## Why Phi? Simplified: A brief Fibonacci tour of the Solar System

Posted: October 22, 2015 by tallbloke in solar system dynamics
Tags: , , ,

A couple of years ago I made my original discovery that all the planets of the solar system are connected by golden section or phi relationships between their orbits, spin rates, conjunction periods and conjunction cycle precession periods and expressed in the Fibonacci series. I’ve been searching for a way to present the findings in a simple, clear way that anyone can easily understand. Last week, during a sleepless night of back pain, I hit on a nice solution.

All the commensurabilities in the following layout are pretty accurate for an overview of the system. Mars is a special case, being a small body getting shoved around between gas giant Jupiter and Earth. It has power series numerics relating it to a near neighbour reminiscent of the dwarf planets Pluto and Eris, which are beyond the main system, and further from the Sun’s gravitational pull. They relate more to Neptune’s orbital period.

The Fibonacci series can be generated from a quantising fractal starting with a golden rectangle split into two triangles. The series runs 1,1,2,3,5,8,13,21,34,55,89,… and is also generated by simply adding the two latest numbers to obtain the next number. 1+1=2, 2+1=3, 3+2=5 and so on. The ratios formed by adjacent numbers converge on the golden section or phi as the numbers get larger.

Enough preamble, here are the numbers. Accuracies are given as percentages in brackets.

Mainline sequence
Group-one: Neptune and Uranus – period ~168 years
1 N orbit (98%)
1 U-N conjunction (98%)
2 U orbits (99.9%)

Dividing the group-1 period and solar distance by ~3 we get:

Group-two: Saturn and Jupiter – period ~59 years
2 S orbits (99.4%)
3 J-S conjunctions (99.4%)
5 J orbits (99.9%)

Dividing the group-1 period and solar distance by ~21 we get:

Group-three: Earth, Venus and Mercury – period ~8 years
5 E-V conjunctions (99.8%)
8 E orbits (100%)
13 V orbits (99.4%)
21 V-Me conjunctions (95.3%)
34 Me orbits (98%)

Speculative spin-orbit relations in the same 8 year period

12 V rotations (99.8%) (Due to Venus retrograde spin, it’s day length is in a 3:2 relationship with Mercury’s)
50 Me rotations (99.2%) (Mercury spins 3 times during 2 orbits making 1 Mercurial day)
89 solar polar rotations (99.5%)
233 semi-solar-equatorial rotations (99.7%)

Discussion

An interesting aspect of the solution is the link between the solar radial distance differences and the timescale differences of each of the planet groupings. This hints at quantised structure in the lognormal arrangement of the solar system. Note that the quantisation node difference multipliers between group-1/group-2, and group-1/group-3 are themselves near Fibonacci numbers 3 and 21.

The long term cycles

The three main planet pairs U-N, J-S and E-V have conjunctions cycles consisting of Fibonacci numbers and which precess over long periods that also relate in Fibonacci ratios.

~3600 year U-N  cycle of 21 conjunctions
~2403 year J-S  cycle of 40x3 conjunctions (every 60 years the 3rd conjunction is within 2.5 degrees of the previous)
~1199 year E-V cycle of 150x5 conjunctions (every 8 years the 5th conjunction is within 2.5 degrees of the previous)

The E-V conjunction cycle precession period is in a 2:1 ratio with that of J-S.
The J-S conjunction cycle precession period is in a 3:2 ratio with that of U-N

Mars and the dwarf planets Pluto and Eris

Mars is pretty small at around 1/10 of Earth’s mass, and is squeezed between bigger neighbours Earth/Venus and gas giant Jupiter. It doesn’t have the punch to force its own place in the mainline series. But it does still relate to it with powers and Fibonacci numbers.

Taking the square of our group-three 8 year period we get:

34 Ma orbits = E orbits (99.9%)

Big thanks to my co-researcher Stuart ‘Oldbrew’ for this neat Mars solution and the Pluto-Eris-Neptune orbital period ratios below.

Neptune:Pluto = 3:2 (99.7%)
Pluto:Eris = 3²:2² (9:4) (99.96%)
Neptune:Eris = 3³:2³ (27:8) (99.66%)

Eris, on average, completes 0.61 orbits in 2 times the Neptune-Uranus group-1 period. This puts it in a phi ratio with the start of the ‘mainline sequence’. Note also that the Pluto-Eris group is around 2 times the distance from the Sun as the Neptune-Uranus group, giving us a 1:2, 1:3 and 1:21 set of ratios for the quantisation node point to solar distances. These are inexact, but are ‘nearest whole number’ ratios. Pluto completes 1.5 orbits in the same period of ~336 years, hence it’s 2:3 orbital period ratio with Neptune. The perihelion distances ratio of Pluto and Eris is 1:root Phi (99.5%).

Conclusion

So there you have it, order in the chaos. Take all mainstreamer stories of planets being where they are due to ‘collisions’ and throw them in the bin. Such lazy-brained thinking has no place in science. There’s a reason why Earth’s moon is the same apparent size as the Sun at full eclipse and Earth is the same apparent size as the Moon at lunar eclipse. It just hasn’t been fully worked out yet. Miles Mathis thinks it involves charge as well as gravity. I think it also involves lognormal distribution. We’ll keep working on the problem as we aim to discover: Why Phi?

1. omnologos says:

There are more things in heaven and earth, Horatio…

This reminds me of my own curious discovery about Australia, North America, Africa and the continents in general

2. tchannon says:

That’s weird omnologos

The strange earth core pattern. The underside of the crust will have a similar pattern.

3. tchannon says:

Is it collisions as well as with energy decay cogging into energy pits?

The idea of relationships is no problem, the extent is for me. From this point of view the history of the relationships would be telling.

As I’ve pointed out before this is as much a quantisation problem.

4. tallbloke says:

Tim C: Is it collisions as well as with energy decay cogging into energy pits?

Neptune and Uranus spin at very similar rates
Jupiter and Saturn spin at very similar rates
Earth and Mars spin at almost identical rates
Mercury and Venus are tidally locked to Sun and Earth, with a ratio of 2:3 between their lengths of day.

So if there have been big collisions in the past, there must also be a spin-orbit coupling transferring large amounts of energy between planetary orbits and from orbits to spin rates. And some as yet unknown principle which quantises those spins in adjacent planet pairs, along with their orbits.

The idea of relationships is no problem, the extent is for me.

The data is the data. I’ll add the percentage accuracies to the relationships laid out in the post so you can make a more informed decision as to whether the relationships are related to an underlying physics or contrived ‘numerology’.

the history of the relationships would be telling.

The fact that humans have only been writing history down for 0.00001% of the solar system’s history is one of the many difficulties involved in solving the puzzle.

As I’ve pointed out before this is as much a quantisation problem

Things get quantised by forces. But we don’t know which forces or how they’re interacting to produce these patterns in solar system arrangement. That’s the problem we need to address. My current best guess is that magnetism and gravity fall off at different rates, and that basic truth underlies the positioning of the ‘energy pits’ you mentioned.

5. oldbrew says:

TB: ‘My current best guess is that magnetism and gravity fall off at different rates’

No need to guess, magnetism follows the inverse cube law.
http://image.gsfc.nasa.gov/poetry/activity/l23.pdf

6. tallbloke says:

I wasn’t guessing that they fall off at different rates, I was guessing that this fact underlies the ‘pushing’ of the orbits and spins (possibly coupled by the solar wind and gravity?) into their Fibonacci/lognormally related positions in the system.

7. J Martin says:

No chance any phi numbers would fit glaciations I suppose ?

8. Hans Jelbring says:

Certainly there are good reasons to investigate commensurabilities among celestial bodies in the solar system. Rhodes Fairbridge introduced the term and has written some articles about them. Personally I have contributed by some which can be seen at http://www.pattern-recogn-phys.net/1/143/2013/prp-1-143-2013.pdf In my opinion these are too frequent to be a result of chance and the cause has to be found in energy transfer between celestial bodies. This means that the energetic states of celestial bodies in the solar system is more a result of long term adjustment than a result of cataclysmic events.

The question if Phi is especially frequent among commensurailities is very interesting.
At first Phi is approximately 1.6180. Phi has a number of interesting properties.

Phi-1 = 1/Phi Consider any two integers A and B ( A < B) and construct C = A + B. Continue to construct D = B + C and go on with it until you reach Z = Y + Z.

Then Z/Y is a very good approximation of Phi regardles of the number you strted with. A special case is when the number starts with:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc. which is what is mostly meant by the Fibonacci series.

Consider the following commensurabilities:

149 x T(jupiter) is 1767.47 years, 60 x T(saturn) is 1767,47 years. Call it T(JS)
89 x T(JS) = 1767.47 This is an example of a very accurate commensurability.

Observe that the Fibonacci number 89 turned up. Divide 1767.47 with 55 and you get 32.135 years not to far from 35 times the laps period between Venus and Mars mentioned above which is 32.00 years which by itself is remarkable.

Divide 1767.47 with 34 and we get 51.98 years not far from 52 earth orbital periods.
Divide the same period with 21 and you get 84.165 years, very close to Uranus orbital period.

Divide 1767.47 with 13 and you get 135.96 years which is close to 136 years. Maybe more interesting it is almost exactly 221 times Venus orbital period.

Yes, there is something about Phi. It does not seem to produce the most accurate commensurabilities but in some way Fibonacci numbers are around when a commensurability is NOT very exact but a fair approximation. Yes, I don´t think this happens by chance.

9. Paul Vaughan says:

“some as yet unknown principle”

Oh come on TB — as if any such thing can exist (…in a conventional mainstream mind).

omnologos (October 23, 2015 at 12:54 am) linked to:

The northeast-Atlantic/southeast-Asia pattern shows up on gravity maps.

What I find most remarkable is the correspondence of the Andes Mountain chain kink (around Bolivia) in South America with the southeast Asian coastline.

This deserves cross-referencing with tectonic plate, volcano, etc. maps.

Simple geometry maybe isn’t so simple to conventional mainstream minds. Is it ignorance or deception? Probably it’s mostly that they don’t realize they’re not bright enough to fool us.

10. oldbrew says:

Hans Jelbring says: ‘Yes, there is something about Phi. It does not seem to produce the most accurate commensurabilities’

It’s the most irrational number there is.
http://www.ams.org/samplings/feature-column/fcarc-irrational4

HJ: ‘Divide 1767.47 with 13 and you get 135.96 years which is close to 136 years.’
That’s 3 Saturn-Uranus conjunctions (136.01y), also 34×4 (34 is a Fibonacci number), so 1 S-U is around 4/3rds of 34 years.

11. tallbloke says:

Hans, thanks for your observations. As OB says, phi is the most irrational number. It is also the number any number pair you start with and generate a series with will converge to. But none will converge to phi as quickly as the Fibonacci series does. I think that since nature tends to be very efficient and appears to operate a principle of least action, that might help explain why Fibonacci relationships are more frequently observed than, say, Lucas number relationships.

12. Paul Vaughan says:

On omnologos’ mirror-map, look at where the Himalayas are with respect to Pacific plate intersections.

(sarc)
…but of course the mainstream knows that such geometric patterns are just “random” &/or “chaotic”.
(/sarc)

13. tallbloke says:

Paul: as if any such thing can exist

Well, maybe we’ve found one. A co-author emailed me a very interesting paper recently. You might understand it better than most (including me).

Fibonacci family of dynamical universality classes

Universality is a well-established central concept of equilibrium physics. However, in systems
far away from equilibrium a deeper understanding of its underlying principles is still lacking. Up
to now, a few classes have been identified. Besides the diffusive universality class with dynamical
exponent z = 2 another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class
with z = 3/2. It appears e.g. in low-dimensional dynamical phenomena far from thermal equilibrium
which exhibit some conservation law. Here we show that both classes are only part of an infinite
discrete family of non-equilibrium universality classes. Remarkably their dynamical exponents zα
are given by ratios of neighbouring Fibonacci numbers, starting with either z1 = 3/2 (if a KPZ
mode exist) or z1 = 2 (if a diffusive mode is present). If neither a diffusive nor a KPZ mode
are present, all dynamical modes have the Golden Mean z = (1 + √5)/2 as dynamical exponent.
The universal scaling functions of these Fibonacci modes are asymmetric Levy distributions which
are completely fixed by the macroscopic current-density relation and compressibility matrix of the
system and hence accessible to experimental measurement.

http://arxiv.org/pdf/1505.04461.pdf

14. tallbloke says:

JM: No chance any phi numbers would fit glaciations I suppose ?

Well as a general observation you might say glacial/interglacial period lengths are close to a 13:89 (thousands of years) ratio.

OB has some interesting numbers relating to Earth’s equinoctal precession period coming up soon too.

15. Paul Vaughan says:

Sun-Climate 101 Update:
trans-Arctic surface freshwater pumping and sea ice export….
(to be continued…)

tallbloke (October 23, 2015 at 7:35 pm) wrote:
“Fibonacci family of dynamical universality classes […] http://arxiv.org/pdf/1505.04461.pdf

Yes, see figure 1 top panel.

This looks like the perfect time to introduce this:

SAOT (stratospheric aerosol optical thickness or depth) spike timing perfectly coincides with 27 day heliomagnetic field (HMF) polarity persistence track shifts …so this is where BDO (bidecadal oscillation) gets a little more complicated than just Jupiter-Saturn versus Hale. J-S is there in the sea surface temperature (SST) record, but it’s Hale in SAOT.

This stuff is not for lazy minds.

Good find TB.

16. tallbloke says:

Paul: Yes, see figure 1 top panel.

I’ll get back to you when I understand the difference between a KPZ 3/2 and a Levy 3/2 🙂

As you say, not for lazy minds. But I think I’ll leave these pdf type theories to those who understand stats better than I. Hopefully they’ll explain it to me in words I can follow.

My search is for the physics in the forces. Engineer’s stuff. 🙂

J-S is there in the sea surface temperature (SST) record, but it’s Hale in SAOT.

Might this be because J-S is more about oceanic effect through LOD and AM transfer whereas SAOT is more about EM coupling via solar wind and the global electrical circuit?

17. Paul Vaughan says:

Reminder: Long-run average 27.03 day solar cycling beats with the lunar draconic month to give 11.05 years. JEV isn’t independent of J+N because N has the slowest gas giant motion on the z-axis. Look at a spinning animation of the GRACE gravity maps. On omnologos’ mirror-map the Americas-mirror defines the IOD (Indian Ocean Dipole). Lunisolar amplitude & phase are predictable, but “27.03” amplitude & phase vary. J2 (earth shape) is the big source of earth-moon uncertainty as OB pointed out a few days ago.

18. Paul Vaughan says:

TB, whatever’s going on with HMF (or confounding with HMF) it’s influencing the geometry of hydrology. The spatial pattern isn’t static. I think it comes down to shifting spatial patterns of pressure on the crust with shifting hydrology and then whenever a threshold is passed locally somewhere (keeping in mind that locales are coupled globally) due to the combination of lunisolar & solar-hydro pattern we end up with stratospheric aerosol feedback. In most cases it may be zero-sum at interannual timescale, but transients are coupled to solar cycle frequency so indeed you need a nonstandard pair of calipers attached to higher awareness to quantize sensibly. For sure the efficient avenue is identification of universals (via simplifiers like symmetry, geometric axioms, conservation laws, law of large numbers, etc.). Plenty of opportunity for deep misunderstandings provoking hatred…

19. tallbloke says:

Paul: Reminder: Long-run average 27.03 day solar cycling beats with the lunar draconic month to give 11.05 years. JEV isn’t independent of J+N because N has the slowest gas giant motion on the z-axis.

Which reminds me of something you said in another document a while back:

http://www.billhowell.ca/Paul%20L%20Vaughan/Vaughan%20130316%20-%2060%20Year%20Cycle%20of%2027%20Day%20Terracentric%20Solar%20Rotation.pdf
(65) * (365.24219) = 23740.74235 days
(23740.74235)*(27) / (23740.74235 – 27) = 27.03074167 ~= 27.03 days
Alternative verification, by looking at it the other way around:
(27.03)*(27) / (27.03 – 27) = 24327 days
24327 / 365.24219 ~= 66.6 years
Technical Aside: Anything between 27.025 & 27.035 days rounds off to 27.03 days, so theoretical rounding-related
beat uncertainty ranges from ~80 down to ~57 years.

Which would appear to bring J-S back into the frame here. The whole system is bound together with these orbital timing confluences.

20. Paul Vaughan says:

“(27.212221)*(27.03) / (27.212221 – 27.03) = 4036.561832 days = 11.0517403 years”

– –

TB wrote of “some as yet unknown principle”

may be plural …including statistical geometry of flows & force

21. tallbloke says:

Paul: For sure the efficient avenue is identification of universals (via simplifiers like symmetry, geometric axioms, conservation laws, law of large numbers, etc.)

I can see that this approach may well LEAD to the identification of the underlying classical physics. That’s why I’m interested in all methods of approaching the problem. I’m just not sufficiently well equipped to juggle the more esoteric maths involved. I’m hoping something will come out of that approach which will point the way to the correct parameterisation of the physical model which can successfully replicate the continual shuffling and shoving which maintains the stability of the system.

22. tallbloke says:

Paul: may be plural …including statistical geometry of flows & force

Very likely if magnetism is involved. Probably why the mainstreamers have steered clear and stuck to whirling poolballs.

23. Paul Vaughan says:

TB wrote:
“Which would appear to bring J-S back into the frame here. The whole system is bound together with these orbital timing confluences.”

Indeed.

Osculating JEV cycle length has imprints of both bidecadal & “60 year” Jupiter-Saturn geometry:

24. Paul Vaughan says:

I’ve dug into some of the key references of “Fibonacci family of dynamical universality classes” with all the time I could spare for such an exercise. Mostly they go on about coupling and kinetic aggregation and how the macroscopic patterns are NOT determined by microscopic properties and it’s a sh*tload of unnecessary words and equations to say something intuitive that could be said a lot more concisely so unless someone can point to an infinitely more terse distillation I conclude that this is just stuff I’ve seen decades ago expressed differently, adding nothing to my ability to explore (….but of course I do hope someone points to some infinitely more terse distillation that falls well-outside of what I’ve ever encountered before…. always watching for & hoping to stumble upon such revelations, epiphanies, whatever-you-want-to-call-them…)

25. Paul Vaughan says:

So the best I can take from this is the idea to tweak wavelet parameters based on a hybrid of this Levy-stable stuff and the arcsinh stuff TC pointed to some time ago.

And does that yield any deeper exploratory insight?

No.

Any way you slice it (whether 3/2, 5/3, or whatever) this is still there:

https://tallbloke.wordpress.com/2015/08/11/niv-shaviv-nice-one-the-sun-still-is/comment-page-1/#comment-106030

That holds via geometric axioms and conservation of angular momentum no matter the parent distribution due to the law of large numbers.

To wipe that out nature has to go Cauchy …and then you’re still not immobilized as an explorer because there’s the median estimator …and nature in this case is not Cauchy anyway — this we know empirically, so we need not waste time on theoretical musing divorced from observation.

So this parameter has no key impact on exploration (…but others I’ve mentioned in the past do: sampling resolution, oscillation grain, envelope extent, & support span).

But does this parameter matter for modellers?
That’s a question for them (…& perhaps for their critics).

26. tallbloke says:

Paul Vaughan says:
October 23, 2015 at 11:18 pm
Osculating JEV cycle length has imprints of both bidecadal & “60 year” Jupiter-Saturn geometry:

That’s an interesting plot. Can you show us what it looks like over a longer period? Say 400 years covering the sunspot record and up to 2100?

27. Paul Vaughan says:

I’ll see if I can find time to dig out the old files next week TB.

Today I’m exploring the feasibility of estimating the proportion of first- & multi-year sea ice using indices of north & south sea ice extent, semi-annual LOD, & annual LOD:

It looks like wind & rain (via cyclone track) assault halocline depth & ice.

It’s nonlinear of course (due to latent, not just sensible heat). Amplitude divergence in the more recent record indicates an increase in the proportion of young ice that’s destroyed with less effort because it’s so much thinner.

I’m convinced already that this is a money shot. It’s the kind of relationship that decades from now will taken as obvious & simple.

To tie this in:
There are probably some golden means (phi) in ice geometry if anyone bothers to look.

28. Paul Vaughan says:

From the links listed lower on that page you might also like this provocation:
http://mb-soft.com/public3/gravit33.html

(“Technically, this is NOT really a Violation because there is an external force acting on the gyroscope, which is the Earth’s gravitation. In the Solar System, there is also an external force acting on the Perturbation of planets with each other, the Sun’s gravitation.”)

29. tallbloke says:

Thanks Paul, the key passage (for me) is just below the one you quote (my bold):

“It has been assumed by all astronomers and Physicists that planets can perturb several parameters of the orbits of each other, BUT that they could never alter the semi-major radii of each others’ orbits. That conclusion WOULD be true IF all the objects in the Solar System orbited in exactly the same Plane. But they certainly do not.

The Solar System objects move in various planes. This fact results in effects that are similar to the non-Conservation of Angular Momentum of the toy gyroscope. Examples are the Earth’s Precession, the Regression of the Nodes of the Moon’s Orbit (and all other orbits), and any other perturbations where the Z-axis is involved. Planets ARE causing precessional effects in each other. Now that the precessions are all established, no significant violations of Conservation of Angular Momentum SEEM to occur, but whenever each of those precessions CHANGES, that is, they ACCELERATE, they certainly represented clear violations!”

Ray Tomes original insight on the possible Z-axis pertubation of the solar core relative to the envelope by the Z-axis motion of the Sun relative to the CMSS caused by planetary motion may yet prove to be the key mechanism driving solar variability.

In my view it also re-opens the question of the extent to which Earth’s LOD may be externally forced by Jovian motion. The Gyroscope discussion linked by OldmanK brings this into the open nicely. Although the authors state that energy providing the instantaneous gain in AM is from gravity, not from the AM of the gyroscope flywheel, it can be seen that when a spinning gyroscope is forced off-axis, the AM of the flywheel is affected. This is due to bearing friction, and the Earth doesn’t run on bearings. However it does probably have two ‘dynamos’, one in the core orientated mostly by the Earth’s spin axis and one in the magnetosphere, mostly orientated by the solar wind. These will interact magnetically, and when one is forced off-axis relative to the other, the EM coupling will change the spin rate, slower or faster. I wouldn’t be surprised if heat isn’t generated too, by back-EMF due to inertia. There does seem to be some correlation between volcanic activity and LOD variation. Maybe this is due to more than crustal deformation by shifted water mass perhaps involving reorientation of the plumes of heat convecting in the vortices formed around the outer core.

30. My question is what would happen if one of the planets in our solar system got impacted by an SUPER LARGE asteroid or a super nova took place what would happen then? Or one of those wondering planets came into the solar system or a neutron star?

What happens to the order of things then that have been concluded during stable conditions, from this process (FIBONACCI) that was presented?

31. tallbloke says:

Hi Salvatore, good question!

If our theory is correct, the system would self correct to regain stability, though there may be a couple of casualties along the way. Clearly, the bigger the perturbation, the longer the period of instability would be.

32. oldbrew says:

You wouldn’t want to get in the way of this one.
http://www.nasa.gov/mission_pages/asteroids/news/asteroid20121214.html

33. Victor Petri says:

Complexity grows exponentially with the Golden Ratio, Phi, and has done so unabruptly since the beginning of time, and will continue to do so until the end of time.

https://humansrunderrated.wordpress.com/2013/04/18/70/

Are my findings with the Golden Ratio.

Why Phi? Because Phi is the only exponential growth value that allows equal growth independent of scale (that’s why you can zoom in on a nautilus shell and still see the same proportions).

34. tallbloke says:

Hi Victor, and welcome to the Talkshop. That is a very interesting comment, and one which I will think very carefully about. Having seen the way fibonacci packs around a torus shape, I think I agree, but I need to investigate 3D spirals Like nautilus shells and the way their proportions change with scale. If you have any numerical analysis you can point to, that would help save me from ‘re-inventing the wheel’ (or spiral). – Thanks

35. Victor Petri says:

@tallbloke
It is in the very definition of Phi
Looking at:

When something is growing, and the future size is dependent on the actual size in the same ratio as the actual size was dependent on the previous size (a+b is to a as a is to b in picture) you have an exponential growth rate that is scale independent (e.g. at any time your future growth as with respect to your current size is in the same ratio as past growth).

36. Chaeremon says:

@Victor Petri (October 27, 2015 at 1:35 pm): the much I appreciate you article about Complexity Emergence and Phi, the easy it appears your hypothesis is disproved by counterexamples 😦

Take the plasmalemma as example, for simplicity we can ignore innovations since its invention. And now, you can determine the past but not the future in your formula about time. The plasmalemma does not change its complexity, its function and purpose must stay as it is, no?

37. Paul Vaughan says:

TB I guess you noticed the bit about near-commensurabilities?
I figured you’d much like that as well.

38. Victor Petri says:

@Chaeremon
Iron has stayed iron since it was formed in stars billions of years ago.

As I try to explain, only mankind is on the path of ever increasing complexity, as our evolutionary history clearly attest.
Consider this illustration of my hypothesis:

39. oldbrew says:

Not long ago we posted this: ‘Why Phi? – a triple conjunction comparison’
https://tallbloke.wordpress.com/2015/06/14/why-phi-a-triple-conjunction-comparison/

It can be easily expanded for triples of Mercury (5 J-S-Merc), Mars (89 J-S-Mars), Uranus (89 J-S-U) and the ‘Grand Synod’ (233 J-S-U-N).

These are all Fibonacci numbers.

A case can also be made for dwarf planet Ceres (34 J-S-Ceres).

40. oldbrew says:

‘The Solar System objects move in various planes. This fact results in effects that are similar to the non-Conservation of Angular Momentum of the toy gyroscope.’

Find out why the objects move in different planes and the apparent problem may be solved.

‘After that, the precessional speed ACCELERATES during the following three months, up to a point where the precessional SPEED is greatest around June 21 and December 21 each year. After that, there is a DECELERATION of the precessional speed during the next three months, to get back down to the zero precessional speed.’

Acceleration and slowing down is a characteristic of an elliptical orbit.
Perhaps the solar system itself could be in such an orbit 😉

41. oldmanK says:

Salvatore>> ” Or one of those wondering planets came into the solar system”. This question was looked into by W Woelfli/ Baltensperger “AN additional planet…..” 2008. What would one experience as gravity from the combined pull? Something as in biblical Enoch “And in those days, Noah saw the Earth had tilted and that its destruction was near”. The combined pull is not vertically downwards, if one can tell where the vertical would be.

TB>> Angular momentum and precession are not the only questionables. The first term in the obliquity equations (all of the variants) is an empirical number, the ‘as is’ but not necessarily the ‘as was’. Salvatore’s question and the fact that the earth is an oblate non solid object can lead to various possibilities.

42. Wayne Job says:

Hi Tall bloke,
I am involved in an experiment that has been forty years in the making, results thus far spectacular, two more experiments over the next two weeks and we are finished. I would like you to get the results and all the background as dissemination far and wide is important as what we have found confounds the standard models. Wayne

43. Asynsis says:

I conjecture that it’s computational complexity universality via asynsis constructal energy optimisation – ultimately an animate universe signature: https://medium.com/@ASYNSIS/cosmogaia-2ffa281c73d