Why Phi? – a Jupiter-Venus-Mercury model

Posted: May 24, 2015 by oldbrew in Celestial Mechanics, Fibonacci, Phi
Tags: , ,

Planetary conjunction [image credit: EPA / Daily Mail]

Planetary conjunction [image credit: EPA / Daily Mail]

For the Jupiter-Venus-Mercury (JVMe) model, we start with this basic synodic conjunction relationship:
61 Jupiter-Venus (J-V) = 100 Venus-Mercury (V-Me) = 161 Jupiter-Mercury (J-Me) conjunctions in 39.58 years.
Orbit numbers per 39.58y: 64.337~ Venus, 164.337~ Mercury, 3.3365~ Jupiter
Jupiter-Venus-Mercury chart

[3 x 39.58 years = 118.74 years]

Since the ratio 61:100:161 is only one conjunction different from 60:100:160 (= 3:5:8), there is a very close match to a Fibonacci-based ratio as 3,5 and 8 are all Fibonacci numbers.

In the model we convert the orbits to whole numbers using a multiple of 3, to obtain a triple conjunction period where there are (very close to) a whole number of orbits of the relevant planets, as per the chart [right].

Long term (2850 years) motion of the JVMe conjunction cycle

Long term (2850 years) motion of the JVMe conjunction cycle [click to enlarge]

Solar Simulator graphics (right) show a long term JVMe solar pattern using snapshots averaging 118.74 years apart.

Over nearly 3000 years and 25 occurrences the apparent position of the triple conjunction relative to that of the Sun itself changes only very gradually, in an anti-clockwise manner roughly following a line that’s one solar diameter from the barycentre of the solar system (the red circle on the graphic – click on it to enlarge).
N.B. 442 AD (top row, centre) looks slightly different due to the effect of the three opposing giant planets Saturn, Uranus and Neptune – see graphic [below, right].

J-V-Me conjunction 442 AD

J-V-Me conjunction 442 AD

In the Why Phi? – a Mars-Earth model and more post we found a Mars-Earth-Venus period of ~64 years.
Note that 64 / 39.58 (basic JVMe period) = ~1.617
Therefore a near-Phi ratio also exists between these J-V-Me and Ma-E-V conjunction periods (Phi = 1.618~).

We can observe that the JVMe period of 118.74 years is almost two-thirds of the Jose cycle (~3:2 ratio) of repeating solar inertial motion (~179 years). This could help to explain its near-repeating pattern of conjunctions as shown in the graphic above.
Every 179 years or so, the sun embarks on a new cycle of orbits.

Note also that 3 Venus-Mercury conjunctions = just under 433.7 days which is well within the estimated average period (430-435 days) of the Chandler wobble:
‘The Chandler Wobble may be a natural harmonic resonance’:

For example a frequency of 54 Chandler wobbles in 64 years (Mars-Earth-Venus period as above) equates to 1 CW = 432.888 days [as an average].

See also:
Ian Wilson: Solar System Timings Evolved Lunar Orbital Elements Linked to Earth’s Chandler Wobble
‘The century-old mystery of Earth’s “Chandler wobble” has been solved by a scientist at NASA’s Jet Propulsion Laboratory in Pasadena, Calif.’

Reference data: http://solarsystem.nasa.gov/planets/charchart.cfm/
Related Talkshop posts: https://tallbloke.wordpress.com/?s=Why+Phi

  1. tallbloke says:

    Very nice work Stuart!
    61:100:161 is itself pretty close to phi ratios.
    The relationships in this post that I find really compelling are the near-Phi ratio between the J-V-Me and Ma-E-V conjunction periods and the 118.74 years = almost two-thirds of the Jose cycle.

    Also worth noting that 118.74/2 is close to 3 J-S conjunctions.

  2. oldbrew says:

    Thanks TB. As the J-V-Me cycle is based on 10 Jupiter orbits there’s a 3:2 ratio with the King-Hele cycle (=15 J):

    NB 61 x 10 = 610, another Fibonacci number.

  3. Paul Vaughan says:

    Search for the 531 day-period wobble signal in the polar motion based on EEMD

    Click to access npgd-2-647-2015-print.pdf

    “[…] 531 day-period wobble (531 dW) […] cannot be found […] using conventional analysis approaches […] the period of the 531 dW is subject to variations […] and its amplitude is also time-dependent […] The 531 dW is also detected in two longest available superconducting gravimeter (SG) records […] resonance of unidentified oscillating mode of the Earth (possibly Earth’s inner core wobble).”

    I would suggest not the core but rather the distribution of water over the surface.

    – harmonic mean of 1 year & 531 day (1.453829855 years) is Chandler Wobble (CW)
    – beat of CW & 531 day is 6.4 years

  4. oldbrew says:

    PV: 5 lunar nodal cycles = 64 x 531.12~ days

  5. tallbloke says:

    Paul V: – harmonic mean of 1 year & 531 day (1.453829855 years) is Chandler Wobble (CW)
    – beat of CW & 531 day is 6.4 years

    From Ian Wilson’s Chandler wobble post linked by OB

    4 x SVE = 6.3946 years_______________________SVE = synodic period of Venus and Earth
    3 x SEM = 6.4059 years_______________________SEM = synodic period of Earth and Mars
    7 x SVM = 6.3995 years_______________________SVM = synodic period of Venus and Mars

    [Note: This means that these three planets return to the same relative orbital configuration once
    every ~ 6.40 years]

    3,4, and 7 are of course Lucas numbers, which relate directly to Fibonacci numbers!

  6. tallbloke says:

    OB: 5 lunar nodal cycles = 64 x 531.12~ days

    On another lunar note:
    118.75/6.4=18.553125 years = the length of the ‘corrected’ Lunar nodal cycle!

    Which is also near the double period of Landscheidt’s IOT (Impulse of Torque) describing the average period of alignment of the Sun, Jupiter and the COM (Centre of Mass of the Solar System).

    Ths is all coming together rather nicely. 🙂

  7. tchannon says:

    The CW is likely to be intermodulation artifacts, shown well by conventional analysis, all of which I have pointed out previously.

    I stopped bothering with the matter after a close look found no exciting force ~6.x years. Without cause and effect there is nothing.

    Okay, if we take the situation as factual, there is modulation, then it must be another force. Paul V. might be right about local complexity where I can think of several candidates for dynamic generation of force. (because the earth is not a static simple sphere)

    Proof reasons particularly want a definite external driver so that the phase angles correlate, the matter becomes rather clear.

    I also stopped as it became clear the available data is incomplete and of dubious correctness.

  8. tallbloke says:

    Ah, one of Tim Channon’s well aimed buckets of cold water. 🙂

    I think he’s wrong though. ‘exciting forces’ arise out of resonant couplings. Here we have a resonant coupling of Moon’s nodal cycle and two triple conjunctions of planets.

    And at the half period of the LNC, we get the average period of Landscheidt’s alignments of Sun, COM and Jupiter, which correlate well with peaks in the Geomag indices.

    9.275/6.38 = 1.453 years = ~Chandler period 531 days

    Ian Wilson’s article here is well worth a read too.

  9. oldbrew says:

    TB: ‘Also worth noting that 118.74/2 is close to 3 J-S conjunctions’

    3 J-S conjunctions = 41 x 530.9 days

    Post: ‘For example a frequency of 54 Chandler wobbles in 64 years (Mars-Earth-Venus period as above) equates to 1 CW = 432.888 days [as an average].’
    64y / (64-54) = 6.4y (beat frequency of 1 year and CW)

  10. tallbloke says:

    Thanks OB, corrected my previous comment. I missed a step with the CW period and the 531 day period Paul referred to.

  11. oldbrew says:

    According to King-Hele 15 Jupiter orbits = 16 ‘mean sunspot cycles’ (link here: May 24, 2015 at 3:47 pm).
    This returns a slightly higher value (11.12~y) for an average solar cycle than some people believe.

    Lunar nodal cycle x Chandler wobble = 22.06 years = 1 Hale cycle, or something very close to it.
    Whether that tells us anything useful is another matter.

  12. oldbrew says:

    A quick check shows there should be 211 King-Hele cycles (1 K-H = 15 Jupiter orbits) per 210 x 9 Jupiter-Saturn conjunctions.

    Since 210 x 9 J-S = 126 J-S x 15 (both = 1890), that feeds directly into my comment on an earlier post re. a 126 J-S repeating pattern, which is 211 Jupiter orbits:

  13. tallbloke says:

    Heyup, OB: wandered off into big number territory again? 🙂

    A few weeks ago you said on suggestions:
    Per Strandberg @ Motls is saying 5 of the ‘wavelets’ = 1 lunar nodal cycle and claiming he is about to produce ‘explosive evidence’ re ENSO.

    Well, LNC/5 = average ENSO period = 1/3 solar cycle = ~3.7yr

    Multiply that by phi and you get 6 years, which is the double period of the crossing of the Lunar lines of nodes and apse.

  14. oldbrew says:

    TB: Fairbridge & co. got there a long time before me.

    What it boils down to is: 210 Jose cycles = 211 King-Hele.

  15. tallbloke says:

    OB: What it boils down to is: 210 Jose cycles = 211 King-Hele.

    Which is approximately phi x the precession of the equinox.

  16. oldbrew says:

    Where’s the precession figure coming from? Wikipedia says ~26000 years.

    TB’s comment here: https://tallbloke.wordpress.com/2015/05/24/why-phi-a-jupiter-venus-mercury-model/comment-page-1/#comment-101525
    seems to answer TC’s point: ‘I stopped bothering with the matter after a close look found no exciting force ~6.x years. Without cause and effect there is nothing.’

  17. tallbloke says:

    Didn’t we come across something which made us think it is more like 23000? I can’t recall what it was just now.

    I note that 5 grand synods of 4627yrs = 23135
    210 Jose /phi = ~23232

  18. oldbrew says:

    Depends which website you refer to, some say 23000, 19000, 25770, 26000 – not very specific is it?

    Example: http://culter.colorado.edu/~saelias/glacier.html

    Update: 19-23000 is something else…
    ‘The gravitational force between the Sun and moon induces the precession in Earth’s orbit, which is the major cause of the widely known climate oscillation of Earth that has a period of 19,000 to 23,000 years.’

  19. tchannon says:

    Sorry Rog, electric water heater, no wind.

  20. oldbrew says:

    TB: ‘LNC/5 = average ENSO period = 1/3 solar cycle = ~3.7yr’

    25 Chandler wobbles = 8 ENSO seems to fit quite well:
    (64/54 x 25) / 8 = 3.7037y (= 100/27)

  21. tallbloke says:

    Well, OK, but I prefer to link this directly to the two principle physical drivers of ENSO – Sun & Moon.

    I think the Sun is the bigger influence of these two, in that it injects the energy in an 11 year pulse. The Lunar tidal aspect then modulates the effect of that pulse. The most parsimonious way the system can express that is in an oscillation that fits both the Solar and Lunar cycles in the simplest possible resonant frequency – i.e. 3:1 with solar cycle and 5:1 with Lunar nodal cycle.

    However, 5 x 11.07 = 55.35 and 3 x 18.61 = 55.83, a difference of close to 1/2 a year. This may be of academic interest only, since the solar cycle length varies quite a bit anyway. Perhaps it modulates the positive and negative cycles of ENSO and the oceanic oscillations on longer timescales. 37 years would bring the 3:1 and 5:1 1/2 year difference back into phase. 74 years is a characteristic period of the north Atlantic, and this is 2 x 37 years, which Landscheidt flagged up as a solar system barycentric period. 37 years is 2 x the LNC approximately.

    Perhaps worth noticing that 74yrs is nearly in phi ratio with your 118.75 yrs too.

  22. oldbrew says:

    Hale cycle / lunar nodal cycle = Chandler wobble period?
    Also where does QBO fit in? If 2 CW = 1 QBO there could be a 5:4 5²:4² QBO:ENSO ratio.

    We know there are westerly/easterly oscillations in both QBO and ENSO.

  23. tallbloke says:

    Yep, I like Hale/LNC=CW

    Not seeing the 5:4 if QBO=2.37 and ENSO=3.7 though.

  24. oldbrew says:

    My mistake: try 5²:4².

  25. tallbloke says:

    Which means they synchronise near the J-S triple conjunction period around the period of the ~60 yr oceanic oscillation. Neato. 🙂

    So to summarise:

    the 3:5 relationship between the solar cycle length and the Lunar Nodal Cycle (LNC) induces the ~3.7yr El Nino Southern Oscillation (ENSO) periodicity
    The Hale cycle/LNC gives the Chandler Wobble period of 1.185 years
    The double of the CW is the Quasi-Biennial Oscillation (QBO) at 2.37 years.
    This beats in a 5²:4² relationship with ENSO to produce one of the oceanic oscillation periods of ~60 years

  26. Paul Vaughan says:

    The beat of 531 day with the year is 3.2 years.
    The beat of 3.2 years with the solar cycle is 4.5 years.

    Framework Reminder: p.6

    Stepping back to gain perspective, this is the offspring resulting from cyclically volatile solar excitation of stratospheric QBO & Brewer-Dobson circulation (BDC).

    Conventional assumptions are OFF. You CAN’T do this stuff with standard Fourier! It’s cyclically volatile with variably-paced cycling (…so Fourier’s in a blind fold.) A more generalized methodological framework is needed. Standard Fourier is just a special case from a set of infinite possibilities on that more generalized framework.

    Annual-12.8 & semi-annual-11.07 wind volatility weaves are slipping past one another every 82.4 years. That’s the ENSO envelope. Show the mainstreamers the DNA and say “Duh!” Sure you can can call it external excitation of an internal mode. There are 11.07 & 12.8 year internal modes excited externally with long run average 11.07 year period …but that thing has variable period, hence SCD which is mathematically equivalent to the frequency shift from the internal 11.07 mode.

    I don’t know a single climate scientist who would understand any of this stuff. They can barely understand standard deviation and probability density function. The farthest it might go for the best of them is “fat tail” (as if that’s an advanced concept). Nevermind volatility weaves and volatility weave rate shifts. …And when Lukewarmist Agencies try through twisted debating directives & strategies to conveniently limit the terms of discussion by (comically) restricting methodological considerations to a single special case (!) from a more generalized framework …well …that certainly does begin arousing deeper, darker suspicions (understatement….)……. (“I told you to keep your blindfold on!” said the abusive thought-police……)

  27. tallbloke says:

    Paul V: In your previous comment you noted:
    – harmonic mean of 1 year & 531 day (1.453829855 years) is Chandler Wobble (CW)
    – beat of CW & 531 day is 6.4 years

    Now you add that:
    The beat of 531 day with the year is 3.2 years.
    The beat of 3.2 years with the solar cycle is 4.5 years.

    3.2 yr is half 6.4 yr, but I’m not sure where you’re going with the 3.2 and 4.5 yr periods. Are you hinting that they are attractors towards the ends of the range of the period between El Nino events?

  28. E.M.Smith says:

    Not up to speed on the significance of all those numbers you’all are multiplying and dividing, so a lot of it reminds me of a parlor game (my limitation, not your problem…).

    Just want to note in passing that jpl.nasa paper per CW. Finds the answer it ocean bottom pressures, then 0attributes that to temp and salinity!? How can the bulk of the ocean change salinity in 1.x years with a 3000 year deep water overturning? How can temp matter when it is nearly a constant over a few hundred feet down?

    Then they ignore the giant moon dragging 10s of feet of water depth arround the planet….
    I’d look instead at lunar tidal modulation by sun and gas giants… Anything move about 1/5 of Earth orbit / year?

  29. E.M.Smith says: May 25, 2015 at 8:46 pm

    “Then they ignore the giant moon dragging 10s of feet of water depth arround the planet….
    I’d look instead at lunar tidal modulation by sun and gas giants… Anything move about 1/5 of Earth orbit / year?”

    Good observation! The claim is that momentum is conserved! To what scale? Neptune and Uranus have such vast orbital angular momentum, that makes Solar rotational angular momentum seem trivial! Are energy and momentum that much separated? Is this but another earthling fantasy?


  30. tallbloke says:

    EM: It’s clear to me that Sun and Moon are the big factors in driving ENSO. But the gas giants have had a hand in shaping our Moon’s orbit, and may still be causing changes in Earth’s length of day, which is another ENSO factor according to Per Strandberg’s hypothesis.

    Notice that 5 x QBO is close to Jupiter orbital period too.

  31. Paul Vaughan says:

    EM: At NASA JPL they suspect the moon as the more proximate cause.

    TB: No regarding ENSO. I outlined the resonance framework on p.6 here.

    The intersection of the annual & semi-annual weaves gives N/2.

    semi-annual 11.07

    annual 12.8

    N/2 ENSO envelope

    Remember that bidecadal CAM is closer to JEV than Hale.

  32. Paul Vaughan says:

    There’s high risk of misinterpretation.

    For example:
    – bidecadal SST follows J-S, not JEV.
    – we’re talking here about a resonance framework, not cycles.

    The sun strums the framework.

    SCD (solar cycle deceleration) measures the deviation of solar strumming from JEV (quality of excitation).

    The volatility weaves I’ve illustrated above are NOT speculation. Rather they’re clear observations and frankly it’s downright sinful when distortion activists obfuscate otherwise.

    Sometimes there comes a point (after years of retarded interference) where it makes sense to call a spade a spade.

    The lukewarmists have become chaos terrorists.

    I’ve not encountered a single climate discussion contributor who knows firsthand how to measure cyclic volatility independently. It’s creepy.

    Given that people can’t understand something this simple even though it’s trivially underpinned by geometric axioms & laws (of large numbers & conservation of angular momentum), it’s pretty clear that the IPCC is going to take control. Sorry to say, but it’s laughable to think they’ll be stopped by people who haven’t the cognitive capacity to recognize profound simplicity even when it’s outlined in highlighter right in front of their eyes.

    …But thank goodness a brave community with no such wool over their eyes is welcome here at the liberated Talkshop, where the thought of free exploration isn’t discouraged at lukewarmist gunpoint.

  33. tallbloke says:

    Paul V: Thanks for the clarification, and for the recognition for the core mission of this blog. People should not be shouted down or ridiculed for testing speculative ideas, nor for forming research groups to co-develop them into stronger hypotheses. Judy Curry’s post today on the danger of a dominant ideology skewing scientific research within science’s institutional sphere is apposite at this juncture.

    As you know, my PRP papers were all about solar system orbital resonance and the effect it has on Earth’s orientation parameters and climatic quasi-periodicities, and solar variation. I’m thrilled that others have come to recognise its importance and are working towards a better understanding informed by its ramifications.

    I recieved word a few days ago that the book we have been working on, which makes summaries of our papers available again to a wider audience, along with some commentary on scientific ethics, has been accepted for publication by a major science publisher. So be of good heart, the IPCC hasn’t won yet. They might have been able to get Copernicus (the innovative science unpublisher) to shut down the journal we published our original work in, but the cream always rises to the top. 🙂

  34. Paul Vaughan says:


    As everyone knows I’m a huge fan of the Pareto Principle.

    I aim not to reinvent popular wheels but rather to strategically complement where community perception appears weakest.

    The mainstream shies away from joyful, harmonious exploration of beautiful natural frontiers of interdisciplinary human perception.

    Earth orientation observations suggest that Earth has internal modes on the J-N & J+N = JEV framework (which combine trivially onto the algebraically limiting N framework).

    “Internal” is the *speculative* part.

    The *non*-speculative parts:
    a) the annual & semi-annual volatility weaves.
    b) volatility weave rate shift complex pair (SCL & SCD = solar cycle length & deceleration).

    Sometimes I think we need to stop to differentiate the grey areas from the black-&-white.

    The volatility weaves & volatility weave rate shift are observed clearly on Earth.
    (To challenge these observations one has to plead for violation of geometric axioms &/or laws of large numbers &/or conservation of angular momentum.)

    Are the black-&-white observations because of external excitation of resonant internal modes on the J-N & J+N = JEV framework? Or is it direct external forcing?

    In central limit the equator follows the sunspot integral. That’s the main thing going on. Then at the next levels of detail SCD governs mean regional aberrations (on the north-south axis) and the relative slip of the weaves shapes the ENSO variance envelope (on the east-west axis).

    I’ve outlined all of this is considerable detail elsewhere.

    The axial structure has to be acknowledged in order for sensible discourse to begin and proceed.

    The crystalline axial structures establish that the attractor root can neither be randomness nor chaos (although such scattering may certainly play a role in attractor residual modeling at this stage of evolving interdisciplinary human perception).

    Putting the immediate question in clear terms:

    Are we observing external excitation of resonant internal modes?
    Or are we observing direct external forcing?

    Put in other words:

    Does Earth have J-N & J+N = JEV internal modes?
    Or are the observed patterns forced externally?

  35. oldbrew says:

    oldbrew: ‘Lunar nodal cycle x Chandler wobble = 22.06 years = 1 Hale cycle, or something very close to it. Whether that tells us anything useful is another matter.’

    It’s also 34 Jupiter-Venus conjunctions (22.06085y).

  36. tallbloke says:

    Paul V:
    Does Earth have J-N & J+N = JEV internal modes?
    Or are the observed patterns forced externally?

    Or is there a third possibility that the gradually changing resonance interactions entered into by the Moon as it has receded from Earth has shaped it’s orbit in such a way that it embodies and reflects those solar system patterns and directly affects Earth strongly as its nearest neighbour?

    I don’t know, but it’s a good quest to try to find out. Chaos certainly isn’t the answer.

  37. oldbrew says:

    JSE: 21 J-S = 382 J-E = 403 S-E [21 + 382 = 403]
    JSV: 13 J-S = 398 J-V = 411 S-V [13 + 398 = 411]
    JSE:JSV = 21:13 = Fibonacci ratio near Phi:1 (frequency ratio of the two triple conjunctions)

  38. Paul Vaughan says:

    tallbloke (May 26, 2015 at 10:44 pm) wrote:
    “Or is there a third possibility that the gradually changing resonance interactions entered into by the Moon as it has receded from Earth has shaped it’s orbit in such a way that it embodies and reflects those solar system patterns and directly affects Earth strongly as its nearest neighbour?”

    That would be J-N. I elaborated on Piers Corbyn’s related suggestion on p.5 here.

    My impression is that Richard Gross (EOP expert NASA JPL) & Ian Wilson suspect something on that frame. Either JPL isn’t confident or there’s dreadfully simple classified info they can’t release. Doesn’t matter. The observations are there.

    Physically nature’s doing what nature does physically and we observe it. I can observe an animal’s behavior without knowing the code of it’s DNA. Again: The observations are there.

    I’ve had quite enough of this wuwt & ce type blogging attitude that the animal’s behavior should not be a focus of interest because we haven’t decoded it’s DNA. That’s just debating tactics, transparently hollow at the core to the more serious people who matter.

    Observations take precedence over physical modeling capacity (…or lack thereof) and that’s a point I’m prepare to aggressively & relentlessly sledge-hammer forever even if I’m held at gunpoint.

    J+N = JEV wouldn’t be the moon alone. Rather that’s Earth-Moon relative to Sun.

    Similarly with J-S, that’s Earth-Moon relative to solar system barycenter.

    Physical modeler’s are missing something fundamentally important in both of these cases (differential motion of earth’s shells and their fragments or whatever). I flatly, aggressively, & firmly reject all arguments that it’s not happening because no one can physically model it. It’s observed.

    To the b*tchy, whiny physical modelers crying “Don’t look at observations! Don’t point them out in public! Don’t try to say they exist!!” I say: Shut up and get back to work. If you can’t do your job you’re fired and replaced by someone competent.


  39. oldbrew says:

    We can observe that 14 x 13 Jupiter orbits = 2159 years (within 2 days).
    Also 14 J = ~13 Jupiter-Neptune conjunctions, so we have as a guide:
    182 J = 2159 years(E) = 1977 J-E = 169 J-N

    169 and 182 are multiples of 13, plus:
    166 x 13, +1 = 2159
    152 x 13, +1 = 1977
    (166 – 152 = 14)

    This could be the basis for a Jupiter-Neptune-Earth model.
    Comparing it to the Jupiter-Venus-Mercury model in this post, we find:
    2159y x 11 = 23749y
    118.74y x 200 = 23748y (difference = 1 year or 0.000042%)
    (2002 J = 23748.95y)

    According to this link: http://geography.about.com/od/learnabouttheearth/a/milankovitch.htm
    ‘Over a 95,000 year cycle, the earth’s orbit around the sun changes from a thin ellipse (oval) to a circle and back again.’
    23749y x 4 = 94,996 years

  40. tallbloke says:

    Paul V: Thanks for the expansive comment.
    Just this for now:
    “Similarly with J-S, that’s Earth-Moon relative to solar system barycenter.”

    Do you have anything more precise in mind than the (not so close) similarity between Landscheidt’s barycentre – J – Sun alignment average period and the lunar nodal cycle half period I noted earlier?

    I’m guessing you do, since you are talking about J-S, not just J.

  41. Paul Vaughan says:

    SST follows J-S, which from Earth’s perspective is an envelope made up of the higher frequency J-N component that beats with the terrestrial year to give CW, as I outlined in a comment on the BDO (bidecadal oscillation) thread:


    “The high frequency component (with J-S envelope) on the osculating year length graph is 0.54243476 years.

    Note the beat with the terrestrial year:
    (1)*(0.54243476) / (1 – 0.54243476)
    = 1.1854807 years = 432.9875671 days

    If climate “scientists” can’t explain the celestial origins of the QBO, maybe we shouldn’t be listening to them about anything.”

  42. Geoff Sharp says:

    Paul, I have no idea what the plotted black line is in your graph, but of interest is the secondary peaks at 1970 and 2008. These secondary peaks line up with the solar disordered orbits caused by JUN+S as per our recent discusssion.

    It would be interesting to see if the correlation extends further back in time?

  43. Paul Vaughan says:

    By definition it extends in both directions on the time axis.

  44. Geoff Sharp says:

    So you could also overlay the spatial SST data over this graph:

    Interesting how the spatial SST modulation is decreased while U/N are together?

  45. Paul Vaughan says:

    anything with J-S period — e.g. Scafetta uses barycentric sun speed:

    Connect the dots:
    The N/2 period ENSO envelope is the beat of 6.4 with 5.9:

    Holme & de Viron (2013). Characterization and implications of intradecadal variations in LOD.

    Click to access nature_sub.pdf

  46. Paul Vaughan says:

    …so just to clarify, this is the beat of the polar motion envelope with the nearest Chandler wobble subharmonic (…or equivalently the beat of (J-N)/2 with J/2.)


  47. Paul Vaughan says:

    equivalently it’s the beat of (J+N)/2 (Schwabe extremes) with J/2 and (as indicated farther above) it’s the beat of J+N with J-N (i.e. intersection of annual & semi-annual weaves)

    …so some will start to wonder if they unwittingly projected this to infill missing Southern Ocean data (v3b2). Maybe that’s why they appear to be backtracking on that now and infilling more with the sunspot integral & SCD patterns (v4).

    In ERSSTv3b2 they made it look like the Humbolt Current shaping ENSO variance, but it’s clear they’re not thinking about this clearly. Maybe they eventually will if they develop enough patience to understand aggregation criteria firsthand. At present they may be blindly projecting haphazard aggregates (weighted spatiotemporal integrals & aliases). They may have overreacted once they started realizing this was happening and that may explain how they knee-jerked to arrive at the transparent v4 mess that needs sober reflection. I bet there was conflict between the technicians and “superiors” when the direction was set.

    Certainly they can look at aggregation in terms of polar motion & QBO beats if they’re uncomfortable with nearest lunisolar subharmonics on the spatial J & N frame that defines the extremities of system solar & barycentric beats. They can comfortably pretend (wink, wink in the public eye) that it’s all internal …and we’ll translate across most-nearly-aligned reference frames (nearest harmonics & nearest subharmonics, depending on whether primarily temporal or primarily spatial), of course.

  48. tallbloke says:

    “it’s all internal”

    Oh Moon; steady our planet’s fluttering heart. Lol.

    6.4 x 5.9/(6.4 + 5.9) = 3.07
    Which is quite close to the period between crossings of the lunar lines of nodes and apse.

    I just noticed this post on Ian Wilson’s site

    And this one. Looks like I missed a lot of good stuff while I was busy politicking.

  49. oldbrew says:

    A strong J-U-N period is 22 U-N: 273 J-U: 295 J-N in 3770.93~ years.
    (21+1 U-N : 21 x 13 J-U : 21 x 14,+1 J-N)
    Orbits: 22.883 N, 44.883 U, 317.884 J

    128 Saturn orbits is about 1.65 years less.

  50. tallbloke says:

    OB: Interesting. I think between 21 and 22 U-N is around the the period of the full precession of the UN conjunction cycle too.

  51. Paul Vaughan says:

    2 sides of 1 coin …or 2 N-sides of 1 J-coin, if you prefer:
    J-N = 12.8
    J+N = 11.07

    Innermost & outermost jovians necessarily dictate solar system barycentric (J-N) & heliocentric (J+N) limits. Not talking here about the biggest amplitudes — rather talking about extreme components, as it is extremes that shape variance envelopes.

    Don’t confuse means with extremes!!!

    Some background:

    JEV = Jupiter-Earth-Venus period = J+N = long-run Schwabe solar cycle average period

    long JEV cycle period or JEV super cycle period = Neptune period = N (advisory: somehow the community isn’t picking this up even though it’s being repeated — consequent suggestion: use NASA Horizons online ephemerides to check — it’s easily verified in 1 quick sitting)

    J with N
    (164.79132)*(11.862615) / (164.79132 – 11.862615) = 12.78279303
    (164.79132)*(11.862615) / (164.79132 + 11.862615) = 11.06602004
    (164.79132)*(11.862615) / ( (164.79132 + 11.862615) / 2 ) = 22.13204008 = harmonic mean

    J/2 with N/2
    (82.39566)*(5.9313075) / (82.39566 – 5.9313075) = 6.391396515
    (82.39566)*(5.9313075) / (82.39566 + 5.9313075) = 5.533010019
    (82.39566)*(5.9313075) / ( (82.39566 + 5.9313075) / 2 ) = 11.06602004

    ENSO variance envelope =
    intersection of annual & semi-annual weaves (illustrated above

    (12.78279303)*(11.06602004) / (12.78279303 – 11.06602004) = 82.39566
    (12.78279303)*(11.06602004) / (12.78279303 + 11.06602004) = 5.9313075
    (12.78279303)*(11.06602004) / ( (12.78279303 + 11.06602004) / 2 ) = 11.862615

    6.4 year polar motion envelope with 5.9 year LOD component:
    (6.391396515)*(5.9313075) / (6.391396515 – 5.9313075) = 82.39566
    (6.391396515)*(5.9313075) / (6.391396515 + 5.9313075) = 3.076381453
    (6.391396515)*(5.9313075) / ( (6.391396515 + 5.9313075) / 2 ) = 6.152762907

    5.9 year LOD component with Schwabe/2 (solar cycle extremes):
    (5.9313075)*(5.533010019) / (5.9313075 – 5.533010019) = 82.39566
    (5.9313075)*(5.533010019) / (5.9313075 + 5.533010019) = 2.862619931
    (5.9313075)*(5.533010019) / ( (5.9313075 + 5.533010019) / 2 ) = 5.725239862

    Keep in mind that 4(J-S) = 79.46014346 since
    (29.447498)*(11.862615) / (29.447498 – 11.862615) = 19.86503587

    Remember that J-S is also having an effect on the shape of the SAOT tower cluster envelope. At the event series level of detail, this may matter. N/2 may be a long-run statistical envelope, whereas J-S is influencing the timing of events sandwiched into the envelope. I base this cautionary suggestion on repeated, tediously careful analysis of SAOT tower cluster temporal translation symmetry.

    Correcting the brainwashing the community allowed the Lukewarmist thought police to do:

    Nevermind trying to investigate this stuff with standard Fourier-type methods. That’s a guaranteed dead end as that approach only hunts for an infinitesimal fraction of the types of patterns nature can generate.

    An infinitely more generalized approach to pattern hunting is needed.

    Were I running a blog I might completely ban the presentation of unwindowed, untuned, non-scale-resolved spectral analyses simply to encourage DUE innovation rather than age-old same-old blind-fold.

    Lukewarmists love, worship, adore, & cherish standard-fourier-type methods because they’re 100% guaranteed to hide all but an infinitesimal fraction of nature’s patterns. “I told you to keep your blindfold on!!” harshly scolded the lukewarmist thought police.

    I might let the method back in later (for a supplementary role) after a period of forced innovation.

    Of course I’m not running a blog, so the purpose of these suggestions is simply to provoke and encourage outside-of-the-box hunting. (The Lukewarmists are saying: “Stay trapped in the box!!! hehe…”.)

  52. Paul Vaughan says:

    typo alert: on the 82.4 year ENSO variance envelope graph where it says “ERSST PC1&2” in blue it should say “ERSST PC2&3

    Remember that the ENSO variance envelope and SCD both bite into Greenland mass balance:

    background (on Greenland ice sheet mass balance, including several illustrations):

    This is where people are getting themselves mightily confused speculating about NAO-AMO relations.

    There are 3 root causes of North Atlantic pattern, as I outlined in ERSST EOF 1234.

    One of them is about how extremely ENSO spreads it’s wings.
    Another is about how solar cycle frequency shifts the poleward heat-flux fire-hose.
    And of course, at the base, all of that stuff is riding on the more gentle sunspot integral.

  53. Paul Vaughan says:

    This is getting funny.

    For those who need it to be lunar:

    Tropical 27.321582
    Nodal 27.212221
    Anomalistic 27.55455
    Synodic 29.530589


    Start building from there (and the tropical year) and you’ll get:


    Some will be naturally inclined to look here first:
    (6.409530885)*(5.996981134) / (6.409530885 – 5.996981134) = 93.17139513
    (6.409530885)*(5.996981134) / (6.409530885 + 5.996981134) = 3.098198409
    (6.409530885)*(5.996981134) / ( (6.409530885 + 5.996981134) / 2 ) = 6.196396817

    BUT I advise: We have spatial dimensions with asymmetries, so ANY nonlinearities will point to nearest-alignments on resonant subharmonic frames (…and who’s going to try to argue that there are NEITHER asymmetries nor nonlinearities anywhere in the Earth system???… (sarc) that’s brilliant genius! i give up — in a match with you it’s no contest!! (/sarc))

    Chandler subharmonic nearest 6.409530885:
    5 * 1.184858913 = 5.924294566

    (6.409530885)*(5.924294566) / (6.409530885 – 5.924294566) = 78.25454837
    (6.409530885)*(5.924294566) / (6.409530885 + 5.924294566) = 3.078683831
    (6.409530885)*(5.924294566) / ( (6.409530885 + 5.924294566) / 2 ) = 6.157367662

    So in short I think we can call the SAOT tower cluster mystery a wrap.


  54. Paul Vaughan says:

    more links for those exploring the trail independently:

    from Holme & de Viron (2013)

    even lukewarmist thought police are on the trail, suggesting this is going mainstream:
    (posted 5 days ago)

    Holme & de Viron (2005) data:

    Ian Wilson graphed it here:

    I’ve verified the pattern (using second order central differencing).

    It’s curious that Ian didn’t reference the 2013 paper (to which I linked upthread).
    Ian only referenced the 2005 paper:

    Holme & de Viron (2005). Geomagnetic jerks & a high-resolution LOD profile for core studies.

    Click to access gji2510%5B435-439%5D.pdf

    Of historical interest:

    SBC (Special Bureau of the Core) was shut down in 2009 and shortly thereafter in 2010 Dickey, Marcus, & de Viron put out their “no core effects needed” paper.

  55. Paul Vaughan says:

    Dickey, Marcus, & de Viron (2010). Closure in the Earth’s angular momentum budget observed from subseasonal periods down to four days: no core effects needed.

    “GGFC Special Bureau for the Core, 2001-2009
    Please note that this IERS component ceased operation in 2009.”


    The N/2 ENSO variance envelope explains envelope mysteries left hanging in 1990s Mann papers and more recent Scafetta papers.

  56. oldbrew says:

    TB: ‘OB: Interesting. I think between 21 and 22 U-N is around the the period of the full precession of the UN conjunction cycle too.’

    Your PRP paper (The Hum) says U-N precession is 3600 years = 21 U-N.
    Also: 3 x 22 (66) U-N = 23 Neptune-Pluto = 89 Uranus-Pluto (66+23)

    That’s 3 times the period used here:

  57. tallbloke says:

    OB: Your PRP paper (The Hum) says U-N precession is 3600 years = 21 U-N.

    That was a rough estimate made 18 months ago. Things have moved on since. 🙂

    Paul V: Great stuff, thanks! I’ve reposted Ian Wilson’s post for discussion.

    Which leaves the issue of the longer term changes in LOD identified by Gross, and my correlation to them using SSBz (the gas giants vertical displacement relative to the solar equatorial plane). Plus detrended global temp anomaly bonus…

    Now it could be that this is a coincidence and the longer term envelope can be explained by longer term inner solar system + J realignments and their effect on the Moon’s orbit plus the interconnected nature of solar system timings… or maybe there’s still a deeper mystery to be solved regarding the gas giants angular momenta effects (and/or EM effects via sol??) on the rotation rates of tiddlers in the inner system.

  58. Paul Vaughan says:

    TB, let me try this in different words than I’ve used in the past.

    The z-axis gives the right frequency, but not the right phase.
    An axis in the xy-plane gives both the right frequency and the right phase.

    …and the curve has the exact same shape.
    …so this suggests a particular alignment with the tropical year.

    At times it may have looked to some like we were, but we were never really in disagreement.
    We were just looking at mathematically equivalent patterns from different angles.

  59. tallbloke says:

    Paul, thanks, this explains my confusion over what you meant by ‘rotating 90 degrees’. I’d very much like to see your plot of the X-Y plane horizons model vs Gross’ LOD.

    There are differences between Z and X-Y, due to differing orientations of the orbital plane inclinations, but not enough to matter at the resolution we’re discussing in terms of curve shapes.

    I’m still interested in Z-axis, because:
    (i) I still think Ray Tomes’ theory has as much merit as any other.
    (ii) The planetary curve is ahead of LOD by 30yrs, which may be consistent with the ‘damped oscillation’ apparently exhibited by Earth in response.
    (iii) As Tome’s correctly points out, the Sun’s axial rotation nixes any barycentric effect on a 24 day timescale (and the Earth daily), whereas the gas giants stay above and below the solar equatorial plane for many years at a time.

  60. Paul Vaughan says:

    tallbloke (May 31, 2015 at 2:15 pm) wrote:
    “The planetary curve is ahead of LOD by 30yrs”

    Tuned to a particular axis in the xy-plane, the lag is 0.
    (That’s what I mean by phase match.)

    Physically nature is just doing whatever nature does physically.
    What I find interesting (and diagnostically neglected by so-called “physical” modelers) is the patterns.

    At the very least, the physical modeling conjecture should not by design require violation of geometric axioms and laws (of large numbers & conservation of angular momentum). (I don’t have to be a physical modeler myself to diagnose when the so-called “physical” modelers are in violation of geometric axioms and laws.)

    * * * * * * *
    Whenever patterns turn up suggesting beats of axial & synodic periods, that points to recurrence of conjunctions at the same heliographic longitude &/or time of year.
    * * * * * * *

    For example recently I condensed what Geoff Sharp has been saying for many years into a concise algebraic expression.

    It’s a trivial exercise to derive such expressions, as they are determined by the mere intersection of straight lines in phase space.

    Things are a little more interesting when there are snaking lines (like SCD). A snaking line moves the intersection points (with straight lines) in phase space.

    You don’t even need to know which straight lines are important to generalize the effect of a snaking line on the collective set of straight lines.

    It’s mind-boggling that people don’t get that ….maybe too caught up noticing individual trees (?) to notice the whole forest??

    Dunno, but it’s another curiosity observed while exploring nature …human nature in this case. (Sometimes it gets creepy….)