links:
Why Phi: is the Moon a phi balloon?

More related posts

Comments
  1. oldbrew says:

    A NASA article about the anomalistic month (section 4.3) says:

    ‘The direction of Earth’s orbital line of apsides also changes but at a rate far slower than the Moon’s. Having a direct (eastward) shift with a mean value of 0.0172° per year, it takes about 20,500 years for Earth’s major axis to make one complete revolution. This is only 0.0004 of the lunar rate, so it can be treated as fixed for the purpose of the following discussion.’
    http://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html#synodic

    360 / 0.0172 = 20930.232 years (432 years more than the estimate quoted by NASA)

    A quick comparison with our precession period above (25763 sidereal years) shows:
    20930.232 x 16 = 13 x 25760.285

    In other words a (very close to) 13:16 ratio between the two periods, or half of 13/8 if you like.

    NB the period NASA is describing is the time taken for the perihelion to return to the same date.
    http://www.windows2universe.org/physical_science/physics/mechanics/orbit/perihelion_aphelion.html

  2. tallbloke says:

    The amazing thing about this is the way the fibonacci multiples keep hitting the physically relevant periods right out to long timescales. Top work OB!

    The other important thing coming out of our research is that it is demonstrating that forces arising out of orbital resonance integrate to set the orbital-planar angles which drive the long precession cycles in a way that itself produces a harmonising resonance between not just the Earth, Moon and Sun, but between all the solar system planets, and possibly the Sun’s longer term cycles too.

    We’ve also been looking at glacial/interglacial periodicities and will have more on that soon.

  3. oldbrew says:

    Thanks TB.

    I forgot to say the period equates to 144 Jose cycles so I’ll add that to the text (144 is a Fibonacci number).
    The Jose cycle is 9 Jupiter-Saturn conjunctions and takes slightly less than 179 years.

    That means the 13:16 ratio (comment above) is about 117:144 Jose cycles (9 x 13 : 9 x 16).

    Rhodes Fairbridge refers to ‘the 179-yr cycle of the solar inertial motion’.
    http://link.springer.com/article/10.1007%2FBF00148211

  4. tallbloke says:

    The 179 year cycle is made up of 5 x ~36 year periods where Solar inertial motion goes through increasing/diminishing subcycles. This 36 year period is in a 2:1 ratio to the ~72year long lunar tide observed in high latitude Atlantic SST. Sun, Moon and Earth are synchronised by planetary motion which affects all of them.

    Ian Wilson recently demonstrated the links between Earth-Venus and Earth-Jupiter timings and the Lunar orbit. The JEV timing relationships with solar cycles have been known for many years (Desmoulins, Tomes, Wilson). The gas giant timings and effects have been investigated by Jose, Landscheidt, Charvatova, Sharp, Abreu et al and others. The mechanisms for solar effects have been theorised by Wolfe and Patrone, Grandpierre, Scafetta and others. The solar-terrestrial relationship has been investigated by many, including the authors of the special edition of PRP – which was shut down by IPCC lead authors and the partisan director of Copernicus-the innovative science unpublishers(tm).

    Now through the persistent efforts of Ian, Paul Vaughan, Stuart and myself, and many talkshop contributors, the full solar system scheme is starting to become evident and coherent. Exciting times are ahead for our solar-planetary theory.

  5. oldbrew says:

    TB says: ‘The 179 year cycle is made up of 5 x ~36 year periods where Solar inertial motion goes through increasing/diminishing subcycles.’

    There are 5 Saturn-Neptune conjunctions in just over 179 years (179.273y).

  6. tallbloke says:

    Yes, and 9 (or 32) Jupiter-Saturn conjunctions in ~178.74 years.

  7. TLMango says:

    Also… 179 occurrences of the 144 year cycle is equal to 25776 years.
    Don’t forget Ray Tomes’s ‘Harmonic Theory’.
    {2,3,4,6,8,9,12,16,18,24,36,48,72,144}

  8. oldbrew says:

    Re the lunar nodal cycles (LNC): the figures do line up after 6 precession cycles (74799 / 9 = 8311), but we’ve used 6×9 = 54 to show the match to Fibonacci numbers in both LNC and apsidal cycles.

    It’s just a better way of demonstrating their Phi-based ratio to each other.

  9. oldbrew says:

    From the Scafetta paper (see comment 3 in the post above):

    ‘The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium such as the Oort, Wolf, Spörer, Maunder and Dalton minima, as well as the 17 115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years.’ [bold added]

    Post: ‘the shorter period of 115 tropical years, which is about 13 LAC and 102 FMC (34 x 3): 13 + 102 = 115’

  10. tallbloke says:

    Nice one. Told you it was all coming together.🙂

    You could edit Scafetta’s obs into the post too, for those who don’t have time to read comments.

  11. TLMango says:

    Scafetta in his ‘Multiscale Harmonic Model…..’ showed that there was a nice correlation
    between the 114 year cycle and Ljundqvist’s temperature data. But…. the Sporer minimum
    has a double trough and the millennial warm period has a double peak (Be10 data). So the
    cold minimums interestingly enough end up having a ~144 year periodicity.

  12. oldbrew says:

    Re. comment 3 in the post and Scafetta’s ‘115-year long oscillations’:

    Ten lunar nodal cycles = ~186 years (185.992) i.e. almost a whole number of years (Earth orbits).

    186/115 = 1.61739 (Phi = ~1.618, 55/34 = 1.61765)

  13. tallbloke says:

    Which is also the whole number of nodal cycles closest to the Jose cycle of ~179 years
    And the beat period 179 and 186 comes out around 2 x the Halstatt cycle

  14. oldbrew says:

    Not forgetting that Yndestad’s 74.4 year lunar period occurs 5 times for every 2 x 186 years i.e. a 5:2 ratio.

  15. Paul Vaughan says:

    74 isn’t scale-resolved, so the interest in it appears to be an unfortunate misinterpretation.

  16. oldbrew says:

    Yndestad’s paper refers to ‘the 74 year cycle of polar position movement.’

    No details of where the number comes from AFAICS.
    I think we’re really looking at 66 full moon cycles = 74.4074 sidereal years

  17. Paul Vaughan says:

    I’ve known of the work since 2008. By 2010 or so my understanding of wavelet methods had matured enough to know 74 isn’t scale-resolved. I apologize if I misled anyone before then.

    I have 115 stuff to share later — (in too much of a rush right now….)

  18. Paul Vaughan says:

    (50.93234233)*(35.30054121) / (50.93234233 – 35.30054121) = 115.0180478
    (12.11054088)*(11.08061845) / (12.11054088 – 11.08061845) = 130.2935828

    (130.2935828)*(115.017867) / (130.2935828 – 115.017867) = 981.0401197
    (130.2935828)*(115.017867) / (130.2935828 + 115.017867) = 61.09005507
    (130.2935828)*(115.017867) / ( (130.2935828 + 115.017867) / 2 ) = 122.1801101

    Where do the input numbers come from?
    derivations here:
    https://tallbloke.wordpress.com/suggestions-15/comment-page-1/#comment-109379
    (alert: typo in that post corrected further below in that thread)

    Some more numbers folks might like to compare:

    (29.447498)*(11.862615) / (29.447498 – 11.862615) = 19.86503587
    (19.86503587) / 2 = 9.932517933
    (11.862615)*(9.932517933) / (11.862615 – 9.932517933) = 61.04648218

    (164.79132)*(84.016846) / (164.79132 – 84.016846) = 171.4062162
    (208.2486478)*(171.4062162) / (208.2486478 – 171.4062162) = 968.8587638

    (35.30054121)*(30.80633442) / (35.30054121 – 30.80633442) = 241.9737966

    I still haven’t gotten around to spelling out the new way of looking at 1470. Some day there will be time.

  19. Chaeremon says:

    The lunar orbit of 300 solar years expressed in a few small Fibonacci’s

    Principal time-frame figures used: 30, 40, 300 (from Noah’s Ark).

    Fibonacci’s used: 2, 3, 5, 2^3 (8), 2^2^2 (16), 34.

    Principal terms and relations (observational data):

    --- 40 sidereal moons = 3 years (+ ~3.0 days) = 37.0~ synodic
    --- 10 x 3 years = 371.0~ synodic
    --- 100 x 3 years = 3710.0~ synodic
    --- 99 synodic = 8 years (short of ~1.5 days)
    --- 2 x 8 + 3 years = 19 years (~3.0 -(2 x ~1.5) = 0 days slack)
    --- 254 sidereal = 235 synodic = 19 years (from Metonic rel.)
    --- 3710 synodic = 4010 sidereal (3710 + 300 years)
    --- 242 draconic = 223 synodic (from Saros rel.)
    --- 3710 synodic = 4026.0~ draconic
    --- 251 synodic = 269 anomalistic (author unknown)
    --- 3710 synodic = 3976.0~ anomalistic

    Schedulable periodicities derived (not extrapolated …):

    --- 4026 draconic - 4010 sidereal = 16 times line-of-nodes
    --- 4010 sidereal - 3976 anomalistic = 34 times line-of-apsides
    --- 300 years - 34 line-of-apsides = 266 times full-moon-cycle

    Schedulable cycles covered by the time-frame:

    --- 300 years / 16 line-of-nodes = 18.75 years LNC period
    --- 300 years / 34 line-of-apsides = 8;28/34 years LAC period
    --- beat period (a+b) of 18.75 LNC and 8;28/34 LAC = 6 years

    Note: line-of-apsides and line-of-nodes advance against each other (a+b beat).

    Ramifications: the 18.6 “classic” LNC and 8.86 “classic” LAC in the literature are physically unobservable fictions. Since the coordinates of apsides and nodes change dynamically (they wobble against each other and, in addition, they are mutually dependend and also depend on the actual perihelion & equinoces), the LNC and LAC cannot be obtained in form of plain statistical extrapolation (a capable algorithm is work in progress).

  20. oldbrew says:

    Referring back to the ‘lunar models’ post:
    https://tallbloke.wordpress.com/2015/01/06/two-long-term-models-of-lunar-cycles/

    The number of wobbles = the period in tropical years divided by the sum of (line-of-nodes and line-of-apsides) in the period. Each number is derived from the ones above it.

  21. Chaeremon says:

    @oldbrew (December 13, 2015 at 9:30 am) astounding the 6 years wobble, isn’t it😎

    Can my post be corrected, “;28/266” has typo, should be “;28/34” — thanks.

  22. […] an earlier Talkshop post we discussed the quarter ‘axial precession’ cycle (sometimes called ‘precession […]

  23. […] It’s also about 5 days short of 13 lunar apsidal cycles and 2 days more than 102 (34×3) full moon cycles. These periods (56 of them per 339 Metonic-year cycle) are analysed in more detail in the ‘quarter precession’ post : Why Phi? – some Moon-Earth interactions […]

  24. […] 6441 TY (see Why Phi quarter precession post) we get 79,664 SM = 339 x 5 x 47, -1 The ‘-1’ tells us it’s the end of the […]

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