Considering this material as an example of entrainment by harmonic resonance produces the following observations.
Harmonic cycles in the solar system that are in close numerical relation to each other, especially through duple and triple cycles, are likely to be connected to each other by resonance. The SSB/GY harmonic relation is an example of combined duple and triple cycles. The relation between these numbers is the same as the relation between a low C, a middle G and a high D in music, connected by the duple relation of the octave and the triple relation of the perfect fifth, with the low C corresponding to the precessional wobble cycle of the earth’s Great Year, the high D to the solar system barycentre, and the middle G to their point of harmonic contact in the temporal structure of the zodiacal age. G stands in 3/2 relation to both C and D. In the specific notes corresponding to the SSB/GY model, the middle G is the square root of the GY period when the SSB is the unit.
I do think it is plausible that there is a ‘lock-in’ mechanism at operation in this entrainment. To understand this we need to imagine the whole solar system as a spinning top, with myriad cycles all in harmonic relation to each other. This system is highly isolated, as far from other stars as a spinning top in the middle of a sport arena is from spectators. So, considering the celestial dynamics of the system, there is nothing more fundamental than its own gravitational cycles to produce the internal rhythms of the system. These cycles are integrated in the SSB movement, which has been shown to have a clearly defined 179 year pulse.
In this isolated long term stable dynamic structure, our solar system has a basic frequency, the SSB cycle, with a constant wave length of 179 years, while earth also has a basic frequency, the Great Year, of length 25765 years. I call the Great Year the basic frequency because its gyroscopic wobble is the main long term dynamic cycle of the earth.
I think it is highly plausible that the ‘high D’ emitted by the SSB produces a harmonic resonance in the ‘low C’ emitted by the GY to produce a ‘middle G’ in the form of the 2147 year long precessional age. Again, we can model this in musical harmonics. Setting up an organ or engine to produce a low hum in an acoustic chamber, and then playing a high note with frequency 144 times that of the low hum, it is possible to create a harmonic relation at the 12 times level, ie a high D against a low C can make a middle G.
It is well known in music that intervals of precise natural multiple frequency lock in to each other, while out of tune notes can have a shuddering dissonance.
Thinking of the earth in the maelstrom of solar dynamics, it is like our planet is tumbling through space supported by a web of interacting bodies, all of which are in an overall ‘shepherding’ relation to each other. Lunisolar precession produces 99% of the basic structure of the Great Year, but the pace of the wobble is regulated by the remaining planets, principally the JSNV 179 year SSB cycle.

The attached picture incorporates material from discussion into the OP diagram. It shows the JSNV conjunction cycle, whose main current sequence runs from 1881 to 2060. It also shows the JS sunspot cycle with arrows showing predicted dates and ovals showing how the JS wave cycle relates to the secondary waves over three cycles. The alignments of Sun, Venus, Jupiter, Saturn and Neptune produce a pronounced spike in the SSB graph. Alignments of these four planets and the sun can be seen by comparing ephemera for 2060 and 1881.

Attached Images

COM POS 1500-2100 Sunspot JSNV 179 year phase.GIF (64.3 KB, 5 views)

Well, this is your proposal. If you want it to stick, you should be willing to do the work.

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"Reality is that which, when you stop believing in it, doesn't go away."
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"A lie can travel half way around the world while the truth is putting on its shoes."
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Avatar courtesy of Bunny.

You jest. The cake comment was just in relation to a suggestion from Warren Platts that I use Newton's law of gravity and a spreadsheet to make a table of the relative effects of all planets on the position of the centre of mass to see how significant earth and Venus are compared to the outer planets. Such a table would inform but not affect the findings I have presented, and does face the rather tricky three body problem in spades. I was simply hoping that some cooperative soul might have ready access to this data and could point me towards it. The mathematics of SSB calculation were a concern of Sir Isaac Newton. His work using planets out to Saturn has since been refined with the discovery of the outer gas giants. It should be easy to find a table listing the relative contributions of all the planets to the SSB movement pattern. Such a table is somewhat incidental here. Analysing the dynamics of the planetary contributions would extend the cyclic decomposition of the available SSB data, but there is more than enough to research the existing JPL dataset which integrates all planetary contributions to the distance between the sun and the centre of mass.

Let's clear up an apparent misunderstanding here. A remote planet's effect on Earth's precession is proportional to the gravitational torque it imposes on our equatorial bulge. That torque is not necessarily proportional to the outer planet's displacement of the Sun and inner planets relative to the barycenter.

Let's analyze a simplified example starting with only the Sun, Earth and Jupiter. The presence of Jupiter displaces the Sun about half a million miles from the barycenter. Earth's orbit remains roughly centered on the Sun but is perturbed by Jupiter's gravity, which also imposes a precession-inducing torque on our planet.

Now let's add another planet of Jupiter's mass ten times farther out. To maintain dynamic balance, the Sun will now be about 10 times farther from the barycenter, with Earth's orbit going along with the Sun. However, the new planet's contribution to the torque on Earth will be only about 1/1000 that of Jupiter, because that effect drops off as the cube of the distance, for the same reason as the dropoff of the tidal force. This planet's perturbation of Earth's orbit is reduced by a comparable amount.

Conclusion: A distant planet's perturbation of an inner planet in any way is disproportionately small in proportion to its contribution to the barycenter position.

My rough estimates are that Saturn's torque is only a few per cent of Jupiter's. Uranus contributes about 1/1000 as much as Jupiter, and Neptune even less. Venus averages about as much as Saturn, and at inferior conjunction peaks at many times that of Jupiter.

More on this later. I have an appointment coming up and I must quit for now.

Here are some of the numbers I calculated.

_____Mass (Earth = 1)__Torque (Jupiter = 1)_________Barycenter displacement (Jupiter = 1)

Sun___333,000______________147,000____________

Moon____.0123______________326,000_____________

Mercury____.04__________________.018_____________. 00001

______________________Max.__Mean____Min
Venus______.82_________17___.363____.071_________. 0003

Mars________.11_________.821___.049___.003________ .0001


Jupiter_____318_________2.28____1.00___.52________ _1.00

Saturn______95__________________.048_____________. 548

Uranus______15__________________.0009____________. 169

Neptune_____17__________________.0003____________. 312

The large amounts of barycenter displacement from the three outermost planets made the familiar 179-year pattern clearly visible, but look how tiny the corresponding torque shares are compared with Jupiter. For a remote outer planet of any given mass, the barycenter displacement is proportional to its distance from the Sun, but its precession-inducing torque on Earth is inversely proportional to the cube of the distance. On a graph of this torque the 179-year cycle would be virtually invisible.

Meanwhile Venus packs a wallop at each inferior conjunction, peaking about 17 times Jupiter's average amount. Mars comes close to Jupiter at close oppositions.

Clearly, Venus, Mars and Jupiter are the heavy hitters, and their effects are very much lightweights compared with those of the Sun and Moon. I stand by my arguments in a prior post that even relatively strong torque pulses would not shepherd the precession rate into a resonance, and the effects of the tiny magnitude of the pulses from the outermost planets appear to be vanishingly small.

Thanks Hornblower, this sets a quantitative context for my argument. You have showed that Neptune and Saturn have miniscule direct causal effect on the precession period. This falsifies the hypothesis that the outer planets are a main direct causal factor governing the precession period. It is great to set the discussion in a quantitative context. However, it does not address my observation that these harmonised cosmic patterns participate in a system-wide resonance period of 179 years, as does the earth. This gives the data behind Warren Platts earlier comment that torque means Venus is a much bigger contributor to the precession period than Saturn, Uranus and Neptune. Warren also pointed out there are 112 Venus-Earth cycles in 179 years. I think this suggests the Venus torque is a strong regulator for the precession period. This Venus cycle is in common ratio with cycles of the outer planets, all of which share a common pulse period of 179 years. Considering planets as like regulators, such as on a steam engine, the overall harmonic phasing of the system remains a scientific issue open to further research. Thanks for the good summary. My view is that your finding on Venus did indeed show a relatively strong torque pulse that WOULD shepherd the precession rate into a resonance. Essentially, we have Venus buzzing by us every just under phi years, a period in quite precise resonance to the Jupiter-Saturn-Neptune cycle over 179 years. So, there are a set of related harmonic ratios in the solar system, with both gravity and torque producing events which share a 179 year period. I am asking if there is some underlying harmonic resonance which combines gravity and torque in complex cycles.

Wrong. The period for the precession of the equinoxes is almost entirely (99.8 percent) due to the torques of the Sun and Moon on the Earth's equatorial bulge.

For a calculation as elementary as I can make it and present it here, see the precession dialogues:

Part One, Part Two, Part Three, Part Four, Part Five, Part Six, and Part Seven.

The planets have very little effect on the precession of the equinoxes. The fact that at the moment, given the current obliquity, that it equals nearly 144 periods of motion of the solar system barycenter is coincidence and nothing more.

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Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

Everyone knows that the Sun and the Moon are the "mainspring" for driving the Earth's precession. The question is whether Cytherian zyzygies that are in turn calibrated by the Sun's orbit around the SSB might possibly act as an escapement mechanism that could improve the constancy of the precessional period:

That is, the precession might be like a giant gearwheel in the sky with 144 * 112 = 16,128 teeth

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Fitting a three-parameter curve of uncertain form to ten points with three exceptions certainly brings one to the far edge of the known world. -- Bradley Ephron

Try using the "code /code" command for tables. It's supposed to print everything like an old courier typewriter:

but it still takes some fiddling, and so it's still a pain . . . . but at least it's possible to get things to line up using spaces rather than underlines.

__________________
Fitting a three-parameter curve of uncertain form to ten points with three exceptions certainly brings one to the far edge of the known world. -- Bradley Ephron

Warren, thanks for your technical advice on putting tables into the message box.

I continue to stand by my argument that the frequency of our torque pulses is of no significant importance in analyzing the precessional response of a gyroscope. To repeat, for all of our readers including the OP: If I am not mistaken, the gyro does not rebound and oscillate in response to a momentary pulse. It simply nutates and precesses a small amount and then stops in a new position when the pulse subsides. A sustained series of such pulses eventually will nudge it around a complete revolution, and if the steps on the next cycle do not line up with those of the previous cycle, it is no big deal that I can see.

When I said that Venus "packs a wallop", I was only comparing it to Jupiter's component. It still is tiny compared with what the Sun and the Moon are doing all the time. I would predict only a vanishingly small amount of nutation from Venus and virtually no measurable pulsating effect from the other planets.

You wouldn't know it from some of the twaddle in this thread, other threads, and some web sites.
Come on, Warren, get serious! Celestial mechanics have not believed in crystal spheres, gears, pulleys, "mainsprings" and "escapement mechanisms" as the cause of celestial motions since the time of Copernicus.

Newtonian gravitation is sufficient to explain the precession of the equinox. My precessional dialogues that I am always linking to calculated only the main lunisolar terms of the precession and got within 0.2 percent of the measured value. I was off by this amount not because of neglected causes such as the planets and higher order moments, but because in the interest of brevity and keeping the discussion elementary I ignored the eccentricities of the Earth and Moon, the inclination of the Moon's orbit, and the variational inequalities in the Moon's orbit. I hope to carry out a calculation soon that will take these into account as far as the squares of these small quantities and I expect to get within a tenth of a second of arc per century just from this alone. The contributions from the planets, relativity, and higher order moments are quite small. The flitting about of the Solar System barycenter is entirely irrelevant to the matter of precession.

__________________
Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

Well, I didn't mean it literally.

You're the expert, of course, and so I'm almost positive that you (and Hornblower) are correct and that me and Robert have got it wrong. But let me get this straight: You're hoping to nail down the precession to within a tenth of a second of arc per century without taking the planets into account at all? Because I found this paper on Earth nutation theory (RESOLUTION B3: ON NON-RIGID EARTH NUTATION THEORY proposed by Joint Discussion N. 3 and endorsing the conclusions of the IAU-IUGG Working Group of The XXIIIrd International Astronomical Union General Assembly) where down toward the bottom, they recommended that when developing more refined models, "the perturbing bodies to be considered: in addition to the Moon and the Sun, the direct planetary effects of Venus, Jupiter, Mars, and Saturn, should be included."

Granted, nutation and precession are different processes; but aren't they related? If so, wouldn't it be possible for nutations to have tiny effects on the precessional period?

__________________
Fitting a three-parameter curve of uncertain form to ten points with three exceptions certainly brings one to the far edge of the known world. -- Bradley Ephron

Yes to both very good questions.

Nutation is a nodding or bobbing motion of the spin axis that occurs when a varying torque is applied.

Let's start with a simple model in which a gyro is spinning and processing under a steady torque. Now apply some additional torque momentarily, in a direction that would reduce the obliquity of the axis. Initially the axis rises slightly, and then levels off as the precession comes up to speed. When the torque is shut off the obliquity comes back down and levels off as the precession reduces to its original rate. That obliquity variation is the nutation. If the pulses are repeated throughout a main cycle the spin axial pole traces out a wavy pattern instead of a simple circle, and the average precession rate is slightly faster than it would have been without the pulsating component.

In this model the large steady torque corresponds to the lunisolar torque, and the small pulses correspond to Venus at inferior conjunction. The latter come at intervals of 1.6 year, but are not all of the same magnitude. Any gravitational torque is at its maximum when the object is at solstice longitude and is at or near zero at the equinox longitude. Thus that 1.6 year cycle is modulated by the 8-year cycle in which conjunctions of Venus return to the same ecliptic longitude. Not a simple pattern.

In actual fact the lunar and solar torque components are not constant. Again, this is because of the dependence on the declination of the perturbing body. The former occurs in two big pulses per month, and the latter in two per year. That alone gives us some nutation at those frequencies. In addition the Moon's orbital inclination to the equator varies widely over a period of 18.6 years, causing the magnitude of its torque to vary with that frequency. This gives us the bulk of the nutation, about 9 arcseconds on either side of the mean position.

My reasoning above is based on what I read in that link I posted earlier. The author's style (gratuitous exclamation points, etc.) and some of his hypothetical applications are a bit quirky, but I think his basic theoretical exercises in the mechanics are correct.

I am not denying an effect on the precession rate by the planets. I merely argued against any sort of shepherding resonance.

Solar system torque produces precession of the earth’s equinox (the Great Year GY) and solar system gravitation produces regular cycles of the solar system barycentre (SSB).

These torque and gravity cycles are in harmonic ratio at 1:144, suggesting that investigation of resonant relation could uncover an underlying governance regulation entrained in contained complex systems. In direct terms, the precession is like an acoustic chamber into which the SSB projects a resonant wavelength. The SSB resonance does not directly regulate the precession period, any more than an opera singer makes a wine glass that their voice can shatter.

There may be an indirect physical relation (harmonics) whereby the SSB and GY participate in a deeper common order of the solar system. The Venus-Earth cycle of 112 conjunctions per 179 years could illustrate this linking factor between the SSB and GY.

12:1 resonances of the wavelengths of the Great Year (GY) precession and the Solar System Barycentre (SSB) produces the ~2147 year period of the Zodiacal Age (ZA). The equation is: 144:12:1 = GY:ZA:SSB = 25764:2147:178.9 years. As a musical illustration of the ratio, both SSB:ZA and ZA:GY have the same 12:1 perfect fifth wavelength relation as the guitar strings bottom E and the 1/3 harmonic (7th fret) B of top E. The SSB and GY cycles have underlying causal connections which produce combined effects at this common 12:1 harmonic resonance.

Due to this shared perfect fifth harmonic relation between wavelengths, the 2147 year period of the zodiacal age is the harmonic common point producing a physical relation between the SSB and GY. The zodiacal age is the period over which the equinox precesses against the galaxy by thirty degrees, in periods defined as the signs of the tropical zodiac. The harmonic SSB-GY resonance seen in the zodiacal age provides a mathematical harmonic basis for the signs of the zodiac, a fundamental structure for the physics of tropical western astrology.

Using this astronomical framework to structure time, history can be interpreted in 178.9 year SSB blocks. Such a series of blocks can take as arbitrary starting points the years 0, 179, 358, 537, 716, 895, 1074, 1253, 1431, 1610, 1789, 1968 and 2147. These modern periods begin at Galileo’s discovery of the moons of Jupiter, the French Revolution and the closure of the Sorbonne. These blocks illustrate the phasing of the SSB cycle, aggregating to the zodiacal age and Great Year, providing an empirical framework for the historical structure of time.

The JSNV cycle is similar to the Saros cycle of eclipses. Successive JSNV cycles begin and end due to the small misalignments within the JSN cycle. In overlapping ~1500 year periods, successive families of JSNV conjunctions separated by 179 years start out weak, become precise and then weaken again. (The Saros Cycle could be called the Anne Elk dinosaur theory of eclipses, in that eclipse families start thin at the pole, become fat at the equator, and are thin at the other pole over their 1300 year life).

The JSNV alignments advance by one tropical zodiacal sign per 179 years. During the zodiacal age in which the March equinox is precessing through the constellation of Pisces (~0-2150), the JSNV alignment occurred in Pisces in 53, in Aries in 232, in Taurus in 411, in Gemini in 590 and between Cancer and Leo in 769, petering out through 948, 1127, 1306, 1485, and 1664 to a wide orb in Aquarius in 1842-4. The closest JSNV conjunction in this cycle, marking its centre, is in 769. A new ‘Saros’ cycle of JSNV conjunctions had a centre in Pisces in 1524, succeeded in 1703 in Aries, the current phase beginning in 1882 in Taurus, and a next phase from 2061 in Gemini. The JS cycle slips against the JN and SN periods by about 0.2 years per cycle, so Neptune now conjuncts a different wave peak of the nine-phase JS 19.8 year cycle every 179 years than it did 2000 years ago.

To indulge in an astrological comparison, we see the JSNV conjunctions in Pisces in 54 and 1524 occurred when Paul and Luther wrote major documents informing successive phases of Christianity, events with strong symbolic parallel.

Due to multiple simultaneous cyclic planetary inputs, the 179 year phasing of the SSB cycle is a librating constant, as is the GY. Fourier analysis should be able to decompose the relative power of all wavelengths within the complex SSB structure.

Uranus has a dissonant effect on the 179 year SSB structure. The effect of Uranus can be seen in the SSB graphs as a secondary wave precessing against the JSNV 179 year wave at a rate of 7 years per cycle. I assume this secondary wave is a product of the 7 year difference between the 179 year JSN cycle and the UN cycle of 172 years.

Post #105 looks like nothing more than paraphrases of prior posts, including some from previous ATM threads that timed out a long time ago. I see no further evidence that the roughly 144:1 ratio of the precessional period to the interval between the familiar giant planet patterns is indicative of an actual resonance of any kind. If human eyes could see to a limiting magnitude of 9 rather than 6 or so, and see Uranus and Neptune without optical aid, this could be right out of ancient times, before the emergence of our modern understanding of orbital and spin dynamics.