Oldbrew and Tallbloke: Why Phi? Part 2 – The Gas Giant Planets

Posted: September 6, 2013 by tallbloke in Analysis, Cycles, data, Phi, solar system dynamics

This is the second post in a series attempting to unlock the door to the secret life of our solar system. In part one we presented some observations demonstrating a selection of the relationships between the motion of the planets, cyclic climatic and solar periods found in palaeo-proxy records, and ratios in the Fibonacci series, including many which are very close to the ‘Golden Section’ or phi. In this post we’ll take a closer look at the ‘gas giant’ Jovian planets; Jupiter, Saturn, Uranus and Neptune.

jovians

The first and most obvious visual observation to make is that the Jovians form two distinctive pairs. Jupiter and Saturn have a yellow-orange striped appearance, whilst Uranus and Neptune are more of an amorphous blue. But there are plenty more reasons to regard them as a ‘pair of pairs’ as we’ll see in the analysis below.

Diameter
The next most obvious thing about appearance is size. Taking the diameters, we see another reason to regard them in pairs: J 142,984 km, S 120,536 km, and U 51,118 km, N 49,532 km. Summing the diameters of the pairs: J+S = 263,520 km. U+N = 100,650 km. The ratio between these summed pairs of diameters is: J+S/U+N = 2.6181818 = Fibonacci numbers 144/55. This is also very close to phi2 = 2.618034

Rotation
A glance at the Jovian axial-rotation periods shows that once again there are close pairings. Jupiter is similar to Saturn, as is Uranus to Neptune. Let’s take a closer look at the figures, using data published by NASA, converted from hours to minutes: Jupiter 595.5 minutes, Saturn 639.3 Uranus 966.6, Neptune 1034.4.

Assessing them in pairs, we’ll take Uranus and Neptune first. A close match turns out to be 46:43, which we can check:
46 x 966.6 = 44463.6
43 x 1034.4 = 44479.2
That’s 99.965% accurate which is easily adequate for the analysis.

Turning to Jupiter and Saturn there is a slight problem, in that Saturn’s rotation has recently been declared by NASA to be variable, or at least not accurately known. That’s because the current Cassini probe measured it close to 647 minutes, whereas the much earlier Voyager probe data showed less than 640 minutes. So we’ll start by seeing what happens if we assume a 46:43 Jupiter-Saturn ratio as we found with Uranus and Neptune. 46 x 595.5 = 27393. 27393 / 43 = 637.0465. This calculated Saturn number is 99.64% of the original Voyager figure, giving us grounds for thinking the 46:43 ratio may well be in play here too. Note also that 46 + 43 = 89, a Fibonacci number which falls between the two others we found in the diameter ratios, 55 and 144. Comparable ratios and sums for other planet pairs: Mercury:Venus = 28:116 adding to 144, Earth:Mars = 118:115 adding to 233, Mars:Jupiter = 6:15 adding to 21, and best of all, Saturn:Uranus = 2:3 adding to 5. We were astonished when all these precise ratios summing to Fibonacci numbers came to light.

What if anything can be said about the ratios of the rotation rates between the two pairs of planets? Starting with the combined figures, and assigning a notional average of 642 to Saturn: Ur + Ne = 2001 minutes. Ju + Sa = 1237.5 minutes. Dividing to obtain the ratio: 2001 / 1237.5 = 1.617. Since Phi is a shade over 1.618 it’s an extremely close match. Amazing.

There are further connections to Phi too: Ur / Ju = 1.623. Ne / Sa = 1.611 (using 642 for Saturn) = 1.624 (using 637) = 1.599 (using 647)
These figures range from 8/5 (1.6) to 13/8 (1.625) but on the known data all are compatible with a Phi/Fibonacci relationship.

Orbits and Synodics
Starting with the orbit periods themselves, the planetary pair concept is still important. We can observe that against a period of 233 years:

Jupiter+Saturn x sqrt(2) = 233/4 approx.
Uranus x sqrt(2) = 233/2 approx.
Neptune x sqrt(2) = 233 x 3/2

149 Ju orbits = 60 Sa = 89 Ju-Sa conjunctions. Again we see Fibonacci number 89. The ratio 60:149 is ‘one away from’ 60:150 which is 2:5 or 0.4. This is a ratio of two fibonacci numbers we also saw in part 1.

102 Ur orbits = 52 Ne = 50 Ur-Ne conjunctions
Here we have: 102 = 34×3, 52 = 13x2x2 and 50 = 5x5x2, in
Fibonacci terms.

Although 51:26 is also valid and is a ‘one away from’ from 52:26, or 2:1, the double period is preferred for reasons we’ll give later.

Moving on to the synodic periods, the fundamental periods for the Jovian pairs (using NASA data) are: Jupiter-Saturn 19.8588 years (J-S) and Uranus-Neptune 171.389 years (U-N)

The period often called the ‘Grand Synod’ consists of 233 J-S conjunctions, which is also just short of 27 U-N conjunctions – hence the name, Referred to as ‘G.S.’ from here. One very curious result we obtained for the Jovian pairs was by calculating their beat frequency. We’re unsure of the physical validity of the idea of a beat frequency of two synodic periods, but the result was startling:

Using U-N = 171.38899y and J-S = 19.858823y:
(U-N x J-S) / (U-N – J-S) = 22.461425

One ‘Double Halstatt cycle’ ‘Grand Synod’ 4627.1058yrs (233 J-S) / 22.461425 = 206.00232 = De Vries cycle
206.00232 x 3 = 618.00696

4627.5027(= 27 U-N) / 22.461425 = 206.02
206.02 x 3 = 618.06

(618.00696 + 618.06) / 2 = 618.03348

After dividing by 1000 we are within a millionth of Phi = 0.61803399

Examples of J-S data relating to Earth and Phi and Fibonacci
34 J-S = 618 J-E (Phi =0.618…)
55 J-S = 1000 J-E
89 J-S = 1618 J-E (phi = 1.618…)
144 J-S = 2618 J-E (phi2 = 2.618…)
233 J-S = 4237 J-E (Phi³x1000, +1)

The Big Picture
To understand what happens on longer timescales, a useful starting point is the figure for the average number of J-S per U-N. To make it easier to follow we can use a ‘model’ of the system that works by converting J-S and U-N to idealised values using the ratio 425/422. We note that Saturn’s real orbital period is 89/3 x 422/425.

J-S 19.8588 x (425/422) = 20
U-N 171.389 x (425/422) = 172.6074

This increases the basic values but the ratios are unaffected.
We can convert back again if necessary to show what is going on.

In the model the Grand Synod becomes 233 J-S x 20 = 4660 years.
27 U-N = 4660.4 years
4660.4 – 4660 = 0.4 (2:5)
The number of 0.4’s in 4660 years is:
4660 / 0.4 = 11650 = 233 x 50 = 23300/2 (see below)

The ratio of U-N to J-S is:
172.6074 / 20 = 8.63037 to 1

The number of 0.4 in one U-N is:
172.6074 / 0.4 = 863.037

We can see that 863.037 = 100 x 8.63037
This means: 863.037 J-S = 100 U-N = 17260.74 years.
We noted earlier that 50 U-N is a key period.
Here we have 2 x 50 U-N in another equation.
Also: 50 x 172.6074 = 8630.37

Scaling that up to 863.037 G.S. (remembering each G.S.= 233 J-S) we find:
863.037 x 233 J-S = 23300 U-N = 466 x 50 U-N
Also: 23300 U-N = 466 x 102 U and 466 x 52 N orbits.
(466 = 233 x 2)

Note also that 863 G.S. = 23299 U-N, exactly one less
than the 23300 in 863.037 G.S.
863 x 27 = 23301 but two U-N less are required for 863 G.S.
This results from our earlier calculation:
1 G.S. of 4660y / 0.4 = 11650 = 233 x 50 = 23300/2
So after every 863 G.S. the equation is resolved again.

All the above will be accurate and true with the real data in terms of units and ratios, assuming the solar system continues as it is today. The time span of 863 ‘Grand Synods’ is close to 4 million years.

Comments
  1. wayne says:

    TB, I have refrained from even getting into this discussion for a number of reasons, one is I don’t really want to be viewed as “way-out-there”, I have always tended to stay strictly by the sciences. Myself, sometimes lacking the correct words to describe where I stand I searched and found a selection pretty close:

    Wolfgang Pauli was also fascinated by the appearance of certain numbers, including 137 , in physics.[18] British mathematician I. J. Good wrote:

    There have been a few examples of numerology that have led to theories that transformed society: see the mention of Kirchhoff and Balmer in Good (1962, p. 316) … and one can well include Kepler on account of his third law. It would be fair enough to say that numerology was the origin of the theories of electromagnetism, quantum mechanics, gravitation…. So I intend no disparagement when I describe a formula as numerological.

    When a numerological formula is proposed, then we may ask whether it is correct. … I think an appropriate definition of correctness is that the formula has a good explanation, in a Platonic sense, that is, the explanation could be based on a good theory that is not yet known but ‘exists’ in the universe of possible reasonable ideas.

    Also some things in science first viewed as numerology have actually ended up being correct. Take “atomic triads”, the property of groups of elements that later formed the periodic table and these were related to the columns of elements. So I don’t immediately toss away what you and Oldbrew are saying but I do look with a leery eye.

    One reason for my leeriness is I toyed with the golden and silver ratio over a few years in relation to markets and there are some rather amazing relations in that area, or so I first thought. I programmed chart analysis software and found that one of the closest relation held by all commodities and equities linear regressions bounded above and below with fibonacci ratio power bands (much like standard deviation bands). I was fascinated when the “correct” powers were used these charts, any and all of them!, bounced right off these band lines. It took a good year in spare time to get down to the science of why this was happening. These are generally viewed as random walks and sure enough even if you generate random noise walks simulating a stocks chart these also bounce right off these silver and gold ratio bands. Thank goodness I didn’t lose too much money before I realized two things. One is you never know if a trend is going to bounce or not and since if they bounce they immediately do so you increase your risk of being able to get out. If you could tell you could easily become quite rich. Second is this “line up” and “bounce points” tended to always be after the fact, backward in history, for the current movements were always daily changing the slope of the regression in real time and old prices always bounced but current prices didn’t immediately. Never got to the bottom of why statistically this happens. Just hope you are not following such a fallacy and, like myself back then, just don’t realize why everywhere you look there is Fibonacci ratios involved.

    So, I’ll join this discussion but hold me a an antagonist. I see what at first appears to be some flaws in what you are laying out. Sometimes you use sidereal periods as if the planets are somehow physically “aware” of their orientation to the background universe. Do you really mean this? Other times you use synodic alignments as if that matters for the only way this could have any tie to gravity is if these synodic alignments were also in some manner synced with the other planet’s positions. Just think you need to make sure you are not giving this a non-realistic dependence on some scale of “time”… better, find a relation not dependent on any time scale.

    After a break, before I posted this, I have to correct some said above on those charts. I was thinking “how did I program those bands” for that was at least ten years ago and I remember a bit more. Everything was standard statistics from a book on my shelf, “Probability and Statistics for the Engineering, Computing, and Physical Sciences”, but for one custom modification, that is it started with the standard deviations about the regression, nothing seemed to line up there at all, but offsets from the standard deviations using powers of phi did. It was a rarity when it didn’t. So have I seen Phi performing something I cannot explain? Yes. That is why I’ll at least read what you are saying.

    To me you have to bring the tie of these inter-relations back to graviational effects at some point.

  2. gallopingcamel says:

    There are only 9 planets or is it eight? I am not surprised to hear that there may be gravitational coupling between their orbits even though the calculations are way above my pay grade.

    Something similar may be seen in the case of planets with many moons such as Jupiter and Saturn, The orbits of the inner moons are strongly linked.

  3. tallbloke says:

    GC: Watch this space. Posts on the Galilean Moon system and Saturns moons coming up soon.
    Eight planets now Pluto hes been demoted. We will show that the periods of the transneptunian planets such as Pluto, Eris and Makemake and Quaoar are all intimately linked to the phi/Fibonacci system too, which will probably please Volker Dormann if no-one else.

  4. tallbloke says:

    Wayne: thanks for your considered reply. I’m pleased you have engaged as antagonist here, we need fine and free minds to challenge our observations, methods and presentation so we can improve and refine them.

    So far in these two initial posts, we haven’t speculated about ‘why phi?’. We have simply laid out some observations in order to highlight some of the order we see in the number space. Observation first, theory afterwards. There are a couple of points you’ve raised I want to address.

    “Sometimes you use sidereal periods as if the planets are somehow physically “aware” of their orientation to the background universe. Do you really mean this? Other times you use synodic alignments as if that matters for the only way this could have any tie to gravity is if these synodic alignments were also in some manner synced with the other planet’s positions.”

    On the first point, Jupiter’s sidereal rotation period is 9.9250 hrs and its length of day is 9.9259 hrs. The other Jovians are even further from the Sun and orbit even more slowly so the difference will be less than 1/1000 for all of them. So the comparison of rotations we made here won’t be much affected by which we use. But your point is well taken, since our investigations show that there is a link between spin and orbit, and we’ll be careful with the inner planets. We use sidereal orbital periods because they are accurately known and since we are dealing in ‘whole number of orbits’ relationships, there is no problem, unless you can see one?

    On your second point. If there really is a physical link which accounts for the frequent occurrence of phi/Fibonacci relationships in the solar system (and we don’t see how they could all be there by chance), then it is the harmonics and resulting synodic relationships which drive the orbital periods, and therefore the orbital distances (by Newton’s reformulation of Kepler’s laws), rather than the other way round. This is known and accepted by the mainstream already, as I discovered just yesterday when I found this wikipedia page:

    http://en.wikipedia.org/wiki/Planetary_migration
    “The migration of the outer planets is necessary to account for the existence and properties of the Solar System’s outermost regions”
    “After 500–600 million years (about 4 billion years ago) Jupiter and Saturn fell into a 2:1 orbital resonance; Saturn orbited the Sun once for every two Jupiter orbits.[4] This resonance created a gravitational push against the outer planets, causing Neptune to surge past Uranus and plough into the dense planetesimal belt. The planets scattered the majority of the small icy bodies inwards, while themselves moving outwards. These planetesimals then scattered off the next planet they encountered in a similar manner, moving the planets’ orbits outwards while they moved inwards”

    Our tentative hypothesis, is that since orbital resonance continues to this day, it is continually shuffling and nudging the planets into the relationships which best serve the principle of least action (nature does things in the most efficient way), and the action of entropy, which tends to bring about log-normal distributions, of which the Fibonacci sequence is the prime example.

    Finally, you made this point:

    “Just think you need to make sure you are not giving this a non-realistic dependence on some scale of “time”… better, find a relation not dependent on any time scale.”

    I’ve been thinking about this one too. Since most of our work deals with ratios, the relationships are dimensionless, and still hold regardless of the units used to perform the calculations. We tend to measure in terms of Earth orbits and days, and this could be regarded as ‘arbitrary choice’. However, I’ve discovered that there is a relationship between the period of Earth’s orbit and solar equatorial rotation rate (which is in the plane of planetary orbits). More on that in a later ‘why phi?’ post. If you look at the relations in the post where we showed:

    34 J-S = 618 J-E (Phi =0.618…)
    55 J-S = 1000 J-E
    89 J-S = 1618 J-E (phi = 1.618…)
    144 J-S = 2618 J-E (phi2 = 2.618…)
    233 J-S = 4237 J-E (Phi³x1000, +1)

    You can see why the J-S numbers are 1000 times bigger than the phi values. It’s because 55 of them is 1000 times longer than the Jupiter-Earth synodic period, which is itself around 1/11.86 longer than Earth’s own orbital period. That turns out to be a significant period too as we’ll show soon.

    In the meantime, I invite you to sit back and consider the extra-ordinary number and accuracy of the relationships evident in the system we have laid out. We need someone who is good with stats to work out how to do a significance test. I’m confident that there is an extremely low probability that all these relationships exist by chance. Nonetheless, we need a numerical demonstration of that in order to help convince people there really is something here worth spending time on. Stuart and I have devoted a lot of our time to this, and hope it will bear fruit to further our understanding of why planetary motion periods and the solar periods evident in paleo and instrumental records are synchronised. The prize is the ability to predict the evolution of solar variation with confidence, plus the satisfaction of understanding how the solar system operates and evolves through an orderly system of natural laws. If we’re right, the evolution and maintenance of the system is about rhythmically applied forces rather than chance collisions. Phi contains the inverse square in its internal constitution. That is indicative of a link between Phi, the square root of 2 and gravity.

  5. oldbrew says:

    TB: ‘the Jupiter-Earth synodic period, which is itself around 1/11.86 longer than Earth’s own orbital period. ‘

    Because the calc itself is: 11.862 x 1 / (11.862 – 1) = 11.862 / 10.862

    Re the 34/55/89/144/233 J-S figures mentioned above:
    the corresponding Uranus orbits are 8/13/21/34/55 (99.873% match).

    Another ‘curiosity’ is the number of Earth orbits (years) per Fibonacci number of Saturn orbits:
    21 S = 618.6 y
    34 S = 1001.5 y
    55 S = 1620.1 y
    89 S = 2621.7 y
    (etc.)

    The years figures are a 99.86% match to 1000 x Phi.

    Saturn’s orbit period itself is a 99.3% match to 89/3.

  6. Chaeremon says:

    oldbrew said: Another ‘curiosity’ is the number of Earth orbits (years) per Fibonacci number of Saturn orbits.

    And then the tiny, little, underappreciated, yet best (of all available) understood lunar orbit is commensurate with Fibonacci number of Saturn orbits. The following can be observed at lunar/solar eclipse distance (ask me if this has physical cause 😉

    Occurrences of eclipse pairs in % of possible syzygy pairs (just those which have potential to eclipse), as checked against 7k yrs, all happen within less than 9 days in relation to number of Saturn orbits (wiggle-room shrinks with larger temporal distance):

    3 x S = 1091.5 x syzygy (~89.8% at eclipse distance)
    5 x S = 1819.5 x syzygy (~84.2% at eclipse distance)
    8 x S = 2911.5 x syzygy (~48.9% at eclipse distance)

    But 13 x S (4731 x syzygy) has run out of steam for eclipse comparison, and I have no larger range of trustworthy data for which I would check higher Fibonacci numbers at the moment (I think about tapping the 26k yrs eclipse panorama, Luca Quaglia and John Tilley made their data available).

    For better understanding: eclipses are not required for measuring the lunar syzygy’s in this Fibonacci relation, yet they are powdered sugar on the researcher’s cake because they “force” alignment of so many orbital elements, and this allows more and other kinds of comparison 😎

    Is there perhaps a similar relation to Jupiter orbits in your work, I’d like to check more of this kind 🙂

  7. tallbloke says:

    Chaeremon: What about the list of Fibonacci – Jupiter-Saturn synod to Jupiter-Earth synod relations in the article?
    34 J-S = 618 J-E (Phi =0.618…)
    55 J-S = 1000 J-E
    89 J-S = 1618 J-E (phi = 1.618…)
    144 J-S = 2618 J-E (phi2 = 2.618…)
    233 J-S = 4237 J-E (Phi³x1000, +1)

    Or is it Jupiter alone you need?

  8. The implications for the ‘Big bang theory of the origins of the universe’..
    Chaos ..tending to complete!! order… .

    What is the probability of an explosion regrouping into an organised , coherent structure that has a repetitive repeating infinite pattern based on a mathematical constant .. .. phi
    Chaos is not synonymous with order.

    Its a bit like a computer algorithm. You can write graphic programs to reproduce these phi golden sections.
    The universe and solar system a bit like a fabric constructed with blocks of golden sections

    Totally predictable for the past , present and future

    The implications for climate forecasting…. Humans cannot change the golden section law.

    Any attempts to change the climate via AGW .. The response / tendency is to snap back toward the golden section arrangement….Always

    I was wondering if the maunder minimum is a position on the pascal triangle.

    Like the rows
    1
    11
    is the maunder minimum
    but at the base of the triangle with greater length you have the 178 yr maximum ( de vries)
    What would the numbers represent?
    The amplitude of the solar cycle.?
    What do the numbers represent in the Pascal triangle.

    The basic building block is???

    The number 11? 0r 1 schwabbe cycle
    The blocks build to form larger cycles in an infinite time frame.
    This is related to cosmic time?

    Can you link the planetary orbits to the pascal triangle sequence
    If 1 = Grand minima..zero sunspots
    Where are the planets at Grand minima/.This would be the start of a sequence or building block

    ……………

    Love your work and findings. Just mind boggling!!

  9. tallbloke says:

    Crikey: If only it were that easy. 🙂
    I’ll be posting RJ Salvadors latest model output of solar activity vs planetary motion later today. It captures the grand minima over the last 1000 years well, but read the caveats carefully on his prediction for the future.

  10. Chaeremon says:

    @tallbloke: I prefer Jupiter alone if you think it has connection from within your work. I can imagine that 7k yrs of data may already say something (in analogy to above Saturn cases).

    But yes, the combinations also need attention and I’ll give them a try them soon. I’m a bit reluctant with combinations since their meetings can be displaced by 0°, 90°, etc, and they also can just swirl around (analysis may open a can of worms, so to say). And perhaps there’s not much to find in 7k yrs or 26k yrs of data, or even the opposite is the case here and my data horizon is way too close.

  11. tallbloke says:

    Chaeremon: Jupiter and Saturn meet at almost the same place in the sky every third conjunction. The full precession of the synodic conjunction takes around 2383.056 yrs years, around the length of the ‘longer’ Halstatt cycle (2403 yrs) less 1 J-S. Amazingly this is 120 J-S. Obviously the translation of one ‘point of the triangle’ to the next takes 1/3 of this time, 794.352 yrs, as best as I can tell with my orrery software.
    I expect Oldbrew will let us know what he can make of Jupiter alone.

  12. tchannon says:

    I don’t know what is being said.

    The solar system has existed for quite some time so we only see an end game where the start must have been highly confused.

    An implication is the current situation is effectively an integer pattern.

    There is nothing new in this, a “cogging” will take place as things settle down, much earlier involving bodies no longer present: all we see is what is left.

    This is also a transition state, imperfect, including compromises which have yet to play out and will change as decay continues.

    So all that is going on is compromising energy distribution to evenness within constraints. That this can be related in a common mathematical shape is not a surprise.

    So far as I know there is no example in human memory of a reconfiguration of the solar system but there are chaotic states, could happen.

    Anyone have the solution to the N-body problem? That is what you are dealing with.

    I observe the solar system can be considered an analogue computer showing an intermediate solution where infinity-x situations have already been excluded.

  13. Chaeremon says:

    tallbloke: only 1 x J-S (245.5 x syzygy) shows eclipses (for 12.5% of cases in 7k yrs), checked other Fibonacci numbers but they “land” between eclipse seasons (good for me but OT here).

    Now your ‘point of triangle’, it equals 40 x J-S if I see this correctly (and so: 9824.5 x syzygy), it has eclipse pairs within ~7.6 days wiggle-room, for almost 81% cases – jackpot alarm 😉 In fact there are eclipse pairs (the 3 adjacent ones with less % but noticeable) at temporal distance of:

    9824.0 x syzygy
    9824.5 x syzygy (mentioned above)
    9825.0 x syzygy
    9824.5 x syzygy

    Something seems to be concerned about being physically ‘in-phase’ with so many orbital elements at your ‘point of triangle’, even the tiny little lunar orbit 😎

    Let me repeat to be clear: eclipses are not necessary for measuring syzygy’s, but they can help to find big cycles and unsuspected, well aligned sequences of similar configurations.

  14. Chaeremon says:

    tchannon wrote: all we see is what is left 😎

  15. oldbrew says:

    TC says: ‘Anyone have the solution to the N-body problem? That is what you are dealing with.’

    Yes. In part 1 we showed the 3-planet synodic conjunctions relationships, which is perhaps a sort of solar system triangulation. Without exploring it fully we did explain how some of that works e.g.:

    ‘the immediate neighbours synodic periods form the periods of the non-neighbour synods by addition’

    The numbers are there to view, and they do fit together. The Jovian synodic system in particular is easily explained here IMO:

    https://tallbloke.wordpress.com/2013/09/01/oldbrew-and-tallbloke-why-phi-part-1/

  16. tchannon says:

    I’m looking at this from a different perspective.

  17. tallbloke says:

    Tim C: “This is also a transition state, imperfect, including compromises which have yet to play out and will change as decay continues.”

    Tim, if you remember the paper on the Fibonacci series and entropy you linked the other day, it claimed to show that by organising into a state where it is able to shed the increasing entropy flowing into it, a system within a wider environment can stay stable for an extended period of time before eventually reaching the end of its timespan. One indication that the solar system is in a remarkably stable state is the fact that solar output wobbles a mere 0.1% either side of the mean over the 11 year cycle, and probably not more than 0.3% over a timescale of thousands or perhaps even millions of years. Another is that we have had liquid water on our planet’s surface for 3/4 or more of the existence of the solar system since several billion years ago.

    So we’re probably not seeing a ‘gradual cogging down’ as the system decays, like a mainspring winding down on a clock, but a system which actively reorganises in a way which promotes stability. It will continue to do so while the Sun stays online.

    Does this mean the solar system has ‘a will to live’? – No.

    Does it mean we have found a key to help explain it’s remarkable stability? – I think so, but it’s early days for the theory.

  18. tallbloke says:

    Chaeremon: Something seems to be concerned about being physically ‘in-phase’ with so many orbital elements at your ‘point of triangle’, even the tiny little lunar orbit

    Well this sounds encouraging, even if I don’t fully understand your methods. Is there an ‘Eclipse periods for dummies’ text I can read which will help me understand better how you can use them to project over large timespans?

  19. tallbloke says:

    Tim C: So all that is going on is compromising energy distribution to evenness within constraints. That this can be related in a common mathematical shape is not a surprise.

    Well, no-one achieved it before we came along and worked on it so far as I know.

    I suspect that if our theory works out, it will come as a surprise to a lot of “baffled scientists” who think Uranus and Venus got to have the orientations and spins they have because “there was a collision” (lazy brained numpetry in my opinion). 😉

    And since it helps us inter-relate the solar periods showing up in the paleo records in a logical way which relates to a consistent framework, I think the six months of effort (particularly from Oldbrew) that has gone into this work has been worthwhile.

    Different perspectives are welcome though, so feel free to tell us what yours is.

  20. tchannon says:

    Cogging refers to semi-stable states, for example the ratios you are considering. Slipping a state has happened and will happen.

    The sun? That too might be conditionally in a state.

    None of this invalidates what you are doing but I am trying to get a feel for the overall situation.

  21. wayne says:

    Hi TB. I’ll keep injecting a bit here and there over time, my time is limited right now. Much like what you and I did that completely straightening out the misconceptions on the barycenter question month’s ago, we might add some real science behind what you are seeing in the periods and orbits harmonics.

    I noticed the mention of “cogging”. That’s good. That is what I too know is literally occurring due to gravity effects of each body onto every other body and this gets into the transfer of angular momentum and tidal effects. Have you ever wondered why, in general, nearly everything we view in the universe is more circular than highly elliptic? By a pure mathematic point-mass viewpoint the opposite should be true. With no transfer of ang. mom. high elliptic orbits stay high elliptic orbits but through this transfer (primarily at peri) over billions of years there is a tendency for all orbits about non-rigid bodies to circularize and this does bring in the aspect of harmonics of periods, that is due to the eccentricy itself, your patterns of periods (“time”).

    What I was saying about a “time-less” relationship is like the mention above: “The full precession of the synodic conjunction takes around 2383.056 years”. That is exactly what I would expect. You have a synchronized relation that is slowly co-rotating in relation to the galaxy or the background universe and this deviation should be used for your “adjusted timepiece”. I think everyone agrees that Jupiter is the ruling gravitational source so it probably should be used as the “timepiece”. So if you are going to speak of so many “years” or compare other body’s periods for synchronization try adding that 1/2403 lengthening or shortening to the Earth year as your measurement, might find some of the variances disappear (hopefully).

    That was mostly what I was saying above, don’t try to fix to what we see, let the time period used to calculate the relations be in “Jupiter years” for instance instead for the entire system as viewed from afar is basically slowly co-rotating, like gears with fixed teeth but held in a 3d gimbal and we Earthlings are viewing and measuring the system from within the slowly rotating gimbal itself adding complexity we need to remove firstly.

  22. tallbloke says:

    Tim C: Yes, I think the ‘cogging’ is quantised too. There are a number of cases where we find that a significant number of a given period divides nicely into a much bigger period, with a ‘plus exactly one extra’ tacked on the end. It’s as if the system allows for some flexibility, and will accommodate small ‘quantisations’ here and there, while maintaining main relationships. I’m finding something like that with Venus rotation in relation to Earth and Jupiter-Saturn at the moment. Venus is trying to fulfil a 2:3 obligation to both Earth and Jupiter. It’s more tightly bound to Earth because although the gravitational pull from Jupiter is only slightly smaller than that from Earth, Earth’s varies more, and more often. So Venus keeps the same face to Earth every time they meet, but gains 10 degrees at each meeting with Jupiter until it’s almost exact again 67 J-V synods later. 69 J-V is the inner planet return period around 44.76yr, and that’s a 1/4 of the Jose cycle.

    So it’s as if Venus is making the best compromise it can, by turning retrograde instead of prograde, and it’s axial spin re-alignment cycle fits as close as possible to both Earth and Jupiter Synods, and getting near meshing its cogs beyond that off the 1/4 Jose cycle. Fun stuff.

  23. Chaeremon says:

    tallbloke wrote: Is there an ‘Eclipse periods for dummies’ text I can read which will help me understand better how you can use them to project over large timespans?

    As requested: Eclipse periods for dummies in text form.

    At the basic level I do not start for searching a period, since I have obviously no idea whether or not an interval will ever repeat (just the general case is assumed here). For this and the following steps I use data points as output by Solex. This gives files with one record per eclipse, and I trust Solex’s accuracy (and its ephemeris) over the very long timespans (if the timespan is beyond the 5k yrs canon of NASA then I use other sources for comparison as well). The records can now be matched for temporal distance, say for intervals of x days, and a tolerance z which I reduce in multiple runs.

    The second step is to verify the eclipses found at both ends of the searched interval, there are several methods: web lookup in NASA tables on the site of Xavier Jubier, or thumb through the tables of Prof. Dr. George v. d. Bergh (1955), amateur, “Periodicity and Variation of Solar (and Lunar) Eclipses”, or by visual inspection with Celestia, Stellarium, etc simulations.

    The 3rd step is to find if anybody has already written about a period with the searched interval length, and for this I use A Catalogue of Eclipse Cycles by R. Harry van Gent.

    If there is still nothing known about the searched interval, then I compute the formula of Prof. Dr. George v. d. Bergh, amateur, (+/- number of Inex intervals +/- number of Saros intervals) and check that with Harry’s Eclipse Cycle Calculator (same page). I have a local copy which understands 1/2 moons as well. Harry’s calculator gives essential data for assessing the characteristics of a potential (or known) period: number of eclipse seasons, which node repeats, mean angular displacements (obvious impact of orbital elements), eclipse cycle statistics (forget about the hocus-pocus “calendars” on that page).

    At any rate, I would rather not call a number of syzygy’s periodic when it has not already appeared in a peer reviewed journal, in order to avoid possible confusion or mistake by lack of information. All I can say about an eclipse number of syzygy’s is that they make an interval. But the effective % number of potential pairs can give an learned guess.

    The reason for “series or period or not” is a characteristic behavior: both lunar nodes never stop to produce eclipses, they instead continue at one moon offset from the other pole, without changing their constant latitudinal direction of advance, and thereafter cease the production of eclipses at the previous pole. Not that I know that an impresario of the academic theater has written about this (but perhaps a researcher has already reported, I presently don’t now).

  24. tallbloke says:

    Wayne: Excellent, I really hope we can engage your interest on this one as time goes on. I referred to the number of Earth years because that what everyone recognises as referring to the Halstatt cycle found in the paleo proxis *on Earth*. But in my defence you’ll note I gave the relevant number of J-S synodic cycles too.

    Regarding ‘putting some real science behind it’; Yes! that’s what we need to do. We need an answer to the question: Why Phi? (and Fibonacci)
    We’ve gathered a few hints so far:

    *The internal constitution of the number phi contains the inverse square ‘falloff’, analogous to gravity. (Thanks to Miles Mathis for this insight)
    *The Fibonacci series forms a log-normal distribution, which is thought to be connected with the way entropy works.
    *As well as the Fibonacci sequence converging on phi, phi can be quantised to form the Fibonacci series. This is the way natural processes work: phi is in the kernel of the seed, and contains the principle and the method of growth within itself, and the Fibonacci numbers are the growing tree/leaves/petals/seed heads which express in whole number ratios.
    *Phi turns up in subatomic relational quantities
    *Phi turns up in the binding of water molecules into droplets
    *Fibonacci series pervades the solar system from end to end

  25. tchannon says:

    Hmm… Tim has had a crazy idea. To get this across I need to construct a demonstration.

  26. Roger Andrews says:

    TB:

    I’m not able to add much in the way of specifics to the excellent work all you guys are doing on the solar system, but here are some general comments on your responses to Wayne.

    “Regarding ‘putting some real science behind it’; Yes! that’s what we need to do. We need an answer to the question: Why Phi? (and Fibonacci)”

    From a historical perspective the question comes down to how 2,500 years ago in what is now India a poet codifying rules for writing sanskrit verse managed to develop a numerical sequence that governs the magnetic resonance of mesons in cobalt niobate. Is it possible that the typewriter-pounding monkeys really have reproduced one of Shakespeare’s sonnets? 😉

    “*The Fibonacci series forms a log-normal distribution, which is thought to be connected with the way entropy works”

    Fibonacci isn’t lognormal. You have a lognormal distribution when log (x) gives a normal distribution, but when you plot the distribution of log (Fib) you get a horizontal line (try it). Fibonacci is actually semilognormal, plotting as a straight line when the y axis is log scale and the x-axis linear, not when both axes are log scale. You might want to check into the “connect(ion) with the way entropy works” to see whether this makes any difference.

    You might also take a look at the paper I link to below. It gives a good account of normal and lognormal distributions, but what I found interesting was the pinball machine analogy shown in Figure 2, which combines Pascal triangle look-alikes with a physical (gravitational) mechanism and shows a lognormal distribution that resembles part of a Fibonacci spiral. I get the feeling that it may be telling us something, but I’m not sure what.

    http://www.jstor.org/stable/10.1641/0006-3568%282001%29051%5B0341:LNDATS%5D2.0.CO;2

    “*As well as the Fibonacci sequence converging on phi, phi can be quantised to form the Fibonacci series. This is the way natural processes work: phi is in the kernel of the seed, and contains the principle and the method of growth within itself, and the Fibonacci numbers are the growing tree/leaves/petals/seed heads which express in whole number ratios.
    *Phi turns up in subatomic relational quantities
    *Phi turns up in the binding of water molecules into droplets
    *Fibonacci series pervades the solar system from end to end

    I’m OK with the relationship between Fibonacci and solar system, water molecules and subatomic particles but I’d be inclined to go easy on trees, leaves, petals and seeds. I can’t think of any single force or combination of forces that could explain both the behavior of the solar system and the growth patterns of living organisms, and the more I look at the evidence for the widespread existence of Fibonacci and the golden ratio in the plant and animal world the less compelling I find it. It would certainly be a lot easier to develop a “unified theory” if we could concentrate on planets and particles and didn’t have to explain why the shape of a Nautilus shellfish mimics the the golden spiral, which according to at least one mathematician it doesn’t.

    http://www.docstoc.com/docs/3629043/The-Golden-Ratio-A-Contrary-Viewpoint-Clement-Falbo-Clement-Falbo

  27. tallbloke says:

    Chaeremon: Thank you. I don’t think there’s enough spare room in my braincell at the moment to work on eclipse cycles, so I’ll rely on you to let us know if you find any more ‘jackpots’ from the periods we find which seem to be the convergence point for a number of subcycles. Around 44.77yr is a strong one for the inner solar system. Ian Wilson has done some great work on connecting Lunar periods with planetary cycles too.

    Tim C: 🙂

    Roger A: Thanks for that paper. Good clear account. I note the central limit theorum gets a mention – something Paul Vaughan mentions frequently. I wonder if we built a pinball machine with enough rows of kepler triangles and an inverse square falloff in the bin width, whether we might see a quantisation effect as well as a log-normal distribution. Clearly, the fibonacci series is an emergent property of the solar system, but the hydrogen atom connection and water molecule connections are tantalising too, especially given the planet diameter linkage we found. I need to investigate density pairings, since Urban le Verrier noticed an approximate falloff in density with inverse square proportion in some planets. Density, mass and diameter are all linked by gravity. The bigger the planet, the stronger its self gravity and the more tightly packed its material becomes, so there is complexity which needs unpacking before we’ll find the relations perhaps.

    In ancient times, sacred geometries connected with astronomy were the nuclear secrets of their day. So their details would get coded into poetry or arcane treaties on the structure of poetry to hide information from the profane. According to the authors of a book I have, the (ex)biblical ‘Book of Enoch’ contained details of the observatory at Newgrange in Ireland and astronomical observations. The film ‘Zeitgeist’ contains an account of how the story of the three wise men is actually an astrological text referring to the way the group of three stars forming the belt of Orion point to Sirius, which presages the position of the rising of the winter solstice sun in Egypt, and the inundation of the Nile.

    Regarding Fibonacci in plants, the oppositely rotating 8:13 spirals in fir cones, sunflower seed heads and other species are definitely there. The 222.492 degree angular spacing between leaf stems frequently appears, and maximises sunlight reception. I don’t think your observation that there are many more species which don’t obviously exhibit Fibonacci invalidates those that do. If the Sun was the seed, which unpacked (by increased spin during condensation or by explosion) into a solar system exhibiting Fibonacci relationships, the Hydrogen connection might perhaps be important, though I suspect we’ll have a hard time trying to extrapolate up from the subatomic to the cosmic here. The more likely thing is that as Wayne pointed out, the circularisation of orbits and the natural consequence of perturbations is to reduce chaos and increase stability by sorting the orbits into an orderly system which can persist in time . In this respect, the local system is anti-entropic, for as long as the Sun stays stable anyway. Have a look at the paper Tim originally linked for clues as to why this is possible.

  28. Chaeremon says:

    Roger Andrews mentioned: … to explain why the shape of a Nautilus shellfish mimics the golden spiral, which according to at least one mathematician it doesn’t (hyperlink to a piece of rant is in the above).

    Two points, first: the referenced author demands “… to set standards for obtaining measurements of artwork.” Good luck with that, or is this just the usual “give more funds for more useless research” mantra. Ask an experienced art critic, e.g. Miles Mathis, about measurement standards in art.

    The other point: same author sets the error bar, academically, to 2%. I have shown elsewhere that the correct error bar approximation is ((phi – 1.5) / phi) ~ 7.3% and this is not just only mathematically correct from observable premises, it is also not based on unfalsifiable opinion.

  29. oldbrew says:

    The rotation data doesn’t include the three main ‘non-pair’ relationships of neighbour planets, so we’ll look at that here.

    Saturn:Uranus is 3:2 = 5
    Jupiter:Mars is 15:6 = 21

    Earth:Venus is a bit more complex, mainly due to the long rotation period of Venus.
    If Earth is taken as 365.25, although of course the orbit period is not the rotation period, then
    E:V is 2:3.

    If we say Earth is 1, the ratio is 243:1 = 244 which isn’t a Fibonacci number.
    However it is 5:2 with 610 which is a Fibonacci number, and 3:2 with 366 which in turn is 5:3 with 610. The Venus figure of 243 = 3³ x 3².

    For more on the Saturn spin rate question, a link to NASA’s view can be found here:

    https://tallbloke.wordpress.com/2013/09/02/scientists-baffled-to-discover-that-venus-spin-is-slowing-down/comment-page-1/#comment-58709

  30. tallbloke says:

    Chaeremon: Could you show us or point to a link where we can find the demonstration of the 7.3% figure. Thanks.

    OB: I added in the Mars-Jupiter and the Saturn-Uranus to the main article. The Earth-Venus spin-orbit link is very interesting, and may help us with the ‘why does Venus spin backwards?’ question. I love the way you resolve things down to simple ratios using the Fibonacci numbers as a guide. Proof in itself that we are on the right track in my opinion. Can you work Jupiter and/or Jupiter-Saturn into it somehow?

    I found Venus’ rotation resolves to Jupiter within a degree after 67 J-V synods, and within 5 degrees at alternating 33 and 34 synod intervals. 30 J-V is close to J-S and 69 J-V is 44.77yrs – the inner planet return period:

    EDIT: I just realised that the 2:3 between Venus and Earth’s orbit means 34 J-V is around 22.07 years – hello Hale cycle.

  31. Chaeremon says:

    tallbloke said: … convergence point … Around 44.77yr is a strong one for the inner solar system.

    And at 3 x 44.77yrs the syzygy’s appear with eclipses at both ends (repeat: more than just a few orbital elements in phase and based on observation data), the % as before:

    1660.5 x syzygy (~65%)
    1661.0 x syzygy (~87.4%, wiggle-room less than a week)
    1661.5 x syzygy (~44.4%)

    Fibonacci 5 is out of steam; higher Fibonacci’s may get in phase again, also in my previous posts, but (repeat:) timespans beyond 5k yrs draw their ephemeris from an increasing number of assertions.

  32. tallbloke says:

    Chaeremon, thanks again. Notable is that 3/2 x 44.77 is 67.155, close to the period of the Atlantic Multi-decadal Oscillation. A lunar-planetary driven variance in Earth’s climate perhaps?

    What is the precise time period in years of 1661.0 x syzygy please.

  33. tallbloke says:

    What if the planets and the Sun were both acting in concert to modulate the shape of the heliospheric current sheet and that affected the levels of Svensmarks Earthbound cosmic rays? Perhaps we’d find out more if Tim were to feed the Oulu neutron data into his clever software and see what periods it produces?

  34. Chaeremon says:

    tallbloke said: Chaeremon: Could you show us or point to a link where we can find the demonstration of the 7.3% figure. Thanks

    In mathematics this is easy: converging a set of (rational) fractions to phi must be a closed system (no other number or idea can enter the convergence process).

    So, list the convergents of (1+sqrt(5))/2, using e.g. the “Fraction” orange box here, sum up the difference between adjacent pairs (where have I read already about adjacent pairs @oldbrew and n-body systems 🙂 and say the sum gives x.

    Now (1/phi)/x = phi shows that the converging system is closed by 1/phi (YMMV with more rigorous algebra).

    The largest convergent is 2 and it is minus (!) ~23.6% away from phi, I have no interpretation for 2 in this context (other than OT cytokinesis or repel). But the next to largest convergent is 1.5 and this is ~7.3% away from phi.

    Let’s say that convergence happens with pairs of difference from the smallest to the largest, like it is known for forces acting on bodily approaches in outer space. If the units converge as proper fractions, in our model or in reality, we can think that phi convergence behaves like the above.

    I keep my eyes open for other and insightful observations of the phi convergence process in nature (from smallest to largest), will let you know what I found.

  35. tchannon says:

    RA, you mean log:log. Nothing special about log:lin, not semi anything in my book. (yes you are correct it is log:lin)

  36. Chaeremon says:

    tallbloke said: What is the precise time period in years of 1661.0 x syzygy please.

    In my spread sheet it is 3 x your 44.77 years – 5.423 days. This is all nominal (mean figures as used in the astronomical norm DE421) and the 5.423 days offset are reported from eclipse matches in ephemeris data (same norm). Together it’s 134.28842 years (by the simple trick with sidereal days – solar days). Since I’m not interested in Delta T or LOD, the astronomical setting is sufficient for me.

    And yes, I’m also keen on the progress of the experts of lunar-planetary driven variance in Earth’s climate 🙂

  37. Wayne Job says:

    Thanks tallbloke, being as I am a lowly mechanical engineer some what mathematically challenged, I have however always had a strange attraction to harmonics, your work is facinating.
    The harmony of the spheres is a worth while cause, sticking a barb into the last hundred years of settled science is even better.

    I just had a little dig at Lief Svelgard over at WUWT for his closed mind on a similar topic.

  38. tallbloke says:

    Chaeremon: “Let’s say that convergence happens with pairs of difference from the smallest to the largest, like it is known for forces acting on bodily approaches in outer space.”

    Is there a reference for this? It sounds good.

    “I keep my eyes open for other and insightful observations of the phi convergence process in nature (from smallest to largest), will let you know what I found.”

    Excellent, thank you.

  39. tallbloke says:

    Wayne J: Anyone can play this game, you don’t need to be a maths wizard.

    I just made some more progress with my Venus rotation puzzle.
    To recap: Venus keeps the same face towards Earth each time they meet in a synodic conjunction, because it’s rotation in a 3:2 resonance with Earth’s orbit. I think the reason Venus spins backwards, is because it’s also trying to fulfil a tidal resonance with Jupiter, who’s gravitational force on Venus is around the same magnitude as Earth’s. But Venus turns 10.765 degrees too far each time it meets Jupiter. However, it’s within 5 degrees at alternate 33 and 34 J-V synodic conjunctions, which is not far from the Jupiter-Saturn conjunction period. After 67 J-V synods, it’s within a degree, and this is exactly 2 J-V synods short of 44.77 years, the period at which many cycles in the inner solar system converge.

    So I have a hunch Saturn is involved, and to test this, I checked out a few figures. Here’s what I found:

    The period of Saturn’s orbit around 29.45 years divided by the period of Jupiters orbit around 11.86 years matches the Earth-Venus synodic period divided by the Jupiter-Venus synodic period to within 0.02%. If you multiply the S/J result by Oldbrew’s 422/425 ‘cogging’ adjustment which shows up in many of our calcs, the match improves by an order of magnitude to 0.002%. I used NASA’s figures given to 3dp in days to determine the result accurately. It also matches to within 0.2% the ratio 32/13. 13 is a Fibonacci number and not much creativity is required to find that 32=33+5. 🙂

    The precision of the result makes me pretty sure I’m right about this resonance being the reason why Venus rotates backwards; it wouldn’t be able to fulfil it’s tidal resonance obligations to Earth, Jupiter and Jupiter-Saturn any other way. The standard lamebrain mainstream explanation is that something big crashed into Venus long ago. I think along with all the other relationships we’ve been finding that it’s more likely to be an evolved orbital parameter gradually brought about by perturbations and tidal forces from it’s neighbours than a one-off chance event in a chaotic solar system.

    Perhaps if those perturbations and tidal forces from more than one neighbour can cause a planet to reverse it’s rotation, they can also cause a planet to speed up it’s rotation? This might explain how Venus got to rotate fast enough to fission a moon, which later became the Planet Mercury, according to Tom van Flanderns theory. Mercury is in a 3:2 resonance with the Sun, and according to van Flandern, this couldn’t have come about if Mercury evolved in situ where it is now. It would instead be in a 1:1 tidal lock like most moons in the solar system. So, Mercury spins three times per two orbits of the Sun, and Venus spins three times per two orbits of the Earth. This indicates they both have in-homogeneous density distributions, as would be expected if one was fissioned from the other, rather than being created from accretion as individual planets. The resulting tidal squeezing may well explain why Venus is so hot at the surface, despite none of the solar radiation getting to ground level through it’s thick atmosphere too….

    Another clue as to the strong perturbation forces Venus undergoes is indicated by its almost perfectly circular orbit. Thank Wayne for that insight.

  40. TB said
    Notable is that 3/2 x 44.77 is 67.155, close to the period of the Atlantic Multi-decadal Oscillation. A lunar-planetary driven variance in Earth’s climate perhaps?

    I agree the smaller building blocks are
    1..yr
    11 yr… ( 1 Sun spot cycleSC) =16.94 synodic J-V
    22 yrs….(Hale cycle) = 33.88 synodic
    33..yrs…( one phase of the AM0) = 50.82 synodic J-V
    44. yrs ( quarter Jose cycle) = 67.66 synodic J-V
    55 yrs = 84.7
    66yrs ( 3 Hale cycle/Full cycle of AMO in the 21 st century anyway) = 101.64 synodic J-V
    77 Gleissburg?
    88
    99 yr
    etc
    THe cycles are subsets or embedded? Just like the Fibonacci fabric geometry of triangles?

    THe number 2 is strong as Major units are multiples of 2
    2 SSC = 1 hale
    2 Hales = One qrter Jose
    8 Hales = One jose

    ————————————————————–
    It is better to look at the AMO at its phase length as the phase changes sign.. Pos to neg etc

    The physical connection is the sea level anomaly which is a dipole and changes every phase which is 30 oddyears .
    The water height changes on either side of the Atlantic basin.
    This is a physical force..

    Looking for something that changes the force direction every 30 odd years

  41. tallbloke says:

    Crikey:
    Perhaps changes in Earth’s length of day tied to the motion of the planets above and below the solar equatorial plane might help?
    My first ever post on this blog:
    https://tallbloke.wordpress.com/2009/11/29/planetary-solar-climate-connection-found/
    A while ago I did a few back of a fag packet calcs to work out how much water would upwell/downwell on each side of the Atlantic as the Earth changed axial rotation speed by several milliseconds. It’s a lot.

  42. oldbrew says:

    TB: ‘After 67 J-V synods, it’s within a degree’

    That reminds me of your earlier comment…
    https://tallbloke.wordpress.com/2013/09/06/oldbrew-and-tallbloke-why-phi-part-2-the-gas-giant-planets/comment-page-1/#comment-58994

    …where you say: ‘I expect Oldbrew will let us know what he can make of Jupiter alone.’

    The 2383 year period is 3 x 67 Jupiter orbits and 3 x 27 Saturn = 120 J-S as stated = 3 x (67 – 27).
    (Completed orbits: Jupiter 2384 years, Saturn 2386)

    TB: ‘…not much creativity is required to find that 32=3³+5.’

    Or that 32 = 8 x 2² 😉

  43. tallbloke says:

    “Or that 32 = 8 x 2²”

    Heh, got me again dammit. 🙂

  44. oldbrew says:

    @ Chaeremon

    ‘Is there perhaps a similar relation to Jupiter orbits in your work, I’d like to check more of this kind’

    Try Fibonacci x 4 e.g. 13 x 4, 21 x 4, 34 x 4, 55 x 4 etc. (Jupiter orbits).
    Example: 21 Saturn = 618.6y, 13 x 4 Jupiter = 616.8y

  45. tallbloke says:

    Venus rotation will re-align to the Jupiter-Saturn synodic conjunction every 210.07981 years. Hello De Vries cycle!
    Q: What keeps Venus’ orbit so circular?
    A: Just about every major planet in the solar system by the look of it. No wonder she’s so hot; all the gods want to hug and squeeze her.

  46. Chaeremon says:

    oldbrew said: @Chaeremon: Try Fibonacci x 4 e.g. 13 x 4, 21 x 4, 34 x 4, 55 x 4 etc. (Jupiter orbits).

    And the winner is: 4 x Fibonacci 3 x J = 1761.0 x syzygy’s (142.37315 years) with eclipse at both ends, ~67.6% of the potential cases, just 1/8 day wiggle-room, as above within 7k yrs. Will have to try other Fibonacci numbers as well.

    I hope to have time during the week, before my September vacation at Tenerife beach, to make a new spreadsheet and send it by email.

    P.S. as yet no substantial hug between Venus and Luna. @tallbloke: how many years is the De Vries cycle, google university has ranges beginning at ~200, Ian is using 208, your is 210 (Suess)?

  47. tallbloke says:

    Chaeremon: 210 is long for De Vries or Suess I agree. I should have said “near De Vries”. A couple of Ju-Ve synods either way is within tolerance, due to the slowly changing orientation at successive synods I think. This is probably something that is slowly ‘adjusting’ with the change in Venus’ rotation period I reported on a few days ago.

  48. oldbrew says:

    We touched on this in part 1 of this series but only briefly (‘9-34-43’).

    9 Uranus-Neptune = 34 Saturn-Uranus = 43 Saturn-Neptune
    (43 is just the sum of the other two as that pair are the ‘non-neighbours’)

    The period is 1542.5 years which is one third of a Grand Synod plus around 144 days.
    In fact Sa-Ne, Ju-Ur, and Ju-Ne synodic numbers are always derivatives of the Saturn-Uranus number, as explained in part 1.

  49. Roger Andrews says:

    TB:

    “In ancient times, sacred geometries connected with astronomy were the nuclear secrets of their day. So their details would get coded into poetry or arcane treaties on the structure of poetry to hide information from the profane.”

    Well, all I can say is that the expletive deleted ancients did an expletive deleted good job of hiding their expletive deleted information.

    Now a few leading questions for you, preceded by a statement:

    If I understand his article correctly Miles Mathis theorizes that the reason we detect Fibonacci and/or the golden ratio in the behavior of huge inanimate objects like Jupiter and in tiny living things like plant tendrils is that both are controlled by charge fields that act in the same way regardless of scale. Now I don’t now whether this theory is plausible or not – the subject is way above my pay grade – but I do know that it’s generally a good idea to confirm that an effect really exists before one starts to develop a theory to explain it. And the work that you, Oldbrew and others have been doing goes a long way towards confirming that Fibonacci is indeed a real and pervasive effect in the solar system.

    Which brings me to the questions:

    What do you think the result would be if someone performed a detailed scientific audit of the reported occurrences of Fibonacci and the golden ratio in the animal and plant worlds? Would we find that Fibonacci/golden ratio effects are real and pervasive here too, or would we find that they’re so uncommon as to be written off as random events?

    And how about at the molecular, atomic and sub-atomic scale?

    Regarding the Fibonacci spiral, what do you get when you add the Fibonacci boxes in something other than a spiral pattern, such as left and down or right and up?

  50. tallbloke says:

    Roger A: Thanks for the entertaining comment. The paleo-astronomers have had a lot of fun and interest decoding and reconstructing the information the ancients left regarding their astonomical observations. For example, at the doorways of many ancient observatories is a diamond shaped mark in the rock. But some were flatter and some were vertical and some were nearly square. Then someone noticed that these characteristics depended on latitude, and it was realised it marks the inequality of the number of days between equinoxe and solstice at various latitudes.

    “in the animal and plant worlds? Would we find that Fibonacci/golden ratio effects are real and pervasive here”

    Well every insect with a compound eye would tend to prove it’s pretty ubiquitous. There’s lots of them. It seems to be about the most efficient way to pack things on convex surfaces, and the maximisation of sunlight on leaves, and the growth of shells of light weight yet high strength.

    “how about at the molecular, atomic and sub-atomic scale?”

    I don’t know. Hydrogen is the basic building block though.

    “what do you get when you add the Fibonacci boxes in something other than a spiral pattern, such as left and down or right and up?”

    A wiggly worm. 🙂

    Mathis says it’s the right hand rule in action that makes the spiral keep turning 90 degrees per quarter turn.

  51. oldbrew says:

    @ Roger A

    Are you familiar with the Kepler triangle?

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

    TB: to save me the trouble, have you got that diagram? Thanks.

    [Moderation note] Image replaced with corrected version – Thanks Wayne

  52. oldbrew says:

    RA and others might also be interested in this if they haven’t heard of it before.

    ‘Golden ratio discovered in a quantum world’
    http://phys.org/news182095224.html

  53. Roger Andrews says:

    TB:

    I looked for some examples of the lots of insects with eyes that matched the golden ratio but couldn’t find any. I did, however, find this:

    http://io9.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature

    I think the first sentence of the first comment succinctly sums the presentation up: “Sorry George, this is bollocks.”

    “Mathis says it’s the right hand rule in action that makes the spiral keep turning 90 degrees per quarter turn.” Andrews says that when you add squares in a spiral sequence you’re bound to get a spiral. It’s a predetermined result that proves nothing. What sayeth Tattersall?

    Got to run now. Back later.

  54. tallbloke says:

    Roger A: “the work that you, Oldbrew and others have been doing goes a long way towards confirming that Fibonacci is indeed a real and pervasive effect in the solar system…. BUT …Andrews says that when you add squares in a spiral sequence you’re bound to get a spiral. It’s a predetermined result that proves nothing?


    You start with a Golden rectangle in the phi ratio. Draw a diagonal corner to corner, then fill the resulting triangles with the largest possible squares. This processes naturally quantises squares which get repeated in each triangle in the numbers which form the Fibonacci series. i.e. one yellow, one orange, two tan, three light brown, five darker brown, eight even darker brown: 1,1,2,3,5,8,…

    Note that the process generates a fractal, and fractals are common in nature. There is no choice here about which way you are going to subdivide a golden rectangle, the simple rule that you fill the remaining space in the triangles with the largest possible squares generates the fibonacci sequence *from* Phi, rather than converging *to* it.

    Regarding your concern about the spiral. Nature is brutal, the nautiloids which didn’t add their squares in a spiral didn’t make it. 😉

    But seriously (for a moment), the nautilus doesn’t grow in squares, it grows in the most efficient spiral it can. Which happens to be pretty close to a Fibonacci spiral. Why is that? Well, it’ll be the lightest, strongest, bestest most appropriate for growth rate way to do it. Nature is efficient like that. Organisms which don’t do it the most efficient way are at a competitive disadvantage. So why does that bestest way come out as fibonacci? I suspect it’s because growing by the same ratio each growing season as the previous seasons growth until maturity is reached is the natural way.

  55. oldbrew says:

    RA: your link says [quote] ‘after a few rotations, spiral arms should start to wind around a galaxy. But they don’t — hence the so-called winding problem.’

    Link to ‘winding problem’ – http://casa.colorado.edu/~danforth/science/spiral/

  56. tallbloke says:

    OB: Nice link

    “In the 1950’s it was thought that magnetic fields could be the mysterious generators of spiral structure. However, the mechanism for how this would work was never clearly developed. Furthermore, one would expect that, if magnetic fields were behind the density organizations, the energy density of the fields would be equivalent to that of the mass gravitational energy. Subsequent observations of field strength showed it falling short by a factor of five (BT94). It is known, however, that magnetic fields follow the path of spiral arms.”

    Tee hee. 🙂
    A lot of spiral arm waving going on there.

  57. wayne says:

    Oldbrew, maybe it should be mentioned that on the Kepler triangle diagram you posted above, the edges should be labeled 1 : √φ : φ as √( 1² + (√φ)² ) = φ, for the hypotenuse that is. Seems it was taken directly off http://en.wikipedia.org/wiki/File:Kepler_triangle.svg which has each edge already squared for it gives areas of squares that edges form the triangle’s edges. Not that big of a deal but maybe it should be corrected or mentioned anyway (looks bad being basically wrong, doesn’t compute at a simple glance).

  58. Chaeremon says:

    Roger Andrews said (in reply to tb): Well, all I can say is that the expletive deleted ancients did an expletive deleted good job of hiding their expletive deleted information.

    This must not be so. What spurs my interest in photo-copied (untampered) ancient texts and inscriptions on art is that:

    expletive deleted academics use a guaranteed expletive deleted empty specialist dictionary of ancient scientific times (a.k.a. expletive deleted sacred, secret, enigmatic, etc, expletive deleted meaningless “word” lists),

    and then forge expletive deleted literary “translations” (always in the absence of experiment and observations), also by expletive deleted “correction” of the guaranteed incomprehensible parts and by expletive deleted filling of the “obvious” gaps (empty space in scripts and on art),

    after which they proclaim: this is now the Truest Truth and our method of deception has to be learned by schoolchildren and our method of fraud has to be studied by university students for making a living (the “science” is settled, hiss).

    It is the very hard way of experiment and observation which can bring our modern understanding of ancient reality, and not that of literary forge, back into expletive deleted academically deleted information.

    Example (have to hurry up before the mod strikes): the expression Jupiter must be similar or equivalent to the expression Zeus. By experiment and observation (in a non-trivial, weighty project) this can be analyzed and confirmed. Oldbrew and tallbloke did that for me in their present work, unintentionally and without knowing.

  59. wayne says:

    Have been pondering on this relation but certain aspects I just cannot see. For one I see no after the fact causality of any magnitude, even over the some 4.5 billion years that is close to when the planets formed. To my knowledge a planets orbit and it’s gravitational influence on nearby other planets cannot transfer any sizeable tangential influence on the others. That is, one planet cannot speed up, slow down, of change another planet’s mean orbits diameter therefore its period, the semi-major axis fixes this. However through transfer of angular momentum (changing the other’s radial or velocity vectors) it can alter both’s eccentricity.

    How about looking into whether it is possible that this fibonacci relation was caused by the way the accretion disk was partitioned (by the golden ratio) and what we now see billions of years later is that, yes, I’ll be, they do tend to have ratios that conform to fibonacci ratio approximations and powers and roots. Something like that.

    Almost like Jupiter coalesces as much of the matter as locally possible and what was left over was what formed Saturn, Uranus and Neptune each following the same ‘real physics’ limits on how much it could run into or gravitationally attract over the vast millennia depending on the local density setting each of each’s distance and periodicity but leaving an imprint of what, the fibonacci ratio.

    I would include the rocky planets but they seem to be different. Upon plotting in Excel some wild guesses I came upon a chart (based as ln(period or distance) / ln(Phi) and Mercury, Venus, Earth, and Mars fall on one straight line and the gas planets on another straight line, the two lines intersecting at Mars. And I accidentally erased it !!! Trying to get the exact equations back but this leads me to think that possibly they are different as two groups. Tallbloke, might be why you may have problems across that division. Also, it could have been a mistake itself and should have been erased.

  60. Roger Andrews says:

    TB:

    “Regarding your concern about the spiral. Nature is brutal, the nautiloids which didn’t add their squares in a spiral didn’t make it.”

    But the brachiopods made it, and so did the lamellibranchs, echinoids, graptolites, trilobites, crinoids, ostracods and cephalopods. And so did a lot of other organisms that don’t grow in spirals, like sharks, elephants, toads, yellow-bellied sapsuckers, the palm tree in my front garden and the cyanobacteria from which more advanced life forms began to evolve over 3 billion years ago.

    I have more to add, but it’s late and we old guys need our sleep. Back tomorrow.

  61. tallbloke says:

    Roger A: Sure, I’m not trying to claim phi is the pattern for all of life’s rich and varied morphology. The phi proportion in the DNA helix is interesting though. Anyway, I’d like to get back to our solar system study on this thread, so please continue the discussion about biology on the Mathis thread here: Thanks.

  62. oldbrew says:

    @ Wayne

    I agree your version of the diagram is more correct. It should look like this one:


    What you say you ‘cannot see’ seems a lot like what Miles Mathis was talking about in the two recent posts?

  63. oldbrew says:

    Wikipedia discusses orbital resonance here: http://en.wikipedia.org/wiki/Orbital_resonance

    ‘The orbits of Pluto and the plutinos are stable, despite crossing that of the much larger Neptune, because they are in a 2:3 resonance with it. The resonance ensures that, when they approach perihelion and Neptune’s orbit, Neptune is consistently distant (averaging a quarter of its orbit away). Other (much more numerous) Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune.’

    So the message to a smaller body from a larger body is: find a resonance or else.
    That should mean the survivors are by definition in resonance, to a certain degree at least.

  64. tallbloke says:

    Wayne, OB: It looks like it may have been my fault. OB sent me two triangles. I may have posted the wrong one. Here’s the other

  65. tallbloke says:

    OB: So the message to a smaller body from a larger body is: find a resonance or else.
    That should mean the survivors are by definition in resonance, to a certain degree at least.

    Well, this is where I think we begin to gain insight, and start to tread into dangerous territory…
    Speculative idea:
    I think it may be more the other way round. The large body might assist the smaller body by acting gravitationally on it’s asymmetries to change it’s spin. If it makes it spin faster, then any iron content will generate more of a ‘dynamo’ and magnetosphere. That will interact with the heliomagnetic current sheet. Maybe that can affect the orbital angular momentum and lock the body into the mainline solar system dynamic. Some ‘Mathis mathemagic’ would probably be required…

    SLowly rotating bodies either end up as 1:1 tidally locked moons or get booted out of the system to the dark cold nether regions. That might explain why we have 8 stable big planets, a small number of dwarfs and a well bounded asteroid belt, and not much else except comets on long trajectory orbits.

  66. Chaeremon says:

    tallbloke wrote: EDIT: I just realised that the 2:3 between Venus and Earth’s orbit means 34 J-V is around 22.07 years – hello Hale cycle.

    And at 2 x your 22.07 yrs are 546.0 x syzygy’s with eclipse at both ends (~82% of the potential cases within 7k yrs, just ~1.5 days wiggle-room, 44.14295 yrs to the interval).

    You guys find resonance points in variegated orbital members of our planetary system, for which the Luna probe reports her orbital signal way above noise, in a way that I would like to find treasure troves in the sand at the beach 🙂

  67. Thanks for the assistance TB. I have a lot of reading to do. You have achieved so much since 2009.

    Re De Vries period.
    If 11 is the basic building block unit. ..THe De vries cycle is the 19th row in the series * 11 = 209 yr period

    I hope AW reciprocates by publishing a rebuff to LS. Or has he taken sides and has become a cycle phobiac?

    or should l say chaos manic

  68. oldbrew says:

    TB: the ‘scattering power relative to Earth’ in the linked table says it all.

    Earth 1, Jupiter 8510, Saturn 308, best of the rest 2.51 (that’s 2 point 51).
    http://en.wikipedia.org/wiki/Clearing_the_neighbourhood

  69. Chaeremon says:

    weathercycles said: Re De Vries period.
    If 11 is the basic building block unit. ..THe De vries cycle is the 19th row in the series * 11 = 209 yr period.

    If close to 11 yrs is the building block, the there is the very well documented and used Tritos eclipse cycle (see its triple below) of which R. Harry van Gent writes:

    This eclipse cycle was known to Chinese astronomers as the shuo wang shi hui or the jiao shi zhou and appears to have been developed in the first century B.C. (Needham, 1959). The name Tritos was introduced by George van den Bergh (1951, 1954).

    The Tritos can be used for predicting series of solar eclipses with more than 60 members which alternate in visibility from the northern and the southern hemisphere. At the begin and the end of a solar Tritos series it is possible to have a few ‘missing’ eclipses.

    The ancients also found the [Fibonacci 3] Triple Tritos.

  70. tallbloke says:

    “I hope AW reciprocates by publishing a rebuff to LS. Or has he taken sides and has become a cycle phobiac?”

    Unfortunately so. Willis, Mosher and Leif have succeeded in their aim there.
    All he needs to do is look at the beach ridges on Hudson bay and ask himself:
    “What could produce such regularity other than solar system dynamics?”
    Whenever I’ve asked one of them to answer that question, they simply don’t answer it.
    Not very scientific.

  71. Thanks for the information about the tritos and triple tritos ‘ chaeromon’. This is all new to me.

    I had a read of ‘wikio’ on this topic and found these diagrams with key years very useful
    http://en.wikipedia.org/wiki/Tritos_cycle
    http://en.wikipedia.org/wiki/Inex

    I was interested because of the triplet. I had a look at my time series graphs to see how the INEX, tritos and triple tritos years sat with the AMO cycle and the Sunspot cycle

    Because they have similar periods it is common sense you see a pattern . However the Tritos series was not always in phase with the AMO and Sunspot cycle as the length of the AMO and sunspot cycles are quasi where as the Tritos… is a constant..

    However.!!

    It should be noted that the Tritos has been in phase with the Sunspot cycle at solar maximum since 1958 or SSC no 19 to cycle 23 The tritos has been in phase during our warming epoch. Not sure if this is coincidental
    From 1880 to 1940 the SSC amplitude were smaller and the trios was not as closely linked to solarmax

    In fact out of solar cycles 14-23 ( 9 cycles)..,the tritos eclipse was in the ascending sunspot cycle 7/9 of the cyles, with 2 exceptions and that was 1936 and 1948 where the tritos eclipse was at solar minimum (rare)
    (Possible a change of phase?)
    After 1936 or since cycle 17 , the SSC has been large in amplitude

    What l am saying is that there is a tentative positive correlation between a bigger sunspot cycle and the alignment of tritos over the sunspot maximum.(.Data from 1904 -2002)

    Sample size is small here but none the less quite interesting or a coincidence
    —————————————————————————————–

    Is the INEX another word for the triple trios?

    Noticed you can get a triple INEX as well which is close to the gleissburg at ~88
    http://en.wikipedia.org/wiki/Inex
    ————————.

    TB.. Yes sad ..Re ..AW.. Oh well. He doesn’t know what he is missing out on, on Tallbloke wordpress.. The cutting edge of climate research!!

  72. tallbloke says:

    “Tallbloke wordpress.. The cutting edge of climate research!!”

    Well, some aspects of it I hope. The big prize for us is finding a good explanation for the cyclic periods related to climate change found in paleo proxies and instrumental data, including the AMO/PDO and ENSO. That would then allow us to subtract them out from the instrumental record and see what is left for the climate scientists to explain. If there isn’t much left, then we can project our computations forwards with some degree of confidence which could be regarded as a valid input to policy formation.

  73. Chaeremon says:

    @weathercycles: thanks for assessing the Tritos w.r.t. SSC, this is good to know. I see (or use) Luna mainly as a data sensor, she may be hugged so very often but her dance seems always intriguing (yes, intriguing since unimaginably ancient times).

    The Inex (or its triple, apsidal better balanced) cycle is the most astonishing (and most precise that we currently know of) yet least understood eclipse cycle. It is currently used “mainly” honorably, for mapping of the holy, sacred, allegedly “governing” (a.k.a. academic prejudice) Saros cycle members. Instead, we have to understand that every eclipse appears simultaneously on every named or unnamed cycle – provided there is an integer relation in more than a trivial number of local (and the neighbors’) orbital elements (Fibonacci anybody?).

    Therefore what matters (to me) is the hug and squeeze by Luna’s cavaliers, and the present article has confirmed to me the dimensions of this endeavor. One of my directions: there are so many eclipse cycles which imprint their pattern at specific and narrow ranges in the ecliptic band (and therefore in predetermined seasons and tidal characteristics), but such things are rather OT for the present article.

    @tallbloke: subtracting your finds from the instrumental record for working out what is left, agreed. I can’t wait for this to appear on your blog 🙂

  74. oldbrew says:

    @ Chaeremon – ‘Fibonacci anybody?’

    Inex 10571.9508 d / Saros 6585.3213 d = 1.605381

    That’s a 99.665% match with 8/5 (= 1.6).

    18 Inex = 521 years precisely if that’s any help.

  75. Chaeremon says:

    @oldbrew – ’18 Inex = 521 years precisely’

    Did you connect anything Fibonacci to 521 years or your equation? there are other (n x syzygy) which return to ~same date in the year, e.g. 705 x syzygy (3 x Metonic 19 = 57 yrs), 804 x syzygy “Unidos” 65 yrs.

    OT: I’m repeatedly “surprised” that competent survey engineers measure and reconstruct the dimensions of ancient edifice, but allegedly “cannot” connect 57, 65 to yrs (above) nor 223, 358 (Saros, Inex) to syzygy’s.

  76. Very amazing Oldbrew re theSaros /Inex ratio. Fibonacci connection.

    Linked to planetary motion. No surprise because the solar system is a closed system.
    No part an island.

    The graphical pattern of saros/Inex

    Is that a Fibonacci fabric?
    —————————————-
    Chaeremon
    The triplet is the closest l have found to the AMO cycle that runs parallel with global temp.
    Maybe l will draw up a diagram to show and tell the
    Inex vs AMO .
    .Inex vs SSC..
    in the coming days.
    ——————————-
    Does the Eclipse cycles affect ocean tides?

    Could you explain this comment about the INEX
    “In addition sequential events occur at opposite geographical latitudes because the eclipses occur at opposite nodes.”
    ” repeating at alternating nodes, every 358 synodic months (≈ 10,571.95 days, or 29 years minus 20 days)
    http://en.wikipedia.org/wiki/Inex

    Can this affect ocean displacement ?
    ————————————————————-

    Some more reading
    http://en.wikipedia.org/wiki/Eclipse_cycle

  77. tallbloke says:

    Chaeremon: Oldbrew just posted this on the new thread:
    ‘When we divide the 360 degrees of the circle by the number phi, we get the angles 222.4922… and 137.5077…’

    TB knows this but just to be clear – the reverse of that is:
    222.4922 / 137.5077 = phi

    Another way of explaining the preference for 13/8:
    137.5 x 13/8 = 223.4375 – within 1 of the 222.5 ‘target’
    137.5 x 8/5 = 220 – exactly 2.5 from the target.

  78. Chaeremon says:

    weathercycles wrote: Does the Eclipse cycles affect ocean tides?

    You mean, does the lunar advance have such effect? I view eclipses as just a subset of syzygy’s, so if I understand you correctly: yes they too.

    weathercycles wrote: Could you explain this comment about the INEX
    “In addition sequential events occur at opposite geographical latitudes because the eclipses occur at opposite nodes.”
    ” repeating at alternating nodes, every 358 synodic months (≈ 10,571.95 days, or 29 years minus 20 days)

    The wiki plagiarists write as if the nodes stand still, but you can think the (lunar) orbital plane is advancing tirelessly from minus inclination max to plus inclination max, northwards / southwards (and turning at max), as observable at the horizon. This b.t.w. is so regardless of eclipses occurring or not (eclipses only happen at nodical inclination near zero during syzygy).

    weathercycles wrote: Can this affect ocean displacement ?
    You mean, like driving and directing the oceanic currents? I would like it were so, as if it were a (may be complicated, rather secular) extension of the daily tides.

  79. tallbloke says:

    Weathercycles and Chaeremon: Have a read of my second ever post on this blog for a look at longer term lunar influence on oceans:
    https://tallbloke.wordpress.com/2009/11/30/the-moon-is-linked-to-long-term-atlantic-changes/

  80. oldbrew says:

    @ Chaeremon : ‘Did you connect anything Fibonacci to 521 years or your equation? ‘

    You could try this: 521 / 200 = 2.605 (13/5 = 2.6)
    Or 521 / 322 = 1.618

    It depends what you’re looking for really.

  81. tallbloke says:

    521 falls at one of the golden ratios between Fibonacci numbers 377 and 610. 377+144=521 610-89=521

  82. Chaeremon says:

    tallbloke said: Have a read of my second ever post on this blog for a look at longer term lunar influence on oceans.

    Thanks for the hint. Harald Yndestad refers to a 74.4 yr tide which I cannot detect before it suddenly appears from calendar year 2014 (!) on in ephemeris data (haven’t searched before 1980 yet). This needs more attention than I can spare before going to Tenerife island this week.

  83. tallbloke says:

    Enjoy Tenerife Chaeremon. Make sure you visit Thor Heyerdahl’s museum at the Pyramids of Guimar.
    If you do go there, I’d like one of the T shirts they had on sale when I visited. It has a drawing of the Ra expedition ship with Thor’s handwriting underneath which says:
    “Borders? I’ve never seen one in the oceans, but I believe they exist in the minds of some men”