Why Phi: giant planets update – part 2

Posted: October 29, 2014 by oldbrew in Maths, solar system dynamics

Solar system planets [image credit: BBC]

Solar system planets by size
[image credit: BBC]

Using a simple formula we’re now able to see the link between Jupiter and Saturn orbits. As in the original giant planets update post the numbers are quite large but easily connected to the ‘Why Phi’ concept.

Using the orbit period of each planet we derive the synodic period, i.e. the time taken for the path of faster planet Jupiter to ‘catch up’ with slower planet Saturn. If we call the orbit periods J and S and the synodic period J-S we can make two calculations:
(360 / S) x J-S and (360 / J) x J-S.
The difference between the two results should be 360.

It turns out in this case that both results, when multiplied by 34, return a whole number: 20497 Jupiter and 8257 Saturn.
That means the number of conjunctions is 20497 – 8257 = 12240 J-S.
So the final figures are:
12240 J-S (34 x 360) = 20497 J = 8257 S = 243148 years (89 x 2732)

Since 34 and 89 are Fibonacci numbers there is a phi² (89/34) ratio between the number of conjunctions of the two gas giants and the number of years (= Earth orbits).

Also an exact number of orbits of three planets in a given period implies a 3-way relationship on that timescale.
In other words there should be an exact number of Jupiter-Earth and Saturn-Earth conjunctions in the same period, and the calculations confirm this.

The number of J-E conjunctions is divisible by 13 providing another phi² ratio (34/13) with J-S.
(NB the number of S-E conjunctions is the sum of J-S and J-E so is not directly phi-related)

—-
Addendum to the earlier ‘Why Phi – giant planets update’ post:
The post should also mention that the quoted Uranus-Neptune figure of 34² x 3³ contains a period of 27(3³) U-N in just under 4628 years.
4628 = 89 x 13 x 2²

Since J-S was 1768 years or 34 x 13 x 2² we can see that, by cancelling the ’13 x 2²’ part of the equations, the ratio of those two periods (4628y for U-N and 1768y for J-S) is 89:34 or phi²:1.
***
Reference data

Comments
  1. Me_Again says:

    Where did the 34 come from?

  2. oldbrew says:

    ‘Where did the 34 come from?’

    Number recognition plus guesswork. The initial calculation ((360 / S) x J-S) returned a number that looked like it should multiply by 7 to near a whole number (it contained ‘4285’).

    The whole number was (almost) 1700 which is half of 3400. On a hunch I went back to the original number and multiplied it by 34. Result was 8257 exactly.

    Anyone can try it on a calculator. To get the J-S figure the formula is: (S x J) / (S – J) using the S and J numbers in the ‘Reference data’ link above.

  3. Me_Again says:

    With ignorance and respect for those ‘that can’, that sounds awfully like the ‘bible code’ syndrome.

  4. oldbrew says:

    Remember this is based on actual data from NASA observations. If there’s a problem with the calculations let’s hear it. I’ve explained how it was done 🙂

    In fact let’s do the cross-check. J = 11.862615 years, S = 29.447498 Years
    11.862615 x 20497 = 243148.01
    29.447498 x 8257 = 243147.99
    20497 – 8257 = 12240
    12240 = 34 x 360

    That’s it. Source: http://solarsystem.nasa.gov/planets/charchart.cfm/

  5. Me_Again says:

    Perhaps I did not make myself clear. I don’t understand why the apparent random number 34 appears in things or can be randomly inserted into any calculation. Could you have 96 or 77? I’m not a mathematician. To me it is convincing, plausible, in the same way I was convinced the Bible Code was true too, in other words I’m dependent on someone else’s greater knowledge of a particular subject.

  6. vukcevic says:

    hi oldbrew
    Some years ago when I devised the solar formula http://www.vukcevic.talktalk.net/PF.htm
    based on the solar electro-magnetic feedback, I came to kind of ‘realisation’ that the Jupiter Saturn orbits could be synchronised by the electro-magnetic field.
    Jupiter magnetosphere extends to more than 5 AU and at the time their electromagnetic conjunction two magnetospheres merge. The pulling effect must be minute one, but repeated every 19+ years across 4 billion years, its cumulative effect had to be present
    I will take your numbers in years:
    S = 29.447498
    J = 11.862615
    JSc = 19.859
    S/J =2.482378
    JSc/(S/J) = 7.99999 or as near as you can get JSc/(S/J) = 8
    originally my result was slightly less accurate since I used only 3 decimal places.

  7. Me_Again says: October 29, 2014 at 11:09 pm

    “Perhaps I did not make myself clear. I don’t understand why the apparent random number 34 appears in things or can be randomly inserted into any calculation. Could you have 96 or 77? I’m not a mathematician. To me it is convincing, plausible, in the same way I was convinced the Bible Code was true too, in other words I’m dependent on someone else’s greater knowledge of a particular subject.”

    Good question! 34 is not random it is Fibonacci(9) the integer sum of Fib(8)=21 and Fib(7)=13. The Fibonacci series may well be Bible Code, but that sequence happens so often in nature, it cannot be discarded as random. The significance in the relationship between the orbital period of the large planets is but a conjecture, but also cannot be discarded, as it appears to effect the whole Solar system, and the location of the Sun. Are they coupled or not? In what way?

  8. Me_Again says: October 29, 2014 at 11:09 pm

    To not leave you hanging try:
    http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html#100

    Makes most folk scratch their heads, if not something more intimate!

  9. wayne says:

    Oh no Will, the prime factors of the fibonaccis. Makes my eyes hurt. But through the pain I already see patterns… yes many many patterns, and excluding the first four primes of 2, 3, 5 and 7 all factors for F(x) of 50, 100, 150, 200, 250 and 300 are not only of course odd but they all curiously end in one unlike all of the other fibonaccis that I could scan until my eyes gave out. What could this mean? 😉

    Well, back to debugging latex. At least it is not quite as hard as writting in native postscript by hand.

  10. Me_Again says:

    Thanks Will, Wayne, Oldbrew.
    The proverbial lightbulb just went on. Sorry guys but those of us who read about the Fibonacci numbers in a novel by a certain man don’t carry the first 97 numbers in the frontal lobe permanently. However I can now see that the 34 wasn’t plucked from the upper stratosphere or the depths of the pelagic wastes. I’m plainly missing out on something that drives your turbines and I feel a tinge of jealousy and wish I had the ability to have the bug. However in my favour I did really wow! when I first read about phi in the natural world which is where my turbines are turned. I’m currently studying quorum sensing in microbes and early symbiotic/collective activity and I think I must now have a fib table next to me just in case there are growth numbers with a link or even polysaccharides chain lengths which have the relationship in them.

  11. oldbrew says:

    Hi Vukcevic, I’m very interested in the electro-magnetism ideas.

    On a technical note the ‘JSc’ figure with those orbit numbers is 19.865y not 19.859y.
    Paul Vaughan confirmed that recently. That makes your result about 8.002

    The NASA planetary fact sheets are not up to date with their own chart (see ‘reference data’ link).

    Me_again: re. the multiples of 34 – it’s what the data shows, so we have to consider what that might be telling us. When it’s paired up with another Fibonacci number, in this case 89 it points to a phi relationship between the two.

    Going back to the earlier post: 89 Jupiter-Saturn conjunctions = 1768 years (1767.988)
    1768 = 34 x 13 x 4
    That’s straightforward orbital data. 13, 34 and 89 are Fibonacci numbers.

    See the ‘addendum’ to this post re the Uranus-Neptune equivalent.

    Will J: your questions are valid IMO.

  12. oldbrew says:

    Formula: (360 / S) x J-S
    Let’s show the figures to illustrate how it works.

    360 / 29.447498 (S) = 12.225147
    12.225147 x 19.865035 (J-S) = 242.85297
    242.85297 x 34 = 8257.0009

    Answer: almost exactly 8257 Saturn orbits per 34 x 360 J-S (12240).
    That necessarily means the number of Jupiter orbits is 8257 + 12240 = 20497.

  13. vukcevic says:

    oldbrew says:
    October 30, 2014 at 9:24 am
    On a technical note the ‘JSc’ figure with those orbit numbers is 19.865y not 19.859y.
    Paul Vaughan confirmed that recently. That makes your result about 8.002

    Thanks, I will update my numbers, still 8.002 far to close to 8 to be ignored.
    Since J and S orbits are elliptical and in different planes, I have a notion that JSc number could only be approximate.
    The ‘magnetosphric’ conjunctions would depend on the strength of the solar magnetic output at the time, stronger sun would make Jupiter’s magnetosphere’s tail thinner and longer, so it would happen earlier and last shorter time.
    But of course whole thing could be simply gravitational, resulting in a far greater accuracy.
    .

  14. tallbloke says:

    Will J: The significance in the relationship between the orbital period of the large planets is but a conjecture, but also cannot be discarded, as it appears to effect the whole Solar system, and the location of the Sun. Are they coupled or not? In what way?

    There is an intimate relationship between phi, Pi, root 2 and the inverse square falloff of gravitation and electromagnetism. We tend to think that the conjunction periods of planet pairs are the outcome of their orbital periods. In fact, it the other way around. The resonant harmonics arising from conjunction timings lead to energy being transferred between orbits that actively drives the planets into the orbits they occupy.

    These are usually close to but not exactly in simple harmonic ratios. If they were exact, more energy would be transferred, and the orbits would be driven away from the ratio. Once they are, the energy transfer diminishes and they start to fall back towards the harmonic ratio. A point of equilibrium is reached.

    We have also found phi relationships between orbital period and spin rates of planets. Our hypothesis is that the effect on the Sun is not only to determine its course relative to the barycentre of the system, but also to modulate the differential rotation rates of the solar surface plasma at various latitudes. That’s why the motion of the planets can be used to replicate the solar variation revealed in 10Be records on the Earth.

    Rick Salvador’s latest model uses only orbital periods, conjunction periods, and close sub-harmonics of them. It successfully replicates 4000 years of 10Be TSI reconstruction

  15. oldbrew says:

    Mercury is an interesting case. Its orbit:rotation ratio is very close to 2:3 and so is its aphelion:perihelion ratio (Aph = 69.8 AU, Per = 46 AU).

    And there’s ice at the poles, despite being the closest planet to the Sun.

    http://time.com/3522803/ice-mercury-space/

  16. tchannon says:

    Have you written a program to automate this?

  17. oldbrew says:

    Automate what, TC?

  18. tchannon says:

    Discovery of close ratios.

  19. oldbrew says:

    Could be useful to have some sort of list.

    The ratios of Jupiter-Earth to Jupiter-Saturn are also interesting – maybe that’s another post.

  20. tallbloke says: October 30, 2014 at 1:49 pm

    (“Will J: The significance in the relationship between the orbital period of the large planets is but a conjecture, but also cannot be discarded, as it appears to effect the whole Solar system, and the location of the Sun. Are they coupled or not? In what way?”

    (There is an intimate relationship between phi, Pi, root 2 and the inverse square falloff of gravitation and electromagnetism. We tend to think that the conjunction periods of planet pairs are the outcome of their orbital periods. In fact, it the other way around. The resonant harmonics arising from conjunction timings lead to energy being transferred between orbits that actively drives the planets into the orbits they occupy.)

    Thanks Roger! Has anyone done the comparison per radian rather than per cycle?
    That could be a lot of energy swishing around!

    ,

  21. E.M.Smith says:

    Enjoying the discussion. Not to be picky, but I’m going to harvest a ‘nit’ here….

    The title is “Why phi giant…” yet the why is never found. Yes, that the phi ratio exists is demonstrated. Yes, it is interesting. Yes, the method of finding the existence is expounded. But “Why?” Nowhere to be found….

    IMHO, that is the basis for the question from Me_Again. Why 34 comes from why phi. And while I understand that ‘why’ is likely unknown at this point (and perhaps unknowable until some wisdom accumulates); I had been looking forward to knowing “why?”, and now I’m not….

    Had it been called something like “Exploring natural phi ratios in giant planets…” I’d not have been led to expect that which was not there….

    Perhaps one of my favorite sayings needs to be put before me, so I remember to follow it…

    “Why? Don’t ask why… down that path lies insanity and ruin. -E.M.Smith”

    So maybe I’ll just try to be happy with the “Exploring natural phi ratios in giant planets”…

    While thinking about growth patterns of nautilus shells and potential analogue events in planetary growth… And pondering why…

  22. wayne says:

    Roger (TB), I am very inline with E.M. and Will, and even Me_Again’s questions. Why? Why pick phi? Not that I think you will not find anything where you are searching, you may, but the chance of doing so in the manner you are all approaching this question seems would be rather astronomical and proving it mathematically for science may be even magnitudes more difficult.

    The exact position of any interactions in relation to the sidereal space position and orientations seems to me be meaningless. That Jupiter and Saturn may align with, lets say, Sirius on a date and hundreds of orbits later they once again closely align again with Sirius any that happens to have a ratio near the golden ratio seems to have zero meaning except to astrologers maybe.

    What is the real question here? I thought the base was that possibly the planets gravitational interactions in some way may affect the sun which in turn affects all of the planets atmospheres. Is that still the underlying question? That planets mass therefore gravity may just affect the sun itself?

    If that is still the end goal I have the feeling that you are leaving out one huge factor and that is how planet positions interact with the sun’s revolution. Every planet pair aligns twice every revolution of the inferior planet in relation to the superior planet and therefore the center of the sun but what about the sun’s revolution about it’s axis? If the twenty seven or so days it takes the sun to revolve were to synch in some manner with such alignments of the gas giants orbits you just might be onto something.

    Even though when you look at these bodies as point masses they are all in free fall about their respective centers of mass with zero differentials but they are not point particles with huge gravitational pull, they have mass spatial distributions that do create gravitational distortions (tidal effects) that can very slowly ‘shake’ each others mass that each body is composed of.

    Maybe something like that should be part of your investigation but you would have to include the sun’s revolution also into account or it seems so to me. Some affect being there spread over thousands of years seems not there that we or the sun would ever ‘feel’.

    The only question this might intersects with is the solar system over eons then such phi harmonics may be relevant, or not, or in an opposite sense as I pointed out in one of your previous post on this. Phi is irrational and my prevent any harmonics from forming giving our solar system stability.

  23. oldbrew says:

    Bear in mind investigation continues so this isn’t the last word on the subject.

    I’m aware that too many numbers can be a turn-off 😉

  24. wayne says:

    Hi oldbrew,

    I’m just trying to make you and Roger aware of some of the confusion that myself and others commenting seem to be raising. I re-read once again the original post by Roger and that may be all there is to it. No effects or climate ties needed or implied except that there seems some pattern within the solar system orbits that ties to phi. That simple.

    But this focuses on phi and not the Fibonacci series. Any starting positive non zero number starts a series that converges on phi in that manner of a(n) = a(n-1) + a(n-2). You have of course 0,1,1,2,3,5,8,11…. but you also have 0,2,2,4,6,10,16,26…. and 0,5,5,10,15,25,40,65… and a spectum of phi series but we see that you seem to only be investigating one of those specific serires. Is this about phi or is this about the Fibonacci numbers?

    That is but one question but I will stop there for right now awating that answer.

  25. tallbloke says:

    Wayne: You are quite right that there are many series that converge to Phi, and that we are concentrating primarily on the fibonacci series. There’s a reason for that. The *observational evidence* is that the common resonant harmonic ratios in the solar system are 2:1 3:2 5:8 2:5 and 8:13. It’s that simple. Phi and phi^2 relationships are found all over the place, between orbits, spins, masses, densities etc.

    As I explained above, the ratios are rarely exact, because too much power would be transferred which would destabilise the orbits, or cause overspin to destruction. But the amount the ratios diverge from the simple ones is found to generate longer term relationships between the conjunction cycles of planets pairs, at periodicities which match long term cycles found in solar output as measured by 10Be and 14C at 208yrs, (de Vries), 2400yrs (Halstatt) and 179yrs (Jose) etc.

    The whole solar system is resonating at multiple frequencies which affect everything in it from solar differential rotation to Earth climate cycles.

  26. wayne says:

    oldbrew, sorry but I cut my comment too short. While you answer that question what about in the case of rational or real number series in the same manner such as 0, 2.34, 2.34, 4.68, 7.02, 11.7, 18.72,…. all converging in that manner of a(n-1)/a(n) equaling 1.618033…. or phi. Are you using those too?

    That is, are absolutely any ratio at all that equals phi allowable in you analysis?

  27. wayne says:

    Oops, should have been a(n+1)/a(n) or a(n)/a(n-1), my mistake. That gives the silver ratio.

  28. wayne says:

    tchannon says:
    October 30, 2014 at 3:50 pm

    Discovery of close ratios.

    tchannon and oldbrew:

    I have already written five or six programs automating this process back when this topic of Phi first began and Roger should already have the source code for each in email archives. I was passing him as they progressed. If they got lost in the flow of time I believe I still have them somewhere if you would like the code. Can’t remember if they were C++ or C# but you could easily convert the logic to R or some other script language if preferred.

  29. p.g.sharrow says:

    Rog, To operate, an induction motor must have a bit of slippage to transfer energy, they will not operate at resonate frequency but at some slower speed as they are dragged about. In a solar system the fields would push or pull, motor or generate, depending on the relative motion of the bodies. The spin of the sun will try to speed up the planets orbit and counter the drag of it’s gravity induced tidal bulge. You are right, each of the planets pushes and pulls it’s neighbors to maintain a fairly stable system. Any abrupt changes due to outside forces will be smoothed out over time. The sun is the big dog in this bed and sets the pecking order.
    Some day Astrophysics will realize Venus is a interloper that does not belong where it is. But the sun and other planets have and are taming it to it’s present position’s demands as they adjust themselves as well. pg.

  30. oldbrew says:

    Start with the most obvious evidence and go from there. A few examples:

    Neptune:Pluto 3:2 orbit ratio
    Venus:Earth 13:8 orbit ratio
    Mercury 3:2 spin-orbit ratio
    The Kirkwood gaps: note the words ‘mean motion resonance’ in the top left corner.
    Kirkwood gaps
    http://en.wikipedia.org/wiki/Kirkwood_gap

    There’s no master plan unfortunately. The movement of the planets is also interesting e.g. the Venus-Earth pentagram and the 3 x 3 pattern of Jupiter-Saturn conjunctions. That could probably be taken further.

    Re the number 34, that’s the lowest Fibonacci number that returns a value within 0.01 of phi when matched with the nearest Fib number, i.e. 34/21 is closer to phi than 21/13 and the lower pairs are.

    Orbits are counted in whole numbers so Fibonacci is the key with phi as the underlying ‘force’ if you like – 0.618 of an orbit has no real meaning 😉

  31. oldbrew says:

    The aphelion (distance from the Sun at furthest point in orbit) ratio of Saturn:Uranus is 2:1 and Neptune:Pluto perihelion ratio is 1:1

    http://en.wikipedia.org/wiki/Apsis#Planetary_perihelion_and_aphelion

    In fact Neptune:Uranus:Saturn is almost 3:2:1 in relative distance at aphelion.

  32. Paul Vaughan says:

    wayne (October 30, 2014 at 9:42 pm) suggested:
    “The exact position of any interactions in relation to the sidereal space position and orientations seems to me be meaningless. That Jupiter and Saturn may align with, lets say, Sirius on a date and hundreds of orbits later they once again closely align again with Sirius any that happens to have a ratio near the golden ratio seems to have zero meaning except to astrologers maybe.”

    Careful here.
    1. The planets don’t all lie in one plane.
    2. Winter is not summer. Rotational axes are tilted and obliquity’s a big deal in climate. Winter & summer circulatory topologies differ discretely, so there’s natural integration of aliasing.

    For example, Vukcevic points to JS 8:5:3:2:1 and Tallbloke is trying to help people realize that the deviations from this are key.

    Let’s consider de Vries.

    The subharmonic of the terrestrial year closest to J-S is 20.
    Iteratively chop that in half to gain some simple insight.

    20
    10
    5
    ——- Note what happens right here.
    2.5
    1.25

    You can only chop into 4 before you start alternating integrated aliasing across the discretely differing circulatory topologies of summer & winter (and across planes of differing inclination in the broader perspective).

    That’s how you get 208 from JS. (Clear as mud?)
    Maybe I can find time to volunteer some concise notes for those who may need just a little more help to see how Tallbloke’s tip goes to the next level beyond what Vukcevic has sharply clarified. …

  33. oldbrew says:

    Wayne says: ‘That is, are absolutely any ratio at all that equals phi allowable in you analysis?’

    Anything to do with planets that shows a Fibonacci ratio is potentially of interest, but it depends what it is.
    Orbits need to be whole numbers as a rule e.g. 8 Earth = 13 Venus (almost).

  34. wayne says:

    Thanks everyone, that clarifies the question. So this is more of a “Why Fibonacci?” search. but I still ask why? It seems if you would loosen up that constraint you just might find there is a whole lot more to do with Phi than just those on the Fibonacci series. Just a thought.

    I’ll step back into the background.

  35. oldbrew says:

    Wayne: there’s no constraint. I might put up another post where things can be looked at in a slightly different way – I’ve got some material for that. Along the lines of a workshop perhaps.

    From a NASA feature:
    ‘The great distance from Saturn and resonance with Titan has also kept Hyperion from becoming tidally locked facing Saturn. Hyperion rotates roughly every 13 days during its 21-day orbit.’

    http://solarsystem.nasa.gov/planets/profile.cfm?Object=Hyperion

  36. oldbrew says: October 31, 2014 at 6:56 pm

    (Wayne says: ‘That is, are absolutely any ratio at all that equals phi allowable in you analysis?’)

    “Anything to do with planets that shows a Fibonacci ratio is potentially of interest, but it depends what it is. Orbits need to be whole numbers as a rule e.g. 8 Earth = 13 Venus (almost).

    OB, Why whole numbers as a rule? Is 8 x Phi closer? How about 13/Phi? Not bitching, just a question, on this fascinating subject. Is it Fibonacci, or GSR to some power, using “any” orbital period as “a” reference integer?

  37. wayne says: October 31, 2014 at 8:34 pm

    “Thanks everyone, that clarifies the question. So this is more of a “Why Fibonacci?” search. but I still ask why? It seems if you would loosen up that constraint you just might find there is a whole lot more to do with Phi than just those on the Fibonacci series. Just a thought. I’ll step back into the background.”

    Come on Wayne, look again at the factors of all the Fibs. Enough stuff there to locate every toilet on this planet, somehow!

  38. p.g.sharrow says:

    The Sun is a giant spinning Electromagnetic motor,self powered. It’s lines of force spiral out as in the shell of the Nautilus. Why would the Fibonacci ratio be evident? Why not? pg

  39. Paul Vaughan says:

    J-S =
    (29.447498)*(11.862615) / (29.447498 – 11.862615)
    = 19.86503587 years

    S harmonic nearest J:
    (29.447498) / 2
    = 14.723749 years

    J beat with S harmonic nearest J:
    (14.723749)*(11.862615) / (14.723749 – 11.862615)
    = 61.04648218 years

    alternately:
    J beat with J-S harmonic nearest J:
    (11.862615)*(9.932517933) / (11.862615 – 9.932517933)
    = 61.04648218 years

    harmonic nearest J-S:
    (61.04648218) / 3
    = 20.34882739 years

    beat with J-S:
    (20.34882739)*(19.86503587) / (20.34882739 – 19.86503587)
    = 835.5462281 years

    alternately:
    beat of S/5 with J/2:
    (5.9313075)*(5.8894996) / (5.9313075 – 5.8894996)
    = 835.5462281 years

    The preceding summarizes hierarchically nested Jupiter-Saturn slipping.

    Now note what happens with iterative halving:

    19.86503587
    9.932517933
    4.966258966
    ——————near-resonance with terrestrial year lost after 2 halvings
    2.483129483
    1.241564742

    So the near-resonance central limit is:
    (835.5462281) / 4
    = 208.886557 years (Phi Knot)

    As Tallbloke emphasized, de Vries is due to deviations from perfect resonance.

    Were the hierarchically-nested JS resonance perfect, de Vries would have infinite period (since synchrony would never break). Repeating the above calculations with Jupiter & Saturn periods rounded off to nearby Earth year clarifies the implications of perfect 8:5:3:2:1 :
    (30)*(12) / (30 – 12) = 20
    (12)*(10) / (12 – 10) = 60
    (30)*(20) / (30 – 20) = 60
    (20)*(20) / (20 – 20) = ∞

    20
    10
    5
    ———
    2.5
    1.25

    ∞ / 4 = ∞

    So there would be an eternal wait for de Vries with perfect resonance.

    Talkshop Flashback: Recall that years ago P.A. Semi compiled familiar illustrations of solar system cycles. NASA has since upgraded to a new DE, so you won’t find exactly 835 years in Semi’s illustrations, which were based on the earlier DE.

  40. oldbrew says:

    PV: re PA Semi’s 835 years – 42 J-S is 834.33y which is 1/3rd of 2503 years.

    2503 years is (almost) 85 Saturn and 211 Jupiter orbits, and 211 – 85 = 126 conjunctions = 21 x 3 x 2.
    The J-S conjunction is located (almost) where it was 2503 years earlier (calcs. below), relatively speaking.

    2503 / 12 = 208.583y = de Vries ?
    191 Jupiter-Earth = 208.583y as well
    And it’s the half period of: 21 J-S = 382 J-E = 403 S-E

    Formula: (360 / S) x J-S

    360 / 29.447498 (S) = 12.225147 (degrees of Saturn orbital movement per year)
    12.225147 x 19.865035 (J-S) = 242.85297
    242.85297 x 3 = 728.5891
    728.5891 – 720 (= 2 x 360) = 8.5891
    8.5891 x 42 = 359.47422 (99.854% of 360)

    3 x 42 = 126 J-S
    (126 x 242.85297) / 360 = 84.998538 = ~85 Saturn orbits
    19.865035 x 126 = 2502.9944y
    85 Saturn @ 29.447498y = 2503.0373y

  41. oldbrew says:

    Will J: ‘Why whole numbers as a rule?’

    I see it as phi arising from the numbers, but it can also be the numbers arising from phi if you prefer 😉

  42. Paul Vaughan says:

    OB:

    P.A. Semi wrote:
    “We have got no explanation for the longer wave of approximatelly 2600 years (fig. 48f […]”

    The calculation for the more stringent requirement of same spatial orientation is:

    3*(19.86503587)
    = 59.5951076 years

    (61.04648218)*(59.5951076) / (61.04648218 – 59.5951076)
    = 2506.638684 years

  43. oldbrew says:

    My thought was that J S and E meet with whole numbers of orbits (almost) every 2503 years and the number of conjunctions of each pair is a 6 x multiple, so the basic period is 2503 / 6 = 417.166y = 2 x 208.583y (de Vries cycle average?)

    85 S, 211 J, 2503 E
    211 J – 85 S = 126 J-S (6 x 21)
    2503 E – 211 J = 2292 J-E (6 x 382)
    2503 E – 85 S = 2418 S-E (6 x 403)

    NB 403 = 31 x 13 so the J-S : S-E ratio includes a factor of 21/13

  44. tallbloke says:

    E.M Smith: “Had it been called something like “Exploring natural phi ratios in giant planets…” I’d not have been led to expect that which was not there….”

    The original post has a question mark after Why Phi? It’s still an open question, though I think we’ve been edging nearer an answer since. My PRP main paper offers some possibilities. So apologies for your disappointment, we’ll try to remember to keep that question mark present in future post titles.

  45. tallbloke says:

    It’s exciting and encouraging that Paul Vaughan is getting the same numbers as we are via a different method. I think our method illustrates the physical situation in a way more easily visualised, and it has led to our discovery that the periods of the precession of the conjunction cycles of adjacent planet pairs are also in simple harmonic ratios with each other.

    That fact, it seems to me, is what vindicates our view that resonance pervades the solar system, and strengthens by inductive reasoning the possibility that the Sun’s variability is also affected by it.

  46. oldfossil says:

    oldbrew or Paul Vaughan please humor a complete ignoramus like me? If I know the orbital period can I calculate the orbital radius? If Earth’s orbital period was once 240 days was it closer to or farther from the sun?

  47. oldbrew says:

    oldfossil: the semi-major axis = the radius = the cube root of the square of the orbit period in years (so use 240/365.25).

    The value returned is in AU where 1 AU = Earth-Sun average distance. Orbits are smaller the nearer a planet is to the Sun.

  48. Paul Vaughan says:

    OB:

    The calculations I’ve shared illustrate the attractor (central limit), but actual event series jump around the attractor, as can be seen for example by extending your calculations for ~2500 out to ~5000, ~7500, ~10000, etc., etc., etc. and then averaging. I’m summarizing the average over an infinite number of such extensions.

    I’ll share a little more.

    Although the lunar nodal cycle has a period of 18.612948 years, Earth’s year aliases ~6.4 year wave from LNC. (I sincerely hope this doesn’t surprise anyone. It’s easily verified in seconds using NASA Horizons output).

    Jupiter (fastest gas giant) & Neptune (slowest gas giant) most simply outline boundary conditions shaping ~6.4 year inner solar system waves such as 4*(V-E). Note the relation of 4*(V-E) with the nearest harmonic of LNC (which summarizes cycles of LNC slipping relative to V-E):

    (6.394936377)*(6.204316) / (6.394936377 – 6.204316)
    = 208.1425224 years

    Analogous calculations for other solar system bodies gives ~207.5 to ~210 years. (So far I’ve found no analogue that falls outside of this range.)

  49. oldbrew says:

    Thanks PV, harmonics delivering interesting results yet again.

  50. Paul Vaughan says:

    OB, it’s no different than gears in a machine. It’s actually simple stuff figuring out how the cycles slip past one another. The key role of inclination (which has a spatial orientation) — and consequent spatial gradients — is neglected in conventional mainstream sun-climate conceptualization. That’s the real mystery. I’ve never seen any mystery about “wi fi?” It’s a question I would never have asked as the answer is too obvious. I remember that that stuff was even covered in Intro Dendrology, which is mostly about rules for simple classification and not exactly high on intellectual feat. So I’m inclined to believe that due to the complexities added to physics & chemistry by life, biologists might have orders of magnitude more experience with complex, knotted patterns than scientists from other fields dealing only with the inanimate. I can suggest that there is something to be learned from some of the above commentary about the framing. I don’t find it difficult to see how the framing is (accidentally) putting some readers off. On the other hand, it’s also clear from comments above that some have not yet realized the corruption of their thinking (despite their resistance) caused by the darkly aggressive campaign of thought policing at sites like wuwt. Some of the language in a post that appeared at wuwt today crossed a line. The host allowed that language to be posted and so the host must bear responsibility. As of today I’m writing that host off permanently. This is a final judgement.

  51. tallbloke says:

    PV: I’ve never seen any mystery about “wi fi?” It’s a question I would never have asked as the answer is too obvious.

    Do share. I’d love to know why not only are planet pairs in phi related orbital periods and spin rates with each other but also their diameters and densities. I’m all ears, make my day.

    I can suggest that there is something to be learned from some of the above commentary about the framing. I don’t find it difficult to see how the framing is (accidentally) putting some readers off.

    We use ‘Why phi?’ in the post titles so that all the related posts can easily be found using the search box in the left column.

  52. Paul Vaughan says:

    Building a Mystery?
    φ-Φ=1, so translation symmetry is guaranteed.
    That’s a solid foundation on which to build.

    I agree that sticking with “Why φ?” makes practical sense now for easy ID. Earlier misunderstandings are fading as people simply become more practical about discussing a highly interesting topic (no matter how its framed and named).

    Amen to Talkshop freedom from the darkly-twisted distortion-artistry of alarmist-directed sun-climate thought-policing.

  53. Paul Vaughan says:

    φ-Φ=1, so translation symmetry is guaranteed.
    Vacuous? Yes. Vacuity’s a property of the wheel.

  54. Paul Vaughan says:

    TB: It’s dawning on me that maybe several of us are not interpreting the question “Why φ?” the way you hoped or intended. (Perhaps on the up side this is adding layers to the intrigue…)

  55. tallbloke says:

    Paul, the following statement is true to within an error of 1%

    While Jupiter makes 2/3 of an orbit, Earth and Venus meet 5 times as Earth orbits 8 times and Venus 13 times, as mercury passes Venus 21 times while making 34 orbits.

    This makes the standard theory of the planetary orbits ending up where they are through a set of random collisions laughable. It’s obvious that forces act on the planets to push them into the orbits they occupy. There has to be more than one force acting, gravity isn’t going to do this alone, because observation shows that axial spin rates are also related (and not just on tidally affected bodies such as Mercury and Venus) and gravity acts in a straight line. Gravity only resonant harmonics won’t do the job alone. There has to be an electro-magnetic component mediated by the solar wind and the interplanetary magnetic field it generates. This is another medium in which energy is stored and transferred, besides the gravitational potential stored in the gravitational field. Both these fields are acting on orbiting objects to steer the into harmonious relations with each other.

    The mystery lies in the way the two fields differentially act to bring about stable sets of orbits. The fact that observation shows planetary groups preferentially evolve into stable patterns characterised by the Fibonacci series and have pair-masses and pair-densities which relate by powers of phi is a clue to unravelling this mystery, in my opinion.

    A few things we know:

    Fibonacci ratios are resonant. Particularly 2:1 and 3:2 8:13 and 5:2 ratios
    The Fibonacci series is a special case of a lognormal distribution (frequently found in natural phenomena).
    Lognormal distributions also characterise gaseous media undergoing gravitational collapse.
    As well as the Fibonacci series consecutive numbers converging to phi, phi can generate the Fibonacci numbers fractally.
    Phi turns up in subatomic physics and crystallography too.

    Game on.

  56. oldbrew says:

    Not forgetting galactic logarithmic spirals:

    Golden spiral
    http://en.wikipedia.org/wiki/Golden_spiral

  57. Paul Vaughan says:

    Thanks TB.
    That exposition does much to clarify.

    I suppose that a major difference between me & the stubborn mainstream is that I accept observation and do not harshly reject observation when it’s inconsistent with model fantasy.

    My interest is and has always been pattern, regardless of mechanism.

    My ability to recognize a friend’s face doesn’t depend on my detailed understanding (or lack thereof) of the role of DNA as a mechanism for generating the shape of my friend’s face and my brain’s ability to interpret my eyes’ image of my friend’s appearance.

    That’s what I mean when I say many are guilty of allowing the wuwt thought police to corrupt their thinking with the endlessly repeated (for political reasons) “show me the mechanism” harassment.

    If it’s happening it’s happening.

    The beat of φ with Φ is 1.
    This tells me the spacing is regular.

    That’s it.
    That’s where my interest starts and ends.

    I don’t need to know the mechanism to accept and appreciate this.

    (φ-Φ) / φΦ = 1 / 1 = 1

    This is a vacuously simple property of 2 circles.
    It can be stated concisely and is therefore useful & aesthetically satisfying.

    It doesn’t destroy any cherished, overcomplicated model fantasy I had.

    Your curiosity extends to mechanisms.
    My curiosity extends to exploring other patterns without worrying about mechanisms.
    Therefore we’re in no disagreement if we agree on what’s observed.

    Best Regards

  58. Paul Vaughan says:

    Look how 1 splits φ:

    φ / (φ-1) = φ^2
    φ / (φ+1) = 1/φ

    Ordering:
    φ^2
    φ^1
    φ^0
    φ^(-1)

    Simple.

    A full theory of spatiotemporal knotting of fluid turbulence has not yet been developed by humans, but here’s something you can take to the bank:

    The rate of homeomorphic transformation of the climate knot (regardless of its topology) is governed by the sun. We already know this from the laws of large numbers & conservation of angular momentum. (It’s proven in the rigorous sense.) The mainstream refuses to admit this (due to a toxic combination of stubborn ignorance & deception).

  59. oldbrew says:

    Re. orbits and ratios:

    Saturn:Uranus (orbit ratio) = 4 Jupiter-Saturn : 5 Saturn-Uranus (conjunction ratio)

  60. Paul Vaughan says:

    Reads like TB wisdom and a description of what went wrong with wuwt:

    “[…] if one person mentions the unusual combination of A-B and another unusual combination A-C, it may well be that the combination A-B-C, which neither has thought of separately, may yield an answer.

    It seems to me then that the purpose of cerebration sessions is not to think up new ideas but to educate the participants in facts and fact-combinations, in theories and vagrant thoughts.

    But how to persuade creative people to do so? First and foremost, there must be ease, relaxation, and a general sense of permissiveness. The world in general disapproves of creativity, and to be creative in public is particularly bad. Even to speculate in public is rather worrisome. The individuals must, therefore, have the feeling that the others won’t object.

    If a single individual present is unsympathetic to the foolishness that would be bound to go on at such a session, the others would freeze. The unsympathetic individual may be a gold mine of information, but the harm he does will more than compensate for that. […]

    If a single individual present has a much greater reputation than the others, or is more articulate, or has a distinctly more commanding personality, he may well take over the conference and reduce the rest to little more than passive obedience. The individual may himself be extremely useful, but he might as well be put to work solo, for he is neutralizing the rest.”

    http://www.technologyreview.com/view/531911/isaac-asimov-asks-how-do-people-get-new-ideas/

  61. tallbloke says:

    OB: Indeed. Lovely image too.

    Paul: Thanks for your responses. Indeed I am interested in mechanism, and not because wuwt told me to be. From the perspective of an engineer trying to unravel the climate mystery, I need to work out how much POWER of what TYPE is being transferred through Earth at which FREQUENCIES, apart from the various EM wavelengths which make up TSI.

    If, for example, we were to discover that the reason the Atmosphere co-rotates with the surface isn’t due to surface roughness at all, but due to the Earth, it’s atmosphere and magnetosphere being driven as a homopolar motor by the solar wind, and the orbital resonant energy shared between planets were modulating that, then that might lead to new insights on LOD variation, and thence to oceanic cycles. Solar affects wind patterns directly, which affects LOD, but it could be that planetary resonance, which is also in tune with solar variation, also contributes to LOD – a hitherto missing ‘solar amplification’.

    I aim to show that the elegant phi solutions you present are also related, in their application to planetary bodies, to Kepler’s third law, which has both gravity and magnetism and their falloff rates underlying it.

  62. wayne says:

    I would say this is about as close as you can get when trying to physically link all of the planets orbits to a relation with Phi. R² > 0.993, not a bad fit. Maybe you should look into this one ??

  63. oldbrew says:

    wayne: where did the y figures (top left) come from?

  64. wayne says:

    hi oldbrew,

    The Y? Well, from the planet’s periods right off of NASA’s new figures that you or TB gave in the previous article! The chart explains it all but here, follow this first working backwards:

    Jupiter’s y (ie, log(P)/log(Phi)) seems to be at about 8.1 off the chart. So in my nifty single line physics calculator:
    Phi=(5^.5+1)/2 LogPhi=log(Phi) MePer=0.2408467 y=8.1 JuPer=exp(y*LogPhi)*MePer gives Jupiter’s period as close as your eyes were able to extract that 8.1. It is actually 8.09827677 by the calculator which returns JuPer=11.862615.

    See, this time forward, P being the period, like Mercury’s period is MePer=0.2408467 so for any period P you just take log(P/MePer)/log(Phi) and that is the Y axis values for each. Quite simple.

    That is when I hit this relationship I thought you might find it quite amazing. I did.

  65. wayne says:

    Now you can take that same relation and by substitution extend for a chart for the semimajor axis for each. Titius and Bode’s law has a little problem with Neptune and Pluto falling in line and you can see the same in that chart but I feel Jackson’s ‘law’ seems a much tighter fit. Don’t you think? 😉

  66. oldbrew says:

    Looks very interesting, yes. The reason I asked about ‘y’ is that 1.6744 is very close to:
    J-S conjunction period divided by J orbit = 1.67467

    Pluto is very small and is a long way outside the main system so not bothered about that.
    The ‘??’ zone is where the asteroid belt lies.

  67. wayne says:

    Yeah, me too oldbrew, why log(Phi)? That is much like the work I have been doing recently on the hydrostatic properties of the thick tropospheres of other planets (or moons) along with ours, why the close, well nearly perfect, adherance to the degrees of freedom and the cv heat capacity of the composition of various gases found on each? Now’ve got two very curious mysteries but there are answers hiding somewhere in the math.

    The ‘??’ is where it appears there could have been a planet in proper natural position radially (I just picked a period of 4.45 to fill in). The asteroids seem to be more like 5.75 AU and that may be part of the reason they never could form a planet… it would not have fit that pattern you see in the chart (if that actually matters).

  68. oldbrew says:

    ‘The asteroids seem to be more like 5.75 AU’

    No, the main asteroid belt is between Mars (1.52 AU) and Jupiter (5.2 AU).
    The only ’round’ body in that zone is Ceres, easily the largest of the asteroids at around 2.77 AU

    http://en.wikipedia.org/wiki/Ceres_(dwarf_planet)

    Bode ‘predicted that the missing planet ought to have an orbit with a semi-major axis near 2.8 AU’ – Wiki

    ast belt

  69. wayne says:

    Sorry, oldbrew, I said AU and of course I meant the period of 5.75 as that plot is built upon. Just a slip.

  70. tallbloke says:

    Wayne, interesting work!
    Your P of 5.75 gives 3.2AU by Keplers 3rd law. Close to the median of Ma and Ju orbital SMAs (3.36AU)

  71. wayne says:

    Rog, I used 4.45 instead of 5.75 in that plot, just a guess but that gives a semi-major of 2.7 AU that surprisingly not too very far off from the 2.8 AU oldbrew looked up from Bode. The 5.75 period value came from a paper I had recently reread on continued fractions and ratios such as (n²+4)^(1/2)/2 (kind of Phi related) in relation to the planets and that 5.75 was still fresh in my mind. The paper said that 5.75 was the mean of the asteroids periods, I just accepted that as being close enough for a first jab.

    So far, I can’t seem to get any inkling as to *why* they line up as they do. However another way to solve that I gave oldbrew above is instead of:

    MePer = 0.2408467
    y = 8.1
    JuPer = exp(y × LogPhi) × MePer

    try an equivalent solution of that gives more insight:

    JuPer = MePer × Phi^y

    Now there is your Phi all alone and by itself! 😉 That log and exponent were obscuring the essence a bit.

  72. oldbrew says:

    wayne: Ceres is 2.77 AU so your ‘??’ on the graph is equivalent to that.

  73. Chaeremon says:

    @wayne (November 2, 2014 at 4:55 pm) it appears to me you have discovered the first gravitational (Keplerian) wave with this diagrammatic plot of observations. B.t.w. I understand the abscissa is not related to physical unit?

    Do you find the wave also for the jovian moons, that would also be quite amazing.

  74. oldbrew says:

    Looking at Jupiter-Saturn-Earth synodics:
    ((360 / J) x J-E) / ((360 / S) x S-E) = 2.61892

    55/21 = 2.61905 (99.995% match) and phi² = 2.6180339

    The ratio of S:J (orbits) is almost the same as the ratio of 55 S-E : 21 J-E (conjunctions).
    (55 and 21 being Fibonacci numbers)

  75. Paul Vaughan says:

    tallbloke (November 2, 2014 at 3:56 pm) wrote:
    “Indeed I am interested in mechanism, and not because wuwt told me to be.'”

    I should clarify. I’ve no objection to interest in mechanisms. My objection is to a corrupt wuwt thought-policing tactic: promotion of rejection of observations on the grounds that conventional wisdom isn’t yet able to model them.

  76. Paul Vaughan says:

    “(φ-Φ) / φΦ = 1 / 1 = 1”
    probably more recognizable (as a simple beat calculation) when inverted:
    φΦ / (φ-Φ) = 1 / 1 = 1

    also a clarification for anyone who might not know:
    Φ = 1 / φ = φ – 1

    also maybe not obvious to everyone:
    φ^0 = 1
    φ^2 = 1 + φ

    What is all of this saying when the algebraic relations are translated into plain English?

    quite simply:
    equal spacing

  77. Paul Vaughan says:

    wayne (November 2, 2014 at 4:55 pm),

    Try log base φ and offset to zero Jupiter’s residual rather than Mercury’s.
    This leaves a more informatively balanced pattern in the residuals.

  78. Paul Vaughan says:

    gives r^2 = 0.999541 with slope = 1 & intercept = 0 (i.e. tighter, simpler, & cleaner)

  79. oldbrew says:

    Equal spacing: the sunflower

  80. wayne says:

    Roger and oldbrew, you might also take a look into this one. When you look at just the central planets orbits four through eight, they all fit the same relationship (note added minus one) quite incredibly close, R² > 0.999668. Yes gents, there does seem to be some sort of tie to Phi and the orbits at least in the central ones but I really don’t have time to carry this much further. Take this a run with it further and maybe just a mention if deserved. A log/log releationship shows itself in many other natural processes so possibly you need to take a look in that corner of powers to Phi instead of only integer ratios.

    PS: Just noticed Paul Vaughan is now lookin into this, so great!

    [mod note] see correction to graph: Nov 7 @ 8:26 a.m.

  81. oldbrew says:

    Thanks Wayne. We already have links to Fibonacci/Phi in the other planets with the Venus:Earth (13:8) and Neptune:Pluto (3:2) orbit ratios, and Mercury’s own 3:2 spin:orbit ratio.

    Venus rotation:Earth orbit is also very near 3:2 (99.8% match).

  82. oldbrew says:

    J-S / S-E = 19.190628 = average number of S-E conjunctions in one J-S conjunction period
    19.190628 / J orbit = 1.61774 (no. of S-E per year needed to fit 19.19~~ of them into a J orbit)
    55 / 34 = 1.617647
    (phi = 1.6180339)

    ***
    vukcevic said: ‘JSc/(S/J) = 7.99999 or as near as you can get JSc/(S/J) = 8’

    J-S minus J = 8 as well (8.0024)
    J-S x 60/149 = 7.999343
    60 S = 149 J (almost)

  83. Ulric Lyons says:

    Tackling it backwards, 4627 divided by phi, gives 144 J/S synods, divide that by 9 = 317.73814 years, which plugs very tightly into Uranus.

  84. Me_Again says: October 29, 2014 at 9:10 pm

    “Where did the 34 come from?”

    Now I am at the same place! When I had questions like these lately in this thread, I would find a mathematician, who would carefully listen, then reply, “Hey, can you fix my computer?”.
    These folk are weird, but never stupid. If this is to be fair, we both gain!

  85. oldbrew says:

    Ulric: yes I know what you mean e.g. 144/9 = 16 J-S so have a 7:16:23 ratio of S-U:J-S:J-U.

    There’s physical evidence of a 317 year effect described here as you know:

    ‘The Hudson Bay “staircase”, a typical series of 184 successively uplifted strandlines, situated in Richmond Gulf on the eastern side of Hudson Bay, Canada. The sand gravel beaches are preserved by permafrost, and recur with great regularity about every 45 years, representing the cycle of storminess. There are longer cycles of 111 years and 317 years evident in the beaches, which are linked with planetary cycles.’

    http://www.mitosyfraudes.org/Calen2/Rhodes.html

  86. oldbrew says:

    Will J: re. “Where did the 34 come from?”

    Another example in nature: ‘The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.’

    http://memolition.com/2014/07/17/examples-of-the-golden-ratio-you-can-find-in-nature/

  87. tallbloke says:

    Paul V: ” My objection is to a corrupt wuwt thought-policing tactic: promotion of rejection of observations on the grounds that conventional wisdom isn’t yet able to model them.”

    With you on that one.

  88. oldbrew says: November 3, 2014 at 11:01 pm

    (Will J: re. “Where did the 34 come from?”)

    “Another example in nature: ‘The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.’”

    That was the “Me_Again: October 29, 2014 at 9:10 pm” question that I tried to answer!
    Do any of you have an explanation of just what you are “now” considering with the Fibs and the Phi?

  89. oldbrew says:

    Will J: ‘Do any of you have an explanation of just what you are “now” considering with the Fibs and the Phi?’

    Paul Vaughan said ‘equal spacing’.

    Look at the Kirkwood gaps graphic above (October 31, 2014 at 8:52 am).
    A stable system can’t survive exact resonances e.g. precise 2:1, 3:1 etc. orbit ratios for example.
    That’s why there are no asteroids in those zones – Jupiter resonance prevented it.

    Phi /Fibonacci avoids such clashes – that’s almost certainly why it appears in nature too, e.g. the flower petals don’t want to overlap and block each other’s sunlight (see comment at November 3, 2014 at 3:51 pm).

  90. Paul Vaughan says:

    log_φ de Vries ~= solar cycle length
    log_φ 208 ~= 11.09

    _ indicates base

    This wasn’t something I went looking for.
    It simply fell out of the simplest solar system attractor summary I’ve found so far in the few minutes I’ve had to think about this since yesterday. 11.09 defines the attractor’s core and 208 defines its outer boundary.

  91. Paul Vaughan says:

    Allowing planet mass to weight how much say each planet has in the summary, these are the more precise values I get based on Seidelmann (1992):
    11.09761278
    208.5757944

  92. Paul Vaughan says:

    The challenge here is interpreting 0.097612775, which measures how far the empirical mass-weighted φ attractor (based on Seidelmann (1992)) is from perfect whole numbers. Some might be quick to suspect it’s due to lower Fibonacci ratios not yet being converged to φ, but a simple preliminary diagnostic suggests this might have something to do with sun orientation parameters (including differential rotation) perceived from a geocentric reference frame. I’ll need to do more diagnostics before commenting further.

  93. oldbrew says:

    11.09 is also phi² x phi³ (11.09017)

    The de Vries cycle looks like 1/12th of 126 Jupiter-Saturn conjunctions which are a multiple of 360 degrees of movement, making de Vries correspond to ~30 degrees.

    126 J-S = 2503y (~85 Saturn and ~211 Jupiter)
    126 / 6 = 21
    21 J-S = 382 Jupiter-Saturn = 403 Saturn-Earth
    Half of 21 J-S is 1/12th of 2503 = 208.583y

  94. wayne says:

    Paul, where does ‘de Vries’ come from? I find many ‘de Vries’ but none having to do with orbits or astronomy. A paper, a book? Is that a man’s name? The 208, is that related to Jupiter and Saturns orbits? So many terms are tossed about in these threads with no explanation it becomes hard, nearly impossible to follow. Commenters wanting to understand have limited time and soon give up.

    But the 11.09.., that is curious. Way back when I first happened upon the wuwt site I was deeply involved in gravity and ss simulation integrators and I took the time to go way back to get as close as I could to a mean solar cycle length and IIRC it was about about 11.07xx but I still have not seen any concrete evidence of the physical mechanism that would force the orbits into such a releationship for any solar system. If it is real and not a fluke it must also be evident in all solar systems.

  95. wayne says:

    Is Seidelmann 1992 available online somewhere? Now there I find many references.

    [reply] ‘Reference data’ link in post above uses Seidelmann. PV has confirmed that

  96. Paul Vaughan says:

    I bet OB will be quick to point out the 0.097612775 residual’s 5:2 ratio with Mercury.

    My interest is in patterns regardless of how they arise. My patience has expired with people who for political reasons are absolutely viciously determined that we should never look at observations that cannot yet be modeled by humans.

    When I worked as a botanist cataloging natural patterns I never experienced so much relentless harassment from people for simply recording an observation of pattern. There were no political agents trying to persuade me to stop looking at and thinking about branching patterns on trees.

    People who want to work out the structure of tree DNA can do so without harassing people cataloging tree branching patterns. They don’t need to be policing the internet saying “Don’t you dare report empirical summaries of tree branching patterns in public until you’ve proven how they arise from DNA.”

    It’s ridiculous.

    I respect people working on mechanisms (so long as they’re not political thought-policing agents) and I insist that they respect people peacefully exploring patterns (including in public).

    Wayne:

    Seidelmann (1992):
    http://ssd.jpl.nasa.gov/?planet_phys_par

  97. Paul Vaughan says:

    The core of this attractor perfectly balances J+N & JEV. The coherence of J+N & JEV is tight, tight, tight and the precession of JEV relative to J has a cycle period of N, so this should hardly come as any surprise (although it may come as a surprise to people who’ve allowed themselves to be persuaded to ever so submissively close their weak & gentle eyes and don’t dare ever even think to look…)

  98. Paul Vaughan says:

    oldbrew (November 4, 2014 at 4:28 pm) noticed:
    “11.09 is also phi² x phi³ (11.09017)”

    φ^5 = 11.09016994 (207.8301)

    I do hope everyone knew this before you pointed it out. There’s some pretty simple geometry at play.

  99. Paul Vaughan says:

    Just to clarify for those who may be feeling a little dopey with the math:

    We’re talking here about an empirical estimate (based on Seidelmann (1992)) that’s precise to within 0.0007 = 0.07% = 2.7 solar days over the course of 1 JEV cycle = 1 J+N cycle = 1 solar cycle.

    The thought police demand that you look away and never think about this again.

  100. oldbrew says:

    Don’t get too paranoid – even if they are out to get you 😉

    Just kidding there – in truth we know it’s all a big-time propaganda game on one level.

  101. wayne says:

    Thank you oldbrew… found the O.M. Raspopov paper just fine and thanks Paul for the data and I see now, he seems to be the authority on the accurate periods. Wish his book was available… no, wish all library books were available online without spending the time and gas and lack of coffee to make a trip to the library necessary. 😦

  102. oldbrew says:

    Raspopov paper: ‘The authors of this publication are on ResearchGate and have made the full-text available on their profiles’…’Sign up for a free account to access the full-text version from them.’

    http://www.researchgate.net/publication/222417762_The_influence_of_the_de_Vries_(200-year)_solar_cycle_on_climate_variations_Results_from_the_Central_Asian_Mountains_and_their_global_link

  103. Ulric Lyons says:

    The root of de Vries is from the J-S-U quadrature series of 69.0597 sidereal years, with every third event modulated by Neptune at 207.179 yrs. As with the 179 yr return, it is a local cycle and cannot be repeated more than a step without falling out of sync. The only repeatable long cycles are at 317.6745 yrs (J-S-U), and the solar (grand) minima cycle with an average of 110.7 yrs. Which is why those two series are most apparent in the Hudson Staircase.

  104. wayne says:

    Then you also have this very real relationship for the inner planets in our solar system:

    Beta is right at 0.636 but I wouldn’t so quickly assume this to be a rough estimate to the silver ratio just because it is somewhat close. I need to look into what that value is. Sure fits tight!

    Everyone needs to put some effort into marrying those two relations or a reason why they each separately exist, each being very tight fit in themselves. That sure would drag this fib search into a more mathematical aspect of science.

    Wait, just found one possibility, β of 0.636 is so very close to √Φ/2. Now why? Why do these exist, are they physical of some grand coincidence and are these relationships found in other solar systems? These beg for some answers, mathematical equations this time.

  105. oldbrew says:

    ‘β of 0.636 is so very close to √Φ/2. Now why?’

    Earth:Venus orbit ratio is 1:1.6255 approx., so already close to 1:phi.
    Mercury:Venus is 0.3915:1, and 1 / 0.382 is phi².
    1.6255 / 0.3915 is just short of phi³ (about 98%).

  106. Paul Vaughan says:

    Wayne, thanks for sharing.
    Here I listed Tim Channon & Ray Tomes links on de Vries (208 years):
    https://tallbloke.wordpress.com/2013/07/28/cameron-and-schussler-no-evidence-for-planetary-influence-on-solar-activity/comment-page-1/#comment-56363
    On some fronts progress is going fast.
    Some of the stuff we discussed on that thread has solidified without modification and other stuff has since been quickly corrected and revised. We can’t be stagnant like the mainstream. We need to cover new territory rapidly and self-correct. That’s why I believe in operations on the Pareto Principle. 80% bang for 20% buck…. and on the corollary, never mind the remaining 20% bang that costs 80% of time/effort — just rough it out and let paid people with more time finish it on the taxpayer’s dime — they’ll never get there efficiently without our help because their managers won’t let them.

  107. Paul Vaughan says:

    Anecdote: The model I developed has high r^2 but it has a single large residual that gives a mystery schooling: It predicts Neptune should have de Vries period. How many sleeps before the subconscious awakens the conscious mind to a sharp interpretation of this?….

  108. Paul Vaughan says:

    OB: Thanks for getting this thread going. I find it a refreshing change from some of the tedious work I’m doing to animate decadal (~9.07 year) climate cycles. I don’t take this stuff as seriously, but it opens my mind and sparks new ideas on how to shake down the barriers to clearer awareness. I’m now inclined to drop the decadal climate cycle animations altogether and move on to new territory. (There isn’t time for everything, so something has to get dropped….)

  109. Paul Vaughan says: November 5, 2014 at 6:39 am

    OB: Thanks for getting this thread going. I find it a refreshing change from some of the tedious work I’m doing to animate decadal (~9.07 year) climate cycles. I don’t take this stuff as seriously, but it opens my mind and sparks new ideas on how to shake down the barriers to clearer awareness. I’m now inclined to drop the decadal climate cycle animations altogether and move on to new territory. (There isn’t time for everything, so something has to get dropped….)

    Indeed, drop the Scienteriffic, and engage, the Irish potato guy, that has a wee bit of knowledge of what is. The Academics have only a fantasy of what may be!

  110. oldbrew says:

    PV: thanks for contributing to the discussion. Re Neptune, Ulric Lyons said:

    ‘The root of de Vries is from the J-S-U quadrature series of 69.0597 sidereal years, with every third event modulated by Neptune at 207.179 yrs’

  111. Paul Vaughan says:

    Ilya Usoskin (October 30, 2014 at 3:49 pm) on TSI reconstructions
    excerpt: “[…] centennial variability cannot be in any way controlled since the “training” period is too short for that.”

  112. oldbrew says:

    Paper: ‘Exoplanet predictions based on the generalized Titius–Bode relation’

    Abstract: ‘We evaluate the extent to which newly detected exoplanetary systems containing at least four planets adhere to a generalized Titius–Bode (TB) relation. We find that the majority of exoplanet systems in our sample adhere to the TB relation to a greater extent than the Solar system does‘ [bold added]

    http://mnras.oxfordjournals.org/content/435/2/1126

    Quote: ‘The approximately even logarithmic spacing between the planets of our Solar System mo-
    tivated the Titius-Bode (TB) relation, which played an important role in the discovery of the
    Asteroid Belt and Neptune, although Neptune was not as accurately represented by the TB
    relation as the other planets’

  113. Paul Vaughan says:

    “Uranus could have been discovered earlier if the TB relation had been taken more seriously […]”

  114. oldbrew says:

    Or was that Neptune?

    http://en.wikipedia.org/wiki/Discovery_of_Neptune

    Galileo spotted it in 1612 and 1613 but didn’t investigate further, as far as we know.

    ‘Galileo, in one of his notebooks, noted the movement of a background star (Neptune) on January 28 and a dot (in Neptune’s position) drawn in a different ink suggests that he found it on an earlier sketch, drawn on the night of January 6, suggesting a systematic search among his earlier observations. However, so far there is neither clear evidence that he identified this moving object as a planet, nor that he published these observations of it. There is no evidence that he ever attempted to observe it again’

  115. Paul Vaughan says:

    “The physical mechanisms underlying these empirical observations are not fully understood.”
    http://www.mso.anu.edu.au/~charley/papers/BovairdLineweaver2013.pdf

    I still don’t get why people think a physical mechanism is needed to explain a geometric identity. The mechanisms don’t matter to the geometry. It seems to me that people somehow don’t (?) or aren’t able (?) to realize this (??).

    This is not a complaint. It’s a philosophical musing to help emphasize that we don’t all share a common perspective. There must be something fundamentally different about how we’re looking at this from our differing (perhaps even alienated) perspectives.

    That itself is interesting and further adds (quite substantially) to the intrigue. It leaves me wondering things like “what is it that’s not being understood about the geometric identity?” and “how could it be any other way??”

    I’m confident that it would demand a thoroughly unworkable amount of communication to even just identify the root of the differences (if possible at all), so I’m sure it will be left a mystery for awhile, perhaps a long while.

    Perhaps it will take a lot more discussions to resolve this.

  116. wayne says:

    I need to correct the Y axis’s description in that plot of Mars to Uranus, sorry.

    I hit a small problem reproducing it myself. The Y axis should have said log(Period / MePeriod – 1) / log(Phi) and this reproduces the 4, 6, 8, 10 & 12 indexes for the planets. Of course, you can also divide by two and add two to get the more familiar 4,5,6,7,8 for the planet indexes. (MePeriod being Mercury’s actual period scaled to Earth as 1.0)

    So to get the actual period of a planet’s index (N) of 4 through 8, it is this equation:
    MePeriod·(1+Phi^(N·2-2)).

    As you can see this relation really wants the planets to have indexes of 4, 6, 8, 10, 12 and that equation then doesn’t need shifts and scaling to let you use this:
    MePeriod·(1+Phi^N).

    Why this works out the way it does I still have absolutely no answer except to say they are definitely in a scaled and offset power of Phi relationship. With Mercury to Earth plotting (http://i61.tinypic.com/2zf75ap.png) by a completely different relation this brings a more complicated set when looking at all eight or nine bodies so no wonder this simple search for fibonacci ratios has been a bit trying.

    Anyone with even a guess yet?

  117. oldbrew says:

    wayne: have a look at this re Kepler’s third law, see how/if your results relate to it.

    ‘The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi-major axes’ [scroll down for graph]

    [credit: Tim Cullen – see Blogroll]

  118. Ulric Lyons says:

    Well I am impressed, as it does seem that the periodic tendencies of the inner three (~317.7yr) and outer three (4627/3yr) gas giants are resolved at phi proportion, very closely indeed.

    Exploring the synodic period numbers (7-16-23) of the JSU ~317.7yr cycle is revealing.
    16*phi is resolved to a whole number by *9 = 233.
    That shows where the *9 arises.

    And 23*7*2 = 322, which is on the powers of phi series:
    7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843 etc.

    There are 322 J-U synods at ~4448 years:

    Synods in ~ 4627 & 4448 years

    62599.9383 27 26
    16568.7035 102 98
    13101.1445 129 124
    7253.4549 233 224
    5044.8973 335 322
    4668.6530 362 348

    Adding, subtracting or multiplying say 322 with any closer Fibonacci number gives Fibonacci number (or multiple of) results rather than a powers of phi series number result. With one exception, repeatedly subtracting 233 from 322 gives, 89, -144, -377, -610, -843 (powers of phi n), -1076, -1309, and -1542, 1542*3 = 4626.

  119. Ulric Lyons says:

    -1309

  120. Ulric Lyons says:

    Also, starting on the inverse of the sq/rt of 5 = 0.44721359549995793928183473374626
    multiplied by powers of phi, stays centered on the Fibonacci number series.

  121. oldbrew says:

    Ulric: re ’16*phi is resolved to a whole number by *9 = 233′

    16 x 9 = 144 i.e. the Fibonacci number before 233 in the sequence.

  122. wayne says:

    oldbrew, of course that plot above is perfect, that is just Kepler’s third semimajor-axis-to-period law so I fail to get your point of bringing that subject up in relation to what I was showing also above. Now the question, is there one coherent equation with Φ embedded that also fits them all, or at least some large segment, as to why the period or likewise the semi-major length is what it is?

  123. oldbrew says:

    Just trying to stir the thought processes. Keep working the data and see what turns up.

  124. I think GOD gave earthlings the concept of mathematics, only to prevent complaints of what is!
    For earthlings, each “must” be related to every other. What colossal nonsense!

  125. wayne says:

    oldbrew, sorry, I’m just a bit shell shocked right now… used to be shot at.

    I see now that it was not the plot at the bottom but instead the periods and sma’s data you were presenting. I’ll take a look at that expanded view soon. Need to slow back down now. Any chance you have that grid of data or a link in text and not as a picture?

  126. oldbrew says:

    Sorry no, it’s straight from Tim Culllen’s Malagabay blog.

    Inner 3 planets are close to 0.236, 0.618, 1 (orbit) = steps on the phi sequence.
    Mars is always the awkward one probably due to the asteroid belt.

    If we compare the outer planets to 165 years (55 x 3) this is roughly true:
    (J+S) x 4 = 165
    U x 2 = 168
    N = 165
    P x 3/2 = 165

    Some sort of pattern there? Also Uranus is near 1:3 with Saturn and 2:1 with Neptune, a balancing act. J:S is 5:2 and N:P is 2:3.

  127. Paul Vaughan says:

    Wayne, the spacing of rocky versus gaseous planets in our system clearly differs. The parameter n in the Titius-Bode law & the more generalized Dermott’s law needs to be replaced with a superior parameter that acknowledges that due to stronger interactions of neighboring massive planets, not all geometrically permissible orbits are physically stable. It should also be recognized that the outermost large planet has unique (physical & geometric) boundary conditions. (It doesn’t have a massive planet neighboring on its outside.) I suspect this is why Neptune orbits halfway between whole number spacings. The pattern of exceptions in our solar system suggests that combined J & N sweeping (harmonic mean) has constrained the orbits of E & V such that JEV = J+N. Thus N ≠ φ^(φ^5) = 208 years but rather N ~= φ^((φ^5)-0.5) ~= 165 years.

    Regards

  128. wayne says:

    Paul, interesting thought. You are right, the rocky planets do clearly fall under some other relationship or that is what those two plots seems to indicate. I was surprised that you can find a relationship between the three of Me, Ve, Ea and have Φ embedded in the equation and also for the next outer four plus the missing gap near the asteroids also have Φ within yet another equation. I really didn’t think that was even possible when I started toying with the idea queued by these posts.

  129. Paul Vaughan says:

    Φ = 1 / φ

    Wayne, OB linked to a paper that does a good job drawing attention to the role of neighboring mass in determining orbit stability:
    http://www.mso.anu.edu.au/~charley/papers/BovairdLineweaver2013.pdf

    Our rocky planets are far less massive and so are free to occupy all of the geometrically permissible orbits. Our gaseous planets are more massive and so necessary more sparse or else they would interact too energetically for stability.

    OB: Thanks for that link. That paper is quite a useful introduction, including the 2 concise appendices (on TB vs. Dermott models and dynamical spacing).

    Wayne: I tabulated the HL Tauri gap spacing on a newer Talkshop thread if you want to have a quick go at that. 2 or maybe 3 of the inner gaps are evenly spaced on a log-scale, but everything else is evenly spaced without log, so interpreting those data is an interesting challenge, particularly given that it may be a mixture of real signal + methodological immaturity. It has me wondering if inner planets generally form before outer planets. Someone around here will probably know and quickly point to some background materials to help speed up the efficient crossing of complementary disciplines.

    Regards

  130. Ulric Lyons says:

    P.V.
    “The pattern of exceptions in our solar system suggests that combined J & N sweeping (harmonic mean) has constrained the orbits of E & V such that JEV = J+N.”

    There is a small difference, the inverse of half of 4627 provides the ratio fairly well:
    ((1/ (4627/2)) +1) * 4041.658045 (JN axial period) = 4043.405034

    Not that I can see that the JN axial period matters in any way physically.

  131. wayne says:

    Thanks Paul, got a copy now. That paper seems quite interesting. Going to take a while to look at it in detail but I see the gist, minimize the chi²/dof and have already tried to compute that on the relation found here but can’t seem to place all of the variables needed yet. I’ll move to the newer thread… I assume you mean the HL Tauri thread. PSB News Hour just had a segment on that new discovery!

  132. Ulric Lyons says:

    oldbrew wrote:
    “So the final figures are:
    12240 J-S (34 x 360) = 20497 J = 8257 S = 243148 years (89 x 2732)”

    It doesn’t compute, 12240 J-S is 20491.74 J, and 8251.219 S, and 243068.424 years.

  133. Paul Vaughan says:

    Ulric Lyons (November 8, 2014 at 10:37 pm) wrote:
    “There is a small difference, the inverse of half of 4627 provides the ratio fairly well:
    ((1/ (4627/2)) +1) * 4041.658045 (JN axial period) = 4043.405034”

    Do you really think their measurement accuracy is that good?? Who has time for this?

    Ulric Lyons (November 8, 2014 at 10:37 pm) wrote:
    “Not that I can see that the JN axial period matters in any way physically.”

    It defines the aliasing period for the inner planets over the much longer term. Remember the inclination of the orbits. It’s the exact same reason why the lunar nodal cycle of 18.6 years aliases to 6.4 years. Check DE430 and you’ll see. The beat of JEV with J is indistinguishable from N.

    This thread is degenerating into wuwt-style discordant nitpicking, so I’m moving on….

    Cheers for now …..

  134. Ulric Lyons says:

    “Do you really think their measurement accuracy is that good??”

    Good enough to show a few days difference between the periods yes. The JN and EV synods (which is what matters) precess very slowly through the 4627yr cycle.

    “It [JN axial period ] defines the aliasing period for the inner planets over the much longer term.”

    Synodic (and half synodic) periods do the defining, axial periods cannot physically define anything.

    “Remember the inclination of the orbits. It’s the exact same reason why the lunar nodal cycle of 18.6 years aliases to 6.4 years. Check DE430 and you’ll see. The beat of JEV with J is indistinguishable from N.”

    18.6 years aliases to 6.4 years? how?
    And why do the beat of JEV with J? Especially when 14 J is so close to 15 JEV at 60656.246 days.

  135. Paul Vaughan says:

    Ulric Lyons (November 9, 2014 at 1:33 pm) falsely suggested:
    “[…] axial periods cannot physically define anything.”

    That’s a strictly false statement.

    The difference between J & J+N is -0.5 on a log φ scale. This is a factor of 1/√(φ). The axial period defines the differential geometry that limits the physics. The fastest & slowest gas giants together set the boundary conditions because they are located at the boundaries.

    I suspect these facts will appear vacuous to those not taking time to appreciate the spiral topology. Take an infinitely elastic string, hook it to all the planets, and consider the rate at which it stretches by whole circles. That rate is defined by axial periods.

  136. Paul Vaughan says:

    Ulric Lyons (November 9, 2014 at 1:33 pm)
    “18.6 years aliases to 6.4 years? how?”

    It’s a fact that it does. Sample NASA Horizons output annually and you’ll see clearly. If it appears mysterious, there’s an important aspect of the geometry you’re overlooking.

    I advise more humility and willingness to appreciate and learn from others.

  137. Ulric Lyons says:

    “The difference between J & J+N is -0.5 on a log φ scale. This is a factor of 1/√(φ).”

    Really? show your calculations then.

    “The axial period defines the differential geometry that limits the physics.”

    Shame it doesn’t fit any dominant periodicity then, especially 4627yrs.

  138. oldbrew says:

    Ulric: it appears your data is not based on the latest orbital periods from NASA / Seidelmann. If you use the old data it won’t exactly match the figures in the post. Note also:NASA’s planetary fact sheets are out of date.

    See ‘reference data’ link at the end of the post.

  139. Ulric Lyons says:

    oldbrew, with those orbital figures your calc’s would indeed be correct. But with those figures, there would be no clear inferior conjunction of all four bodies every 4627yrs or JSU at ~317.7yrs.
    Using those figures for the U-S synod (16559.49d), *7 is only 317.365 years. If I do seven steps at that interval from the grand inferior conjunction of all four in 1306, it looks like this:

    Clearly something is amiss with those values as JSU should be in much closer alignment.

  140. wayne says:

    Paul Vaughan, I’ve gotten myself spread a bit too thin but I’ll return to those above relations in a month or so. If you or anyone else here can expand on those, do so, I do not hold any claim on their existance. Open to all.

    I’ll poke my head in every now and then.

  141. Paul Vaughan says:

    wayne (November 10, 2014 at 9:53 pm) acknowledged:
    “I’ve gotten myself spread a bit too thin […]”

    Likewise. We’ll resume discussion at some point, but definitely responsibilities are forcing my primary focus elsewhere right now. I appreciate your contributions and look forward to more. Thank you.

    OB: Seidelmann (1992) is my top pick, but I always do sensitivity analyses. You can trust that I won’t be mistaking someone’s favorite orrery for the real world.

    Regards

  142. Ulric Lyons says:

    Paul, I can trust you to be disparaging without even checking the figures. Which with the values that olbrew is using, that the discrepancy is very much as the orrery image displays. The resultant U-S synod is too short, and the U-J and S-J synods work out too long.
    Assuming that they are referring tropical years and not sidereal, with those figures;

    49 S-U synods = 811415.01d
    112 S-J synods = 812621.5328d
    161 U-J synods = 812253.9516d

    Over that range, the 49 S-U ends up around 700d too short, and the 112 S-J around 500d too long.

  143. Paul Vaughan says:

    Some ephemeris defines this orrery model Ulric misrepresents as observation.

  144. Ulric Lyons says:

    This one agrees with TheSky too, including inner planet positions.
    http://www.fourmilab.ch/cgi-bin/Solar
    For U-S, go from 18 April 1307, to 23 Nov 3528, which is +811415 days using your preferred orbit figures.

  145. Ulric Lyons says:

    Most astronomers quote the Saturn sidereal orbit period as 10759.22 days.

    From oldbrew’s reference, that Saturn orbital period also results in an Earth-Saturn synodic period that is visibly too long when animated over a few centuries on my professional astronomy application, by a couple of days.

  146. Ulric Lyons says:

    Notes:
    This table contains mean orbit solutions from a 250 yr. least squares fit of the DE 200 planetary
    ephemeris to a Keplerian orbit where each element is allowed to vary linearly with time. This solution fits the terrestrial planet orbits to ~25″ or better, but achieves only ~600″ for Saturn. Elements are
    referenced to mean ecliptic and equinox of J2000 at the J2000 epoch (2451545.0 JD).
    Reference:
    Explanatory Supplement to the Astronomical Almanac. 1992. K. P. Seidelmann, Ed.,
    p.316 (Table 5.8.1), University Science Books, Mill Valley, California.
    http://www.aero.polimi.it/~lavagna/bacheca/planet_orbital.pdf

    Paul Vaughan says:
    November 11, 2014 at 4:45 pm

    “Some ephemeris defines this orrery model Ulric misrepresents as observation.”

    On the contrary, the model misrepresents the observations.

  147. Paul Vaughan says:

    models = all that’s available (whether NASA, Ulric’s favorite orrery, or whatever)

    So again: The only sensible option is to do sensitivity analysis.

  148. Paul Vaughan says:

    Ulric:
    To the highest possible precision, list the periods you endorse.
    Indicate the source ephemeris with a link.

    The perspective you approve can be included in sensitivity analyses if you do this.

  149. tallbloke says:

    Paul and Ulric: Saturns orbital period likely varies slightly as its eccentricity will be affected by other gas giants. Kepler isn’t perfect. So I suggest, we treat all models with a pinch of salt and each others ideas with respect and consideration. I’m on a patchy inet connection here so I can’t moderate discussion.

  150. oldbrew says:

    @ Ulric: ‘But with those figures, there would be no clear inferior conjunction of all four bodies every 4627yrs or JSU at ~317.7yrs.’

    Re 4627y: that’s probably true, but I didn’t claim there was. Is there any physical evidence re 4627?

    Radiocarbon dating points to a long period of around 2400 years – in fact 2403 matches various orbital data of the giant planets very well.

    https://tallbloke.wordpress.com/2014/03/24/s-s-vasiliev-and-v-a-dergachev-2400-year-cycle-in-atmospheric-radiocarbon-concentration/

    How long is Saturn’s orbit…

    http://coolcosmos.ipac.caltech.edu/ask/122-How-long-does-it-take-Saturn-to-go-around-the-Sun-

    or: http://solarsystem.nasa.gov/planets/profile.cfm?Object=Saturn&Display=Facts

    I agree it’s confusing that NASA’s own ‘factsheets’ don’t tally with the above NASA link. Something needs to be done about it.

  151. oldbrew says:

    Ulric: ‘Clearly something is amiss with those values as JSU should be in much closer alignment.’

    The alignment is there: it’s at 63 S-U which is 34 Uranus and 97 Saturn – check it out (97 – 34 = 63). That’s about 2856.32 years (34 x 21 x 4 plus bits).
    63 = 7 x 9 so there are your blocks of seven S-U.
    Every 3 S-U is a shade over 4 x 34 years (less than six days). 3 S-U x 21 = 63.

    144 J-S is 2860.56y so it’s slightly out of step, but 4 years in 2860 is still a very close match. Some cycles will match better than others I guess.

    PS I seem to be pre-empting my next Why Phi post here 😉

  152. Ulric Lyons says:

    OB
    “The alignment is there”

    No it’s not lol, it’s over 1000 days adrift with the J-U synods too, that’s about 80° out of alignment.

    “Is there any physical evidence re 4627?”

    It’s pretty close if you use more accurate orbital figures, especially the Saturn orbital period.

    “144 J-S is 2860.56y so it’s slightly out of step..”

    There’s much less error if you use the improved orbital figure for Saturn.

  153. oldbrew says:

    You misunderstand me. I mean the alignment is there using the NASA data I referred to.

    If you disagree that the data is valid that’s another discussion. It was last updated by NASA on 6th Nov. 2014 (at time of writing this) so it’s not out-of-date.

    I’ve e-mailed the NASA webmaster about this so let’s see what happens there. We can’t progress with two versions of the ‘facts’.

  154. Ulric Lyons says:

    OB, I don’t misunderstand you in the slightest, using that very data, the J-S synods are 1042 days adrift. So there’s no alignment of all three at 63 U-S synods using those figures.

  155. oldbrew says:

    Ah, I see what you meant – but I did say there was a bit of a mismatch. I’ve just added to that comment above: ‘e-mailed the NASA webmaster’.

    It’s not our fault there are two versions of the data.

  156. oldbrew says:

    UL: ‘It’s pretty close if you use more accurate orbital figures, especially the Saturn orbital period.’

    By ‘physical evidence’ I meant radiocarbon data, spectral analysis, varves etc.

  157. Ulric Lyons says:

    The dominant periodicity in GISP is at ~4627 years. See e.g. 6100 & 1470 BC, 5200 & 570 BC, 4250 BC & 680 AD. and 3000 BC to 1630 AD. Also the cool period in Greenland ~2700-2400 BC is the perfect analogue for the recent centuries, which was a very warm period in the temperate zone. The big spike in GISP at ~1350-1150 BC was a very cold period in the temperate zone, which caused the demise of the Minoan civilisation, as well as many others.

    Similar strings of ~4627yr events can be seen here, including the analogue for the recent warm period, the Eddy Maximum 12 of 2720-2610 BC:
    http://www.geo.arizona.edu/palynology/geos462/holobib.html

  158. Ulric Lyons says:

    I should also mention that 1250 AD onwards on the GISP graph above is highly suspect. Firstly I cannot believe that Greenland kept within less than 0.5°C range through all those centuries, and secondly, the cold solar minima of the LIA should have created warmer spikes in the GISP record.

  159. Ulric Lyons says:

    Sorry typo.. 1250 AD onwards.

  160. oldbrew says:

    OK. Looking at the two datasets the difference between 233 Jupiter-Saturn and 27 Uranus-Neptune conjunctions is negligible: around 0.4y on one and 0.6y on the other. One returns 4627y and the other 4628y, so one year in 4628 isn’t going to make a startling difference to these types of analysis.

  161. Ulric Lyons says:

    With your choice of figures, 233 J-S is 4628.37y, and 102 S-U is only 4624.33y. OK much?

  162. oldbrew says:

    Less than 1 in 1000 difference for S-U, and U-N and J-S are the main players here.
    Plus conjunction periods vary within a small range due to elliptical orbits.

    Let’s see if we get a response from NASA, or we’re just going to be playing ping-pong with stats.

  163. Ulric Lyons says:

    “..so one year in 4628 isn’t going to make a startling difference to these types of analysis.”

    Your 12240 J-S to 8257 S is around 155yrs adrift.

  164. oldbrew says:

    Adrift of what? Whichever data you use the figures will drift apart on those sort of timescales.

    I accept that different data gives different results. The problem is that both sets of data essentially are from the same source i.e. NASA, which is why I’ve asked them to sort it out – if possible.

  165. oldbrew says: November 13, 2014 at 1:58 pm

    “Adrift of what? Whichever data you use the figures will drift apart on those sort of timescales.
    I accept that different data gives different results. The problem is that both sets of data essentially are from the same source i.e. NASA, which is why I’ve asked them to sort it out – if possible.”

    What part of NASA? If Goddard, response is “Cannot you read” then treat you as your asking a question on WUWT! JPL does good work! Do the measure-ers have any clue to what is measured?

  166. Paul Vaughan says:

    Ulric: I’m willing to explore your preferred periods but please cleanly tabulate them. There’s nothing else you can do or say that will speed up others’ consideration of your perspective more. I have time to consider your cleanly tabulated perspective, but I decisively do not have time and patience for protracted arguments that poison what is an otherwise a cordial Talkshop atmosphere.

    OB, have you read the article to which I linked here?
    https://tallbloke.wordpress.com/2014/10/23/evidence-of-correlation-lod-and-solar-magnetic-cycles/comment-page-1/#comment-91293

    It addresses mean orbital period uncertainty with insightful commentary on individual planets. If I were the NASA webmaster receiving your e-mail, that’s a link I’d supply in response.

    Regards

  167. Ulric Lyons says:

    OB: “Adrift of what?”

    Of that using the better Saturn orbital value. As I said here:
    https://tallbloke.wordpress.com/2014/10/29/why-phi-giant-planets-update-part-2/comment-page-1/#comment-92296

  168. Paul Vaughan says:

    TB: Here’s a recent (Oct. 4, 2014) article on Saturn orbital element uncertainty:
    http://arxiv.org/pdf/1410.1067.pdf

    selected quote:

    “The orbits of the inner planets are accurately tied together with current data, but the outer
    planets are not as well tied to the inner planets or each other.”

  169. oldbrew says:

    UL: ‘Better’ is a point of view in this context. NASA – Seidelmann and Wikipedia don’t agree with you. I’ll have a new post in a few days.

  170. Ulric Lyons says:

    The Seidelmann notes discuss how there are large errors with the Saturn value, did you not read it?
    https://tallbloke.wordpress.com/2014/10/29/why-phi-giant-planets-update-part-2/comment-page-1/#comment-92498

  171. Ulric Lyons says:

    Saturn orbit, 10759.22 days: http://en.wikipedia.org/wiki/Saturn

  172. Paul Vaughan says:

    Look at the kind of trouble they have to go to sorting this stuff out:
    http://www.planetary-science.com/content/pdf/s13535-014-0002-5.pdf

  173. Paul Vaughan says:

    That last link was on earth-moon light & tides.

    [extra-galactic reference frame]

    Another example of the trouble they have to go to linking different reference frames
    (in this case terrestrial & celestial):

    Earth’s Rotation: A Challenging Problem in Mathematics and Physics (2014)
    http://link.springer.com/content/pdf/10.1007%2Fs00024-014-0879-7.pdf

    Geodesy’s 3 pillars:
    1. rotation
    2. geometry
    2. gravity

    The Saturn Cassini mission should result in a better Saturn ephemeris by 2017:
    “The error in determining the plane of Saturn’s orbit (latitude) rapidly decreases until the time span of observations exceeds 1/4 of the orbital period […]”

    “The next mission to a gas giant planet is the Juno mission to Jupiter, launched in August
    2011. The Juno spacecraft will orbit Jupiter for at least one Earth year beginning in July 2016.
    This orbiting mission will provide an opportunity to use the same phase referenced astrometry
    techniques with the VLBA, and thereby improve the ephemeris of Jupiter in a similar manner.”

  174. Paul Vaughan says:

    If anyone’s looking for a money quote, I’d say it’s this:

    “The orbits of the inner planets are accurately tied together with current data, but the outer planets are not as well tied to the inner planets or each other.”

  175. Paul Vaughan says:

    “The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury.” http://arxiv.org/pdf/1306.5569.pdf

    They didn’t finish exhausting potential for Messenger-facilitated Mercury ephemeris improvements before DE430&431 release:

    “The measurement residuals show some signature at the Mercury orbit period that cannot be removed by the ephemeris dynamical model. The signature is due to limitations in the estimated spacecraft orbits relative to Mercury. This will be improved with data from the second year of MESSENGER operations that includes orbits with pericenter over the southern hemisphere.” (p.24 of DE430 & DE431 article linked immediately below)

    May be another money quote:
    “The orbit of Jupiter is less well determined than the orbits of the inner planets and Saturn.” (p. 29)

    “Measurements of Neptune cover less then one orbit, so the uncertainty in some orbital elements
    is more than one order of magnitude larger than for Uranus.”
    (p. 39)

    “The orbits of Uranus, Neptune, and Pluto are determined primarily from astrometric observations, for which measurement uncertainties due to the Earth’s atmosphere, combined with star catalog uncertainties, limit position accuracies to several thousand kilometers.”

  176. Paul Vaughan says:

    OB, the “facts” (as you call them) will evolve with observations.
    It’s not like AW where “the science is settled” upfront by thought-policing agents.

    Best Regards

  177. Ulric Lyons says:

    Extreme weather events of 535–536
    http://en.wikipedia.org/wiki/Extreme_weather_events_of_535%E2%80%93536

    Late 535 AD:

    ~2222.3yrs earlier in 1688 BC, the eruption of Santorini (Thera):

  178. oldbrew says:

    UL: Interesting but are we sure 1688 BC is correct? Internet searches seem to favour 1600-1650 BC.

    PV: ‘The orbits of the inner planets are accurately tied together with current data, but the outer planets are not as well tied to the inner planets or each other.’

    In the next post I’ll put up a few ideas about that. Not all avenues have been explored IMO.

  179. Ulric Lyons says:

    The 1688 BC nitrate spike in Antarctic ice cores has been passed off as a melt, though this study suggests that SO4 events could result in nitrate spikes:
    http://drs.nio.org/drs/bitstream/2264/3806/1/Holocene_21_351.pdf

  180. oldbrew says:

    Just to spell it out: you are pointing to the half period of various J-S-U-N numbers at 4448 +/- 5 years e.g. 27 Neptune, 151 Saturn and 375 Jupiter orbits, where major conjunctions will take place.

    When these three align big things can happen.

  181. Ulric Lyons says:

    In that example yes it’s just under 2224yr. It’s not proof that it was Thera though, it could have been a different eruption. The same configuration occurs also on quadrature series, e.g. at 827 BC 1398 AD. What should be happening through that configuration, is first a period of very cold temperatures, then a sudden uplift in the solar signal, which would be from the Saturn-Neptune syzygy, aided by the Jupiter-Neptune quadrature, which is also a warm signal.

  182. […] For this look at Saturn-Uranus conjunction patterns a model will be proposed, then the planetary data compared to it to see how good a match it is – or not. This post follows on from two recent posts which can be found here and here. […]

  183. oldbrew says:

    Updated Saturn data should be available sometime this year.

    ‘Scientists have paired NASA’s Cassini spacecraft with the National Science Foundation’s Very Long Baseline Array (VLBA) radio-telescope system to pinpoint the position of Saturn and its family of moons to within about 2 miles (4 kilometers). The measurement is some 50 times more precise than those provided by ground-based optical telescopes. The feat improves astronomers’ knowledge of Saturn’s orbit and benefits spacecraft navigation and basic physics research.’

    http://www.jpl.nasa.gov/news/news.php?feature=4434

  184. Chaeremon says:

    @oldbrew, look again: Saturn jumps (or the BH BS all jump) upon Saturn conjunction, even though the distance is cosmological, gee:
    “stringent tests of Albert Einstein’s theory of general relativity by observing small changes in the apparent positions of actively feeding black holes, or quasars, as Saturn appears to pass in front of them on the sky.”

    Cited from the NASA page; b.t.w. their full image and caption says “December 31, 1969” ?

  185. oldbrew says:

    New data might help clear up a question about the Saturn orbital period.

    https://tallbloke.wordpress.com/2014/10/29/why-phi-giant-planets-update-part-2/comment-page-1/#comment-92598

    Using Arnholm’s solar simulator I found U-N and J-S conjunctions at the same time in mid-September 1821. But they were in different positions so no S-U conjunction at the same time, which seemed to undermine the ‘grand synod’ idea.

  186. oldbrew says:

    ‘observing small changes in the apparent positions of actively feeding black holes’

    Black holes – do they exist or not?

    ‘“The absence of event horizons means that there are no black holes — in the sense of regimes from which light can’t escape to infinity,” Hawking wrote in his paper.’

    http://www.pbs.org/newshour/updates/hawking-meant-black-holes/

  187. […] in a Phi relationship with other significant Fibonacci multiples of J-S conjunctions, e.g. 89 (see here) and 233 J-S = ~27 Uranus-Neptune conjunctions. For example the number of J-E in 89 J-S is 1619 […]