This post lays the groundwork for a series we will publish over the coming weeks and months. It consists of some of the observations gathered since February when I published my discovery that the Fibonacci series and the Golden Ratio – Phi connect the planetary orbits, the synodic conjunction periods they form with their neighbours, solar cycle periods and cycles found in terrestrial climatic proxy time series. Stuart has done the bulk of the calculator heating work here, with interjected observations, conversations and deliberations with myself.
Observations on the ratios of the solar system’s synodic periods
and their relationship to phi and the Fibonacci series
By Stuart Graham and Roger Tattersall.
September 1st 2013
The terrestrial planets and Jupiter
In this group of five planets, Mercury (Me), Venus (Ve), Earth (Ea), Mars (Ma), Jupiter (Ju), there are four ‘neighbour relations’ Ju-Ma, Ma-Ea, Ea-Ve, Ve-Me. In each of the triplets shown below, there are either two neighbour relations and one non-neighbour relation or vice versa. The neighbour relations, define the non-neighbour relations, as seen below. Using ~44.76 years as the base period, the inner planet return period identified in Ian Wilson’s post here, the number of synodic conjunctions in the 44.76 year period are, from the outermost planet, Jupiter, inwards:
Ju-Ma=20 = 44.7055yrs
Ma-Ea=21 = 44.8407yrs
Ea-Ve=28 = 44.7646yrs
Ve-Me=113 = 44.7254yrs
Ju-Ea=41 (21+20)
Ma-Ve=49 (21+28)
Ju-Ve=69 (21+20+28)
Ma-Me=162 (49+113)
Ju-Me=182 (20+162)=(69+113)
Ea-Me=141 (28+113)
As you can see, the immediate neighbours synodic periods form the periods of the non-neighbour synods by addition.
(It’s also worth noting that the Uranus-Saturn conjunction period is 45.363 years, a 98.7% match)
Abbreviated, in order of leftmost pair (e.g.Ju-Ma=20), rightmost pair (e.g Ma-Ea=21), outside pair (e.g. Ju-Ea=41), this notation can be written for the ratios of the synodic triplets as:
Ju-Ma-Ea 20-21-41
Ju-Ma-Ve 20-49-69
Ju-Ma-Me 20-162-182
Ju-Ea-Ve 28-41-69
Ju-Ea-Me 41-141-182
Ju-Ve-Me 69-113-182
Ma-Ea-Ve 21-28-49
Ma-Ea-Me 21-141-162
Ma-Ve-Me 49-113-162
Fibonacci ratios of note in this planetary group include:
Ve-Me/Ju-Me = 21/13 to within one part in 300 i.e 298/299 or 0.33%
Ju-Ve/Ju-Me = 21/8 to within one part in 185 or 0.5%
Ve/Ea orbit = 13/8 to within one part in 3300 or 0.03%
Ve-Ea synod = 8/5 to within one part in 1267 or 0.08%
Ju-Ve/Ve-Me = 5/3 to within one part in 62 or 1.65%
Ju-Ma/Ma-Ve = 5/2 to within one part in 46 or 2.2%
Ea-Ve/Ju-Ea = 3/2 to within one part in 42 (42/41) or 2.5%
Ju-Ma/Ju-Ea = 2/1 to within one part in 43 or 2.5%
Ju-Ma/Ma-Ea = 1/1 to within 1 part in 23 or 4.7%
The Jupiter and Saturn connections to the terrestrial planets
Scaling up by 4×44.77 from the inner planet return period to the Jose cycle, we find the following relationships between the Saturn-Jupiter synodic period (Sa-Ju) of 19.859yrs and the terrestrial inner planets as follows:
Sa-Ju-Ma 9-80-89
Sa-Ju-Ea 9-164-173
Sa-Ju-Ve 9-276-285
Sa-Ju-Me 9-728-737
Fibonacci ratios of note in this planetary group include:
Sa-Ve/Sa-Me = 13/5 to within one part in 200 or 0.5%
Sa-Ea/Sa-Ve = 5/3 to within one part in 91 or 1.1%
Sa-Ma/Sa-Ea = 2/1 to within one part in 33 or 3%
Ju-Me/Sa-Me = 1/1 to within one part in 82 or 1.22%
The Jovian system
Scaling up again to 4627.11 years, which is the sum of the Halstatt periods of 2224.19 years (112 Sa-Ju) and 2402.92 years (121 Sa-Ju), we find:
From the outermost inwards
Ne-Ur=27
Ur-Sa=102
Sa-Ju=233
Ne-Sa=129 (27+102)
Ne-Ju=362 (27+102+233)
Ur-Ju=335 (102+233)
Once again, the immediate neighbours synodic periods form the periods of the non-neighbour synods by addition.
Number of synods of gas giants in the 4627-year cycle
Triplets:
Ne-Ur-Sa 27-102-129 (9-34-43)
Ne-Ur-Ju 27-335-362
Ne-Sa-Ju 129-233-362
Ur-Sa-Ju 102-233-335
Fibonacci ratios of note in this planetary group include:
60 Saturn orbits equals 149 Jupiter orbits for 89 synods in 1767.44 years
60:149 = 2:5 Within 0.67%
60:89 = 2:3 within 1.1%
89:149 = 3:5 within 0.45%
102 Uranus orbits equals 52 Neptune orbits in 50 synodic periods in 8569.45 years
102:52 = 2:1 within 2%
102:50 = 2:1 within 2%
52:50 = 1:1 within 4%
We will cover the inter-relation of the outer planet synod pairs in a further post.
Additional observations
Another base period noted by Rhodes Fairbridge resulting from his work on the relative heights of the
Hudson Bay beach ridges was a noticeable geo-effective period of 317.741yrs. This is in the ratio of
1:14.5625 with the 4627.11 year cycle period. This period turns out to contain a whole-number ratio for:
Triplets:
Ur-Sa-Ju 7-16-23
Ur-Ju-Ma 23-142-165
Notably, 317.741 multiplied by the Fibonacci ratio 89/55 is almost exactly three Neptune-Uranus conjunction periods:
317.741 x (89/55) = 514.162, and 3 x 171.389 = 514.167, the same value within 0.001%. Note also that
3x3x3=27 is the number of Ne-Ur synods in the 4627.11 year ‘double Halstatt cycle’.
Finally, an odd-ball to think about. On this timescale of 514.167 years:
Ur-Ju/Ju-Ma = 10 x 0.61792, within 0.02% of Phi
In forthcoming posts, we will cover more aspects of this ongoing voyage of discovery, including the Galilean moon system, the so called ‘dwarf planets’, Phi and gravity, and the links between rotation periods and orbital periods, not necessarily in that order.
Tallbloke's Talkshop 
OB & TB:
“(T)he Fibonacci series and the Golden Ratio – Phi connect the planetary orbits, the synodic conjunction periods they form with their neighbours, solar cycle periods and cycles found in terrestrial climatic proxy time series.”
But the Fibonacci series and the Golden Ratio aren’t the same thing. Fibonacci is a sequence of numbers whose ratios converge on Phi but never quite get there, and the ratios of the early Fibonacci numbers – certainly 0,1,1 and 2 – aren’t anywhere near 1.618034. I don’t know if this is a significant issue but thought I’d mention it.
Hi Roger A: True, but we’re keeping all the options open while we work on this puzzle. It’s a fun exercise to plot the values of the successive Fibonacci ratios against the number of terms to see the decay curve it generates. Reminiscent of a broadcast signal losing strength with distance. This recalls to mind Miles Mathis’ observation of the inverse square falloff hidden in the constitution of the number phi discussed a few days ago. This might apply both to gravity and electro-magnetism, the two prime suspects in the plot. Although I haven’t run stats tests to settle the issue, I’m pretty sure that this many close relationships can’t occur by chance. Something causes the solar system to organise itself in terms of Fibonacci ratios and phi relationships. We hope to discover how it comes about through the underlying physics which must be present.
@ Roger Andrews
I wouldn’t disagree with your comment. For anyone new to the concept it’s useful to know that.
Readers might also refer to TB’s original post (linked above, see ‘I published’) – quote:
‘Since it was noticed that five synodic conjunctions occur as Earth orbits the Sun eight times while Venus orbits thirteen times, many attempts have been made to connect the Fibonacci series and it’s convergent ‘golden ratio’ of 1.618:1 to the structure of the solar system.’
Note: convergent. The lower numbers are bound to be less closely related to Phi in the Fibonacci series because they are closer together than the higher numbers (say 21 onwards).
OB: I replaced the 317.741 x phi example with the Fibonacci ratio 89/55 because it’s even closer to 3 x Neptune-Uranus synod (0.001% rather than 0.01%). But given the possible margins in the orbital periods given by NASA, it’s not possible to tell which it really is.
Another thing worth remembering is the example I linked which showed that as well as the Fibonacci series converging *towards* phi, it is possible to construct the Fibonacci series *from* phi by the quantisation technique shown here:
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.
TB – I believe 55/89 is valid because:
3 x 55 Ne-Ur = 28279.2 years
16 x 89 Sa-Ju = 28279.0 years
Nice result! A 0.0001% error. 16 is 13+3 of course. 🙂
By the way, 28279 is a prime number.
http://numberworld.info/28279
The nearest Fibonacci number is 28657 which is also prime. It’s index number, 23, is also prime.
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html
I think we’ll need to examine the remaining synods for the planet groups and see if we can find relationships for them, grading the accuracy as we go. Until we have a complete list, we can’t quantify the possibility of the whole web of inter-relationships being down to chance.
Anyone know of an open source gravity simulation package we can tinker with? We need to start building a model…
OB and TB:
Re your responses to my first comment, I think the question comes down to which one means more – phi or phibonacci? (Excuse the pun.)
To me phi is by far the more robust. It’s calculated by solving a simple equation, and it doesn’t take a large leap of the imagination to see how a simple equation could control some aspects of the behavior of the solar system even if we don’t know how. After all, if e=mc^2 works, why not 1/x=1+x?
To connect the Fibonacci series with the behavior of the solar system, however, does require a large leap of the imagination. This series was developed in India around 2,000 years ago (the Indians are still upset that Fibonacci got the credit) by scholars studying the construction of the sanskrit language – long syllables versus short syllables etc. And after analyzing the frequency of occurrence of long and short syllables and various other things they constructed the Fibonacci series like this:
1+1 = 2
2+1 = 3
1+3+1 = 5
3+4+1 = 8
1+6+5+1 = 13
4+10+6+1 = 21
Now I would like to put “etcetera” at the end of this list, but I’m quite unable to see any systematic progression that would justify the use of the word. Sanskrit is obviously complicated. (Anyone who wants to look deeper into the matter will find more details in the link below, but be warned, it’s heavy going.)
Click to access pdf
So if the Fibonacci sequence controls the relationships between the synodic periods of the planets, then so does ancient sanskrit prosody. That’s much too large a leap. Either we’ve been set up by a capricious deity or the whole thing’s a coincidence.
There, I’ve just rubbished 2,000 years of research. Better quit while I’m ahead. 🙂
I would summarize what you’re saying as follows:
balanced multi-axial differential
http://mathworld.wolfram.com/FibonacciPrime.html
RA,
So you want an intuitive reason?
Three onwards ln(F) forms a straight line.
Now consider maximum entropy law, follows log
Wicked R us, A Maximum Entropy Approach to Natural Language Processing
Click to access J96-1002.pdf
Entropy to look at language roots
Click to access ScienceIndus.pdf
Oh, forgot this The Fibonacci sequence in nature implies thermodynamic maximum entropy
Takashi Aurues
Click to access RIMS20121113Aurues.v05ForSub2.pdf
Further digging is left and right
Tim C: I suggest you read the account of how the Fibonacci numbers came into being in the link I posted above.
Paul V: I plugged “balanced multi-axle differential” into Google Translate but it didn’t recognize the language. Sanskrit, maybe? 😉
Roger Andrews
Pascal’s triangle is shown below [note: the numbers in the extreme left column are not part of the triangle].
1________1
1________1___1
2________1___2___1
3________1___3___3___1
5________1___4___6___4___1
8________1___5___10__10__5___1
13_______1___6___15__20__15__6___1
21_______1___7___21__35__35__21__7___1
To get the number in the extreme left column, move across a row until you hit the first 1 in Pascal’s triangle. Then add all the numbers, as you move diagonally upward from this 1 [make sure that you include this first 1] until you run out of numbers.
Going across successive rows you get:
row 1_________1_____________=1
row 2_________1_____________=1
row 3_________1+1___________=2
row 4_________1+2___________=3
row 5_________1+3+1_________=5
row 6_________1+4+3_________=8
row 7 _________1+5+6+1______=13
row 8_________1+6+10+4______=21
As you can see Roger, this is just the sequence that you posted for Sanskrit but in the reverse order.
1+1 = 2
2+1 = 3
1+3+1 = 5
3+4+1 = 8
1+6+5+1 = 13
4+10+6+1 = 21
Roger Andrews,
What the above post is doing is essentially adding up various possible mathematical combinations.
SKIP THIS POST IF YOU WANT TO AVOID THE MATHEMATICS
A combination C(n,k) is the number of ways of picking k things out of n possibilities, when order is not important and repetition is not allowed. Mathematically it is given by:
_____________C(n,k) = _________n! / (k! x (n-k)!)
where n! is n factorial = 1 x 2 x 3 x 4 x 5 x …..x n.
e.g. Imagine you have three (n = 3) flavors of ice cream e.g. chocolate (C), vanilla (V), and strawberry (S).
If you are allowed two scoops (k = 2), how many COMBINATIONS of flavors can you get (without repetition)? The answer is:
CV
CS
SV
i.e.__________C(3,2) = 3! / (2! x (1!)) = 3
This way pascals triangle becomes
______________C(0,0)
______________C(1,0)___C(1,1)
______________C(2,0)___C(2,1)___C(2,2)
______________C(3,0)___C(3,1)___C(3,2)___C(3,3)
______________C(4,0)___C(4,1)___C(4,2)___C(4,3)___C(4,4)
______________C(5,0)___C(5,1)___C(5,2)___C(5,3)___C(5,4)___C(5,5)
etc.
This means that the Fibonacci sequence numbers are just a sum of (non-repeating) combinations such that:
1 = C(0,0)
1 = C(1,0)
2 = C(2,0) + C(1,1) = 1 + 1
3 = C(3,0) + C(2,1) = 1 + 2
5 = C(4,0) + C(3,1) + C(2,2) = 1 + 3 + 1
8 = C(5,0) + C(4,1) + C(3,2) = 1 + 4 + 3
etc.
The bottom line. The nth Fibonacci number will naturally emerge from a process of summing n steps that starts out at step one by having zero ways of choosing out of n possible choices, and that has the number of possible choices reduced by one each step and the number of ways of choosing increased by one each step.
This is where I think the basic physics is involved.
Tim C: Three onwards ln(F) forms a straight line. Now consider maximum entropy law, follows log
Yes. I came across several papers in diverse subject areas talking about lognormal distributions and entropy recently. Lots of links on this page
http://www.helsinki.fi/~aannila/arto/. Regarding your Fibonacci maximum etropy paper: “Evolutionary theory can be applied to all dissipative structures. Without evolutionary change, no dissipative structure can continue for long”
This puts me in mind of Bejan’s statement of his “constructal law”:
“For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.” http://en.wikipedia.org/wiki/Constructal_law
The Fibonacci series gets close to phi pretty quickly.
1/1=1 -61%
2/1=2 +39%
3/2=1.5 -8%
5/3=1.66.. +3%
8/5=1.6 -1%
13/8=1.625 +0.5%
21/13=1.615 -0.3%
But notice the convergence isn’t in a smooth progression at the nodal points of the whole number fractions. However, if you plot the convergence as an analogue function, it does oscillate either side of phi and converge to it in an almost smoothly (if not linearly) way. (I can’t remember the maths I used to do that many years ago). I think that fact may turn out to be important later when we get into the detail, because of the way tidal locking occurs between gravitating bodies. Lots of 2:1 and 3:2 resonances operate in the solar system, e.g. between moons and planets, and between Mercury and the Sun.
Between Venus and Earth there is something more subtle happening. There is a relation between Venus’ spin rate and Earth’s orbital period which shows a 2:3 resonance. i.e. Venus turns on its own axis three times in two Earth years. Note that this is relative to the stars though, not Earth. Relative to Earth Venus spins 13 times in 8 years. There is also a very close 13:8 ratio in their orbital periods, true to 1 in 3300 (0.03%).
Ian, thank you for the excellent and clear elucidation of the derivation of the Fibonacci series from Pascal’s triangle. I immediately thought of it when I saw Roger A’s comment just before I slept, and hoped someone would demonstrate it while I did. 🙂
Ian says: The bottom line. The nth Fibonacci number will naturally emerge from a process of summing n steps that starts out at step one by having zero ways of choosing out of n possible choices, and that has the number of possible choices reduced by one each step and the number of ways of choosing increased by one each step. This is where I think the basic physics is involved.
I look forward to fully understanding how this links to physical processes. Or even partially understanding it 😦
As a first stab (I hope Ian will respond to by letting me know if I’m thinking along the right lines); In the quantisation fractal I posted above, there is no choice about where to place the first and second squares, because they have to be as big as possible, and there’s only one place each of them can fit. When you get to the third square size, there are two possible locations to put the first of them. For the fourth square size, there are three possible locations, and so on. At the same time, the choice of what size they are is diminishing, because they can’t overlap, and the space is filling up.
This is probably an imperfect analogy to what Ian is getting at, but I hope it may help jog some more (and better) ideas.
Stuart’s periods around 44.7
Ju-Ma=20 = 44.7055yrs
Ma-Ea=21 = 44.8407yrs
Ea-Ve=28 = 44.7646yrs
Ve-Me=113 = 44.7254yrs
Ian’s periods around 44.7
28 × VE = 44.763 years
69 × VJ = 44.770 years
41 × EJ = 44.774 years
20 × MJ = 44.704 years
The common Synods are Ma-Ju and Ea-Ve. Neither figures fully agree. I think it would be a good idea if we standardised on named sources if we’re going to collaborate on detailed analysis. 🙂
Paul Vaughan put up some tables on Ian’s Halstatt thread. Maybe we could choose which we are going to use and I’ll put them on a new ‘talkshop standard planetary periods’ page. Obviously there would be no compulsion to use them, but at least we could state whose ephemeris is being used when we diverge from them.
TB says: ’16 is 13+3 of course’.
Also 2 x 8.
Re Fairbridge and the raised beach ridges we say:
‘This is in the ratio of 1:14.5625 with the 4627.11 year cycle period.’
Further analysis shows: (233 / 144) x 9 = 14.5625
Of course 144 and 233 are Fibonacci numbers and 9 is too if defined as 3².
——-
Roger A raises an interesting point about ‘Phi or Fibonacci’ – do we have to draw a line and say ‘one or the the other’? I’d say they were two sides of the same coin, the clear difference being that Fibonacci deals in whole numbers only.
http://en.wikipedia.org/wiki/Golden_ratio#Relationship_to_Fibonacci_sequence
Consider that Fibonacci number 5 is used to derive the value of Phi in the first place:
(1 + (sqrt(5) ) / 2 = Phi
A possible view of the lower numbers in the Fibonacci sequence and the Phi equivalent:
0 = (starting point)
1 = 0.618 rounded (‘1A’)
1 = 0 + 1 (‘1B’)
2 = 1.618 rounded or ‘1A’ + ‘1B’
3 = 2.618 rounded or ‘1B’ + 2
5 = 2 + 3
8 = 3 + 5
etc.
In the natural world where Fibonacci patterns appear, clearly there can’t be 2.618 of a physical item e.g. petals on a flower. Resolution to a whole number is the only option. Planets don’t have to resolve their behaviour to whole numbers but we do see the tendency to do so, if the items listed above under the heading ‘Fibonacci ratios of note in this planetary group include:’ mean anything at all.
Note we haven’t shown all our available data yet, by any means.
TB: as you know my usual source of planetary data is the NASA fact sheets.
http://nssdc.gsfc.nasa.gov/planetary/planetfact.html
OB:TB says: ’16 is 13+3 of course’.
Also 2 x 8
A better option I think.
Further analysis shows: (233 / 144) x 9 = 14.5625
Excellent. So
4627.11 = the double Halstatt cycle.
4627.11/233 = 19.859 = Ju-Sa
4627.11/9 = 514.123.. – already very close to 514.167 and phi x 317.741
4627.11/144 = 32.1327083.. – which we found was another period at which the inner planet (plus Jupiter) synods triplets got whole number ratios.
This is getting exciting again. 🙂
Maybe we should work on the outer planet pairs synodic relations for the next post.
OB: as you know my usual source of planetary data is the NASA fact sheets.
Which is fine. Paul Vaughan and Ian Wilson are the experts on this topic. I’d like Their input to the question of standardisation. I’ve started a new thread for discussion so we don’t clutter this one. It’s a page rather than a post, so you need to visit this address to find it, until I work out why it isn’t appearing in the top menu of the blog.
https://tallbloke.wordpress.com/standards/
@tallbloke, @oldbrew. I think that nobody can demand from you an accurate approximation from computations with phi, and as long as accuracy is better than or equal to the next/possible computation step then the below is sufficient-in physics and in your remarkable thesis.
Example: fraction 1/9 was declared “rational” since one “can” always (YMMV) compute as many decimals as “pleased”, but this is sound of chimeric academic-speak. How many are “as pleased” in physical reality, and where has mother nature demanded that reality is only given when working with decimals?
This 1/9 example is, in analogy, the same with square roots of integers, like the sqrt(5) in phi. The result is always a continued fraction, in written form phi = 1;1 and the question must be allowed: who stores the instruction for computing the next decimal in an approximation of 1/9 and again: who stores this instruction for 1;1 ? (on a sideline I can imagine that mother nature always knows, as well as it knows how to make use of the smallest possible digit in this equation 🙂
It is more the usual academic theatre, nothing more than a play on words, to call continued fractions and their finite representation “irrational” when, at the same time, representation of 1/9 with its infinitude of decimals is not.
Now, since the first raw approximation of phi is 1.5 this gives your thesis ~7.3% leeway for achieving accuracy ((phi – 1.5) / phi), and so on for more steps (but less leeway!) and closer approximation 😉
I hope the previous is encouraging for your work with phi and its approximations.
Thanks Chaeremon. One of the things noticed so far is there can sometimes be more significance in the decimal places of numbers than you might think.
Re the middle numbers we reported here:
Sa-Ju-Ma 9-80-89
Sa-Ju-Ea 9-164-173
Sa-Ju-Ve 9-276-285
Sa-Ju-Me 9-728-737
…note the following multiples of 81 (= 9 x 9):
x 1 = 81 (9-80)
x 2 = 162 (9-164)
x 4 = 729 (9-728)
Also:
728 / phi² = 278.07 (9-276)
276 x 1.625 x 1.625 = 728.8
(1.625 = 13 / 8)
Expanding the data, the Ve-Me value relating to 9-728-737 is 452 (rounded).
276 + 452 = 728.
The other rounded values are:
Ma-Ea 84 (80+84 = 164)
Ea-Ve 112 (164+112 = 276)
Of course all the numbers are inter-related in a working system.
Thanks Chaeremon.
The remarkable thing is that there are several different ways of generating phi.
The Fibonacci series converges towards it, oscillating either side of phi with diminishingly higher and lower results as it does so, as I discussed above.
The infinite surd Miles Mathis found on Wikipedia is different:
In effect it takes the square root of 1, adds 1 to it, square roots the result, adds 1 to it… and so on. This approaches phi from a lower number, never quite reaching it.
Then there is the simple formula of (1+SQRT 5)/2 = phi
This tells me there is something ‘special’ about the square root of 5 = 2.236…
The Wikipedia page on the square root of 5 tells us a lot about phi too
http://en.wikipedia.org/wiki/Square_root_of_5
The section on geometry is of interest to those seeking visualisation and insight into physics.
“The number √5 can be algebraically and geometrically related to the square root of 2 and the square root of 3, as it is the length of the hypotenuse of a right triangle with catheti measuring √2 and √3 (again, the Pythagorean theorem proves this). Right triangles of such proportions can be found inside a cube: the sides of any triangle defined by the centre point of a cube, one of its vertices, and the middle point of a side located on one the faces containing that vertex and opposite to it, are in the ratio √2:√3:√5.”
The root 3 page informs us that:
“In power engineering, the voltage between two phases in a three-phase system equals √3 times the line to neutral voltage. This is because any two phases are 120 degrees apart, and two points on a circle 120 degrees apart are separated by √3 times the radius“
I’m starting to understand why Kepler was so fixated on relating the planetary orbits to the bounding spheres of nested regular solids, and have changed the graphic at the head of the post, just for fun. 🙂
TB: ‘Relative to Earth Venus spins 13 times in 8 years.’
The rotation period is 243.02 days, so that’s about 3 Venus per 2 Earth years – not 13 per 8?
Also:
7 Venus rotations x 243.02 days = 1701.14 days
29 Mercury -“- x 58.65 days = 1700.85 days
Difference = 0.29 days in 29 Me rotations.
Mercury 1700.85 x (5865/5864) = Venus 1701.14
(obviously 5865 = 100 x 58.65)
243.02 / 0.29 = 838 exactly (Venus)
Not claiming to know why all that is so but there it is. It’s not an isolated example either but that’s for another day perhaps.
Correction – should be the other way round.
Venus 1701.14 x (5865/5866) = Mercury 1700.85
Reason for reversal: 5866 = 838 x 7
An interesting aside, thanks to Paul:
The length of the VEJ Hale-like cycle is ~ 22.14 years. Paul has shown that this can be given by:
Hale-like cycle 22.14 years = 1 / [(2/J) + (3/V) – (5/E)]
The solar sunspot record shows that solar minima has realigned itself with this 22.14 year cycle over the last 400 years!
So the Fibonacci numbers 2, 3 and 5 are intimately involved with the length of the mean solar activity cycle.
There is a relationship between Pascals triangle and SSN cycle
as the base of the series builds to / Hale / Jose etc? in proportions and the fibonnacci series
All l had time for in constructing this series… l just went wow! for little me anyway!
my file source
https://picasaweb.google.com/110600540172511797362/FIBONACCI_GoldenNumbers#5919021573201722658
———————————————————-
Used Bing search engine to query string ‘ gravity simulation’ for TB
this one one link from a list of options
http://uranisoft.com/gravity/
We posted that:
‘From the outermost inwards
Ne-Ur=27
Ur-Sa=102
Sa-Ju=233’
For casual readers: 27 = 3³, and 102 = 3 x 34 which are both Fibonacci numbers, as is 233.
As these are the ‘neighbour pairs’ of the gas giants, that shows the key synodic numbers of the group from which all the other figures are derived (as shown in the post).
OB:
TB: ‘Relative to Earth Venus spins 13 times in 8 years.’
The rotation period is 243.02 days, so that’s about 3 Venus per 2 Earth years – not 13 per 8?
Venus’ given rotation rate is the sidereal period of 243.02 days; i.e. relative to the fixed stars, not Earth. In 8 Earth orbits or 4 lots of 2 years, Venus spins 4 lots of 3 = 12 times relative to the fixed stars. But Earth isn’t fixed, it moves as Venus moves. So we need to know the period of time it takes for an imaginary ‘fixed spot’ on the centre of Venus to line up with Earth again. This period will vary depending on the relative angle of the two planets to the Sun, but it will average out after 8 years, because that’s how long it takes for Earth and Venus to line up with the fixed stars again (except for the precession of the synodic cycle) at the end of the 5 synod cycle. During that time, Earth has ‘gone round the outside’ of Venus’ orbit 8 times, and Venus will have ‘gone round the inside’ of Earth’s orbit 13 times, overtaking Earth 5 times. So thinking about it a bit more, I think this means we’ll see Venus spin exactly 13-5 = 8 times *relative to Earth* (which is what matters in tidal calcs). But I might be wrong, because Venus spins in the opposite direction to the rest of the planets, so it might be 13+5, or some other number. It’s a bit of a brain twister. 🙂
Consider that the reason we always see the same face of our moon is because it spins with respect to the fixed stars at the same rate it revolves around the Earth – once per moonth. So *as seen from Earth* the moon doesn’t spin at all. If it spun at twice the rate it orbits us, we’d see it spin once a month, whereas someone on a distant star would see it spin twice. Think about this for too long and I guarantee that if you haven’t already fallen over, you’ll need a sit down and a nice cup of tea.
Universe today website says:
So why is the rotation of Venus backwards? Astronomers think that Venus was impacted by another large planet early in its history, billions of years ago. The combined momentum between the two objects averaged out to the current rotational speed and direction.
This is a load of bucking follocks. I think ‘Astronomers’ thinkers need oiling.
My thanks to the people who have kindly provided demonstrations of how Fibonacci can be derived mathematically. However, these analyses are all ex post facto. The question is how Fibonacci got incorporated into the metrics of Sanskrit to begin with, and the analyses don’t explain that.
Now I’m going to get back on topic with more questions for Tallbloke and Oldbrew. Here’s an excerpt from your list of numbers and ratios:
60 Saturn orbits equals 149 Jupiter orbits for 89 synods in 1767.44 years
60:149 = 2:5 Within 0.67%
60:89 = 2:3 within 1.1%
89:149 = 3:5 within 0.45%
102 Uranus orbits equals 52 Neptune orbits in 50 synodic periods in 8569.45 years
102:52 = 2:1 within 2%
102:50 = 2:1 within 2%
52:50 = 1:1 within 4%
The ratio of Jupiter orbits/Saturn orbits is matched to the ratio of the sixth and fourth Fibonacci numbers and the ratio of Uranus orbits/Neptune orbits is matched to the ratio of the fourth and third, and so on and so forth. Are the Fibonacci numbers assigned according to a system or are they just the ones that fit the ratios?
RA, visual translation:
J+N = Jupiter + Neptune Axial Period = JEV = Jupiter-Earth-Venus cycle = Schwabe solar cycle = cosmic ray cycle = Moscow neutron count rate cycle = Terrestrial Midlatitude Westerly Wind = Westerlies spatiotemporal volatility cycle dynamic attractor = central limit isolated from daily LOD = Length of Day &/or AAM = global atmospheric angular momentum via rigid constraints from laws of large numbers & conservation of angular momentum
If someone knows of evidence that this multiaxial differential is not balanced, please let me know without delay (& if the “evidence” is based on an orrery, please state its root assumptions — i.e. ephemeris).
I believe the same math will apply to Earth’s set of major ocean gyres (in central limit). How can it not?? (seriously — it’s no different than the differential on a car, except that it’s multiaxial)
With laws like large numbers & conservation of angular momentum, there’s hard constraint and thus clear scope for deductive reasoning that crushes standard mainstream solar-planetary narratives based on demonstrably false assumptions.
Why was Kepler so fascinated with what we call Kepler’s Triangle, eh TB??
Keep driving TB & oldbrew. Push the tach into the red. I look forward to extension of your phi explorations to solar-modulated wind-driven terrestrial ocean gyres. Here’s some inspiration:
Ocean Wave Height Annual Cycle (maximum Significant Wave Height (SWH) climatology = annual cycle animation assembled using Australian Department of Defence images developed from data provided by the GlobWave Project)
cheers
TB: re this from you…
27 x 4627.11y = 610 x 32 x 6.4y (6.4002 ‘fits’) = 233 x 3 Jose cycles
Also 32 itself equals 5 x 6.4
Roger A: Are the Fibonacci numbers assigned according to a system or are they just the ones that fit the ratios?
Just the ones that best fit the ratios. What we’ve presented is a set of coherent observations from the mass of data we’ve accumulated. We don’t yet have a ‘system’, but we’re working on it.
TB: Thanks. Is this your system?
Paul V: I couldn’t find anything on ocean gyres, but this is intriguing:
Roger Andrews says:
September 2, 2013 at 4:55 pm
‘Are the Fibonacci numbers assigned according to a system or are they just the ones that fit the ratios?’
Best fit, on the basis that’s what the system itself will always be geared towards.
Paul Vaughan says:
September 2, 2013 at 5:21 pm
Thanks for that. We may only be scratching the surface so the more tips like yours the merrier.
Roger A: Nice. The fibonacci spiral also fits the Parker Spiral quite well, which has real effects in interplanetary space. And as Miles Mathis pointed out in his second Phi paper, the spiral also demonstrates the inverse square law, which matches the falloff of both gravity and electromagnetic radiation energy. Quite how we’ll apply that insight in a ‘system’ I’m not sure yet, but some ideas are beginning to form.
I hesitate to mention it, because I doubt I could readily reconstruct or relocate it, but I once wrote, for my Vic-20, a Basic program that could take any decimal and give progressively more accurate fractional equivalents. Some routine like that might be of use here.
Brian H: Yes, fractions are good, because Fibonacci related number pop up in the fractions which are hidden by decimal strings. Of course, it’s hard to be systematic when calculating by hand, and cherry picking values has to be guarded against. As we have become more familiar with the number space and the way Phi behaves, insight is gained into the myriad ways it manifests. We are nearer the start than the end of this investigation, but there’s definitely something here worth working on.
Why not use Pluto the outermost planet. The outer orbit defines the perimeter of the system
Does the density of the system change as the outer orbit varies..
I am still Gob smacked that Volker doormanns model found the pluto couplet significant
The solar system is largely a closed system so maybe it is important to pay attention to the periphery or boundary.
Gee.. Things are really moving on this research you all must be thrilled..
Do you have a link to the annual mid latitude westerly anomaly paul? Some nice correlations there.
Does sea level in the ocean basins match the wind anomalies as well?
This all all sounding very gravitational really . Mechanics/forces..
Forces that move air mass and ocean.
Maybe if you section the solar system into pentagon or triangles? Fibonnacci style and calculate density of the sectors.
Excellent revelations emerging. Just blown away by what you are all achieving..
@ crikey
Pluto isn’t the outermost planet, although that’s what a lot of sources still say. Eris is outside it and is the same size as, or possibly a bit bigger than, Pluto.
http://en.wikipedia.org/wiki/Eris_(dwarf_planet)
We have some interesting data on their relationship which will also link to other parts of the system. Watch this space.
I don’t know whether interest in the subject has waned, but I just came across an account of how the Fibonacci sequence became incorporated into sanskrit prosody. It was reportedly developed by a certain Pangala in or around 450BC – 1,650 years before Fibonacci – based on mountains, dragons and Pascal’s triangle. Here’s the link. I can’t speak to its accuracy:
http://www.tokenrock.com/blogs/The-Golden-Ratio-in-Hindu-Mythology-806.html
Roger A: I don’t know whether interest in the subject has waned,
More revelations soon, lots of hot calculators lying around smokin’ here.
Thanks for the article link by the way.
One of the references is on-line
http://www.jstor.org/stable/i225080
Hi tallbloke, just saw an entry at WUWT for some NOAA research http://www.ncdc.noaa.gov/paleo/chapconf/bond_abs.html They are talking about sudden warming periods that occur in the arctic every 1470 years even during ice ages.
They say solar forcings and harmonics of orbital periodicities cannot be ruled out.
Their core samples seem to make this 1470 a set thing, wondering if you can tie it in to your research. If you can you are on a winner as the samples show fast warming of a few degrees and heaps of ice melt both in a glacial and interglacial, thus it is a constant. Wayne
[mod: URL typo corrected, thanks oldbrew]
oldbrew says: ‘Not claiming to know why all that is so but there it is.’
Correction: a Fibonacci-related explanation has been found. Details in a future post.
Thank you oldbrew, I think it may be important and a small key to the puzzle.
[…] Wayne Job on Oldbrew and Tallbloke: Why Phi… […]