The key thing, for now, is that you did not use any of these in the analyses that you are presenting here (and which should so form the first things that other BAUT members question and challenge).I am trying to distill down to just the astronomical results you used as input; I've highlighted (bold, colour) what I think they are, based on what you said above.

Have I matched your words with the lines and numbers correctly? If not, please clarify.

What is your source for "the distance to Andromeda galaxy"?

What is "a long term solar system energy exchange cycle inn the outer planets"?

What are "[the] astronomical cycles of planetary orbital interactions and precession of equinoxes"?

What are "long term alignments of the outer planets and climate cycles"?

What is "the 155 day solar cycle"?

What is your source for "the Sun's rotation period"?

To what extent do your criteria for acceptability extend to consistency between good, relevant experimental and observational results?In this ATM idea you are presenting here, what is the status of the observational results that are often stated as providing strong support for modern concordance cosmological models*?

*Olbers' paradox, the CMB, primordial abundance of light nuclides, large-scale structure.

No, this set MY 0.469,0.231,0.1868,0.1506,0.118 are all Afanasiev geological cycles.I found several sources that all stated either 2.2 or 2.25 million light years. These are no doubt very old sources now. I simply used the average.
This was a reference to a long term integration of planetary motion over many million years. Somewhere I do have the reference to this but would need to look through about 10 note books to find it. If I remember correctly it was a slow energy interchange between Jupiter and Neptune.
The precession of the equinoxes is the time for the equinoxes to complete a full rotation. The other two are the only ones used that are my own work and may not be found elsewhere. They are periods after which the various orbital elements of the planets tend to return to similar alignments relative to each other. This applies to the alignments of the ellipses and maybe also the node. There are some groupings in the element motions but they are not very tight groupings. If I was trying to convince scientists, I would probably leave these ones out as being unknown factors.
There are a number of periods after which more similar planetary alignments occur. These are listed as 4600 and 2300 years in a Cycles book I have with an article by Rhodes Fairbridge, but I originally got from another book entirely by H H Lamb in which he states the comparison with climate and planetary cycles. Fairbridge and others tried to show connections between the motion of the centre of mass (COM) of the solar system relative to the Sun as a factor in solar changes and climate. the exact figures that I use are my calculation for average planetary alignment intervals. One of these (I think 2317 years) is f=3J-S-U-N where J, S, U and N are orbital frequencies of the 4 gas giants and f the resulting frequency. It is the interval between times when especially similar alignments of these 4 planets occur. There is a shorter period ~170 years also. These are reasonably standard ideas.I gave scientific peer review references to this in my earlier post #33. If you are making a complete list of astronomical cycles only, then the 77-78 day, 51-52 day cycles and seveal others mentioned in those articles should also be included. They were unknown to me when I did the earlier work. However I would point out that they all exactly fit the calculated pattern derived before they were known. This is a good test of a theories usefulness.
I don't remember. It is intended to be the equatorial rotation period. Wikipedia says 25.38 days, which is much the same.

Hi Nereid

I just typed a long reply and my darn malfunctioning keyboard deleted it. Will try again.

I am not sure I understand your opening part above, so if this isn';t what you wanted, please explain.

I see no conflict with GR or QM except that I think Narlikar's allowing particle mass to be variable is a correct idea. The main conflict is with big bang because I think that harmonics theory requires multiple cycles of teh longest cycle which will be greater than 10^10 years each. It is essential that the universe have communication between its parts to have standing waves that develop harmonics. Acceleration in big bang is a step in this direction. Those that talk about a bouncing big bang or oscillating universe are consistent with harmonics theory. If big bang is wrong I need to explain about red shift meaning and CMBR.

I have already explained the red shift. For CMBR I think the most likely explanation is thermalization of starlight. Calculations of this were first shown by Eddington before the big bang was thought of and show a 3K value is expected. This means that Olbers paradox is not an issue.

In harmonics theory, the wave structures of particles are understood as standing waves with frequency and wavelength derived by Compton frequency. The compton frequency for nucleons is also about the same as the radius measurements, or 1.3x10^-15 m. If you consider these waves with the known density of the universe it turns out that by about the Hubble scale all tyhe outgoing part of the nucleon standing waves will have come to another nucleon and become incoming waves. Because waves expand as spheres the area is proportional to teh square of the distance. This explains why at a distance of 10^40 times the nucleon size the surface is 10^80 times a nucleon area and teh waves do not propagate further. This explains the event horizon and also the LNH (Large Numbers Hypothesis) of Eddington and Dirac.

Note added later: there are ~10^80 nucleons with a distance of ~10^40 nuclei radii of us.

Harmonics theory explains large scale structure (indeed all structure) far better than any other theory. Without any parameters to vary it gives all the structure. I was arguning with astronomers in usenet in 1994 about this and they said the universe was uniform at large scales and I said it wasn't. I got proved right.

The production of elements is not something I know much about. I do know that Fred Hoyle had an idea that he called "littel bangs" which were repetitive events around the universe. This sort of thing is expected in the harmonics theory. In general all the marginally scientific ideas about catastrophes are explained because at various time intervals many smaller cycles all come together with a longer cycle and huge amounts of energy converghe in certain places (the nodes of the big waves). This will apply to the 586 MY geological cycle and the mostb intense places will be the peaks of teh 128 Mpc wave that I showed earlier. That is why the mass extinctions occur at 26.65 MY intervals.

I am a great believer in observational data. I enjoy it when people like you look at things that way. You have to test a theory against the data, not other theories. Thank you!

Regards
Ray

Just found that I have a labeled version of the common cycles graphic.



I would say that the best estimates from averaging many reports of all these cycle periods are in years:
0.99, 1.98, 2.67, 2.96, 3.39, 4.22, 4.45, 5.54, 5.92, (6.4) 7.91, 8.89, 9.3, 9.63, 11.1, 17.8, 18.6, 22.2, 35.6, (42), 53.5.

Not shown are shorter cycles of 0.33 and 0.66 years. The 0.33 years is the 17.16 weeks one in sunspots. It was actually the first cycle I ever (re-)discovered when I was 16 from Sky&Telescope sunspot numbers which I plotted.

Additionally, solar cycles in days:
155, 77.5, 51.5, 25.4

Note that the 9.3 and 18.6 year cycles are connected to the lunar nodal cycle. These are frequently mentioned in recent decades. Dewey had a 9.2 year period though.

It's lacking some self-containedness. What's the ordinate?

__________________
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

Sorry, the x axis is log10 cycle period in years and the y axis is the number of cycle reports in each log interval.
So the large vertical lines mean that there are many reports for a particular small range of periods. I have labelled all the common periods by reading off the graph, and more accurately below from the best cycle period measurements.

586 is 22 x 26.636, but how does the 128 fit in?

PS: and where did you show it earlier? I've searched this thread.

The 128 is Mpc. That converts to the 586 MY if the Hubble constant is 71.2 km/s/Mpc.

The geological cycles and mass extinction cycle values with exact ratios between them would be as follows, starting from Afanasiev's 586.24 MY.

586.24 293.12 146.56 73.28 36.64 (ratios of 2)
(ratio 11)
53.294 26.647

The following graph shows mass extinctions data to which I have added two regular cycles of 36.64 and 26.65 million years. You can see that when the two come together in phase the 26.65 million year cycle gets reinforced and the peaks are higher. That happens three times every 293 million years. From the mass extinction data the best estimate of the so called 27 million year cycle is 26.7 million years, so that the 11 ratio is established quite accurately as being an integer.



The next time the two come together is in 41 MY.

Hi Nereid

I mentioned the 1.11 million year cycle in the solar system. It is also present in magnetic reversals, and possibly a 9 million year cycle also. Generally magnetic reversals are not considered cyclical, and it is true that there is additional noise present, but I think that the 1.11 MY cycle is quite evident.


Note the URL in the graphic no longer works. The correct one now is http://geomag.usgs.gov/faqs.php

A couple of additional notes about the collection of astronomical cycles that you are making. You will no doubt be leaving out the geological cycles of Afanasiev, but I wanted to add a note on them so that I am being clear about things. The 586 MY cycle is referred to by others and so I consider it as well established. I used other Afanasiev cycles in my long cycle calculation because I needed to span the range from thousands to hundreds of millions of years, but many of these are one off cycle measurements so would not be correctly called "common cycle periods". I have shown that the 1.11 million year cycle is also present in magnetic reversals, so it is a better candidate for being common, having two different disciplines.

To a large extent, the appearance of the patterns n cycles is dependent on using a multi-disciplinary approach. Dewey found them this way and several others as well as me, always from looking at many disciplines. If you stick to astronomy (I understand that it is the subject of the forum and what you know well) the pattern will not be as clear. However the 155 day cycle and related is a very good place to look at if you just stick to astronomy, because the astronomers themselves have reported the harmonic relationships between the different cycles that are observed.

Note that the 26.65 MY mass extinction cycle is very accurately 24 times the period of the 1.11 MY magnetic reversal and solar system dynamics cycle. The ratios 12 and 24 are very common in the strong predicted cycles of the harmonics theory.

Regards
Ray

Could you please present your input data again (astronomical cycles you used), clearly identifying which number is what cycle, and giving a reference that is sufficiently clear that any reader of your post could check it for themselves?Which "distance" is this?

For example, is it the distance from the solar system to the nucleus of M31?

Or from SgrA* to the nucleus of M31?

Or something else?

While M31 may not be far enough away, nor moving fast enough relative to us, for these to matter, I am curious to know which 'notion of distance' you are using for your analyses.Is the reader entitled to ignore these data until you can provide a reference (or at least a clear, quantitative definition)?(my bold)

Which planets? Which orbital elements?The times between "similar alignments" of any subset of planets may, indeed, be easily determined from standard ephemerides.

However, I suspect "connections between the motion of the centre of mass (COM) of the solar system relative to the Sun as a factor in solar changes and climate" are anything but standard, mainstream astronomy or climatology!

Can you please provide references to papers, published in relevant peer-reviewed journals, on "connections between the motion of the centre of mass (COM) of the solar system relative to the Sun as a factor in solar changes" (but not climate, for now)?I'm still quite confused about the relationship between an input (which has an observational uncertainty associated with it) and a rtomes idea prediction, which is "exact".

Let's take this ("the Sun's rotation period") as an example. Suppose it can be constrained, via observation, to be within a very narrow range. Suppose the central value of that range is n days. What range of values can n have and still be considered evidence for the rtomes ATM idea?

How many of these "common periods" are astronomical (or have at least one astronomical cycle in 'common')? Which of the y > 20 cycle periods includes at least one astronomical cycle?

OK, I will get back on this,. For now will answer the other questions.
It was probably the distance from us to M31. Of course ideally it would be the distannce between galaxy centres, so might be out by 1% due to our location not at the galaxy centre. Probably that is the least of the errors.
In general the distance periodicities will be between the centres of things. Of course we ideally want a whole row of things and we take the average or best fit interval between them.

In some cases like the planets, they move a lot so the average distance from the Sun is used. In that case we find four clear quanta (using Kotov's method again) which are about 0.35, 0.7, 5 and 10 AUs. I will make a separate post for this as it is certainly one of the main areas of astronomical quanta and has been proposed first by other people (starting with Titus-Bode) especially Kotov.
Yes, I try to use the latest orbital elements which are available on the web. Much of my work was done with older data (from around 1994) but the planets orbits were known to sufficiently high accuracy then. Some periods like the 2300 year one are very sensitive to accuracy, because they depend on tiny differences between combinations of the periods.
On that we are agreed.

However I have shown that there is a reason for the phenomena that depends on a GR effect of the planets on the Sun's interior. However that is another whole new thread, probably counting as ATM but in fact just an effect never before studied. I will leave it aside for now.

However the correlations between planetary alignments and solar (and weather) phenomena is well established in many papers. The mechanisms are what cause the problems. The tidal effects of the planets on the Sun is fairly mainstream (e.g. articles in Nature) and in fact the strongest tidal pair are Jupiter and Saturn which is what makes the 0.33 year (17 week) solar cycle it seems. NASA have published papers on this some decades back because they were concerned about predicting solar activity when sending men to the moon (they didn't want them fried) and the best method that they could find was planetary alignments.
Here is one http://aprm2002.nao.ac.jp/pdf8/p.423.pdf
Here is one by Fairbridge relating to earthquakes http://www.springerlink.com/content/nl55542wjg7uw716/
This one by Landscheidt is not mainstream but some of the links seem to be http://www.john-daly.com/solar/solar.htm
I would refer you to my recent post on doing statistical tests on the redshift periodicities. In general the percentage has to be small enough so that nothing like the whole interval is within the percentage of the harmonics theory values. This will depend on the data.

In my early work I had just the 4 economic cycles and got them to within 1% accuracy (actually they frequencies have consistent +/- values so that the shorter cycles are more accurate in % than the long ones). When you have just 4 cycles over an octave that is fairly significant. But when more data is available and for longer time series, then two things happen - the periods get more accurate and the fainter cycles begin to show. That is OK, because when you include the fainter theoretical cycles then you need more accuracy to reduce the individual windows* so that the total window space is still small as a proportion.

* By window I mean the percentage allowed around any Tomes harmonic. For the economic data it might be 1% which would mean that with just a few cycles chosen about 1/10 of the space might be used as windows. If most of the observations fall in that space then it is significant. In the solar system, the data is much more accurate than economic data and also there are many more diverse periods. So we can use a smaller percentage size for windows and include more of the faint harmonics from theory. However these two must always lead to a sensible statistical test.

Here is a first attempt. Probably needs some more references, but I didn't bother referencing the planetary orbital periods as I figure that you will believe those.

minutes
2.9 Inner planet spacings (Tomes)
5.8 Inner planet spacings (Tomes)
80 Outer planet spacings (Kotov, Tomes)
160 Outer planet spacings (Kotov), Planetary rotation quanta (Kotov), Binary stars (Kotov), Solar cycle http://www.springerlink.com/content/v5110n4h84006vt2/

days
6.44 quanta of planet and solar rotation (Tomes)
25.38 Solar rotation (wikipedia and anywhere)
51 various solar phenomena (references already given)
78 various solar phenomena (references already given)
155 various solar phenomena (references already given)
1.27 years various solar phenomena (references already given)
2.14 years various solar phenomena (references already given)

years
.33 Solar cycle, J-V conjunctions superior OR inferior
.66 J-V conjunctions of one type
.99 close to but not actually one year
1.98
2.67
2.96
3.39 Heat from solar radiation (Dr Stern, Harvard College Observatory 3.4 years) old reference ??
4.22
4.45
5.54 Found in Sunspot cycle (half main period)
5.92 Half Jupiter orbital period (5.93 actually). Found in sunspots with alternate cycles reversed, Dewey.
(6.4) Chandler wobble http://www.agu.org/sci_soc/prrl/prrl0622.html
7.91 Found in sunspots with alternate cycles reversed, Dewey. ??
8.89 Sunspots (some analyses only) ??
9.3 Half lunar orbital nodal period, tides.
9.63
11.1 Sunspot cycle.
17.8
18.6 Lunar orbital nodal period. http://en.wikipedia.org/wiki/Lunar_node
22.2 Hale sunspot cycle
35.6 Aurora frequency ??
(42) Half Uranus orbital period
53.5 Economics, weather (probably), solar(??)
89 Sunspots
178
2317 Outer planet alignments
4634 Outer ploanet alignments
23000 Milankovitch cycle (multiple spectral peaks)
25700 Precession of the eqinoxes
41000 Milankovitch cycle (multiple spectral peaks)
97000 Milankovitch cycle (multiple spectral peaks)
410000 Milankovitch cycle geological cycle
1.11e6 Solar system dynamics

I have omitted geophysical and climate data which may have astronomical connections.
?? means possibly doubtful or tenuous connection to astronomy

It seems that my putting many questions in one post leads to some misunderstanding.

I shall re-state my questions, one per post.

- - - - - - - - - - - - - - - - - - history - - - - - - - - - - - - - - - - - -
Nereid: What is "a long term solar system energy exchange cycle inn the outer planets"?

rtomes: This was a reference to a long term integration of planetary motion over many million years. Somewhere I do have the reference to this but would need to look through about 10 note books to find it. If I remember correctly it was a slow energy interchange between Jupiter and Neptune.

- - - - - - - - - - - - - - - - - - - the un-answered question - - - - - - - - - - - - - - - - -
Nereid: Is the reader entitled to ignore these data until you can provide a reference (or at least a clear, quantitative definition)?

Please answer this question.

Nereid: What are "[the] astronomical cycles of planetary orbital interactions and precession of equinoxes"?

rtomes: The precession of the equinoxes is the time for the equinoxes to complete a full rotation. The other two are the only ones used that are my own work and may not be found elsewhere. They are periods after which the various orbital elements of the planets tend to return to similar alignments relative to each other. This applies to the alignments of the ellipses and maybe also the node. There are some groupings in the element motions but they are not very tight groupings. If I was trying to convince scientists, I would probably leave these ones out as being unknown factors.

Nereid: (my bold)
- - - - - - - - - - - - - - - - - - - the un-answered questions - - - - - - - - - - - - - - - - -
Which planets? Which orbital elements?

Please answer these questions.

AFAIK, the best current estimate is 2.55 million light years (references may be found here: "The mean true distance modulus of the M31 globular clusters is found to be 24.47 ± 0.07 mag", and "This allows a single step determination of the distance modulus to M31 [...] and the corresponding distance = 784 ±13 ±17 kpc").

[2.452, 2.648] (the second result) is not within [2.178, 2.222] (1% around 2.2).

What quantitative statement can be made about the consistency of your ATM idea with these modern estimates (derived from good observations)?

It seems my question is not very clear; let me try again, with more concrete examples.

Suppose the Sun's equatorial rotation period has been determined, by many sets of independent, good observations, to be 20.12 ± 0.01 days (68% confidence). What statement could you make concerning the consistency between your ATM idea and this observational result?

Suppose the Sun's equatorial rotation period has been determined, by many sets of independent, good observations, to be 29.87 ± 0.01 days (68% confidence). What statement could you make concerning the consistency between your ATM idea and this observational result?

Generalising, suppose the Sun's equatorial rotation period has been determined, by many sets of independent, good observations, to be x ± 0.01 days (68% confidence). What statement could you make concerning the consistency between your ATM idea and this observational result?

Various mathematical astronomers do long term calculations of the planetary motions. They can run backwards and forwards into tens of millions of years and more. In fact such calculations are now used as the prime basis for geological dating for the last 23 million years.

When these calculations are done there are certain planetary relationships that show up as very important. One of the first ones found was the great Jupiter Saturn cycle of ~880 years. This happens because Saturn takes almost 2.5 times as long as Jupiter to go around the Sun. This means that after 2 x S = 59 years you also have 5 x J =59 years near enough. This fact causes huge perturbations in the planets orbits. Saturn varies by some degrees in longitude as a result. These things happen whenever you find a near commensuration in two or more planets which leads to a low frequency with small coefficients in an orbital frequency calculation. In this case we calculate using frequencies f=2J-5S = .0011... = 1/880 years.

These perturbations exchange energy between various combinations of planets. It is all standard physics. The 1.11 million years cycle is the longest one that I know of that has been found. It was in a peer-reviewed paper or reputable source. I do have a reference but if I take time to find it, that will be ten other questions that do not get answers. It would be more fruitful to find a person who does this sort of calculation and get some data on these periods off them and then it will be unbiased data.

Sure, you can ignore the 1.11 million year cycle for now. I will substantiate the things that I expect to be included. It is not worth while putting a lot of energy into that one figure when it is so far out on its own. However it would be helpful to have some idea of your plan. It may assist in me assembling what you are looking for ahead of time rather than just responding to a series of questions.

The theory does not say that an single one cycle will be any particular predicted harmonic. What is says is that cycles periods that are found in multiple disciplines are much more likely to be matches with the harmonics theory derived periods.

It also says that periods that are found as commuting with many individual measurements are more likely to match the listed cycles periods. In the case of the planets and the Sun, the rotation periods do show near commutations. The best way to get these results is with a program that I have that uses Kotov's method. In the case of the Sun and planets you get a better result if you use (rotation period)^0.5, but it still works without the 0.5.

Periods in days
6.39^.5 / 1 = 2.53 Pluto
25.38^.5 / 2 = 2.52 Sun
58.65^.5 / 3 = 2.55 Mercury
243.0^.5 / 6 = 2.60 Venus
Average 2.55^2 = 6.5 days quantum

Periods in hours
9.924^.5 / 4 = 0.788 Jupiter
10.656^.5 / 4 = 0.816 Saturn
23.93^.5 / 6 = 0.815 Earth
24.62^.5 / 6 = 0.827 Mars
17.24^.5 / 5 = 0.830 Uranus
16.11^.5 / 5 = 0.803 Neptune
Average 0.813^2 = 0.661 = 39.7 minutes

These relationships are similar to atomic ones. They are very suggestive, but because the number of data points are low, they may not be convincing to skeptics.

Analysis of all known satellites orbital and other classes of objects do show a series of quanta that are in fact harmonically related and do include some existing common cycles. The following graph is based on satellite periods of all known natural satellites in the solar system (or frequencies, the result is the same) and is labeled in years. It uses Kotov's method of finding communalities. A peak means that more satellites commute with the period, i.e. have a period that is near the period either multiplied by or divided by an integer.

On this one test alone, many of the common cycles periods appear. In general the results of this sort of analysis shows that subtle influences of cosmic waves are tending to cause cycles to come into tune with them.

Realizing where you are heading earlier with your making a list of astronomical cycles, I think that this sort of data is the best that can be included. It digests hundreds of satellite periods into commonly found communalities.

Based on my last post, it is reasonable to note that a number of these cycles are matches to the commonly reported cycles, and so they are present in astronomy. First however I should mention three oversights that I have made.

Firstly, Dewey does report both a 5.92 and a 6.02 year cycle.These are not seen as separated in my graph and I only listed one.

Secondly, although the peak from the list of cycles for a 3.95 year cycle is rather low, I have found it several times as has Dewey and he even mentions it in sunspots with alternate cycles reversed. So I think that one should be added in.

Thirdly, the period 11.86 years which is Jupiter's period around the Sun is the most dominant physical cycle in the Solar system, showing up in various ratios to asteroid perturbations and other things. I have also found it in economic data such as Australian Stock market. So that should be included. Dewey did not have it in his original table (though he hs an 11.73 year period in sunspots while others have 12 years) because he did a sort of hour glass shape, but I have always included it as one of the ones that fits the harmonics.

It was comparing the periods in the previous graph that I saw these oversights.

What is the vertical axis?

What is the number of input data points?

What does "all known satellites orbital and other classes of objects" mean?

Given Newtonian gravity and ~five billion years of interaction, what would this graph look like, averaged over ~600 runs (say)? This last question is an Occam razor one - if plain old gravity and time, in a multi-hundred body system, can produce graphs like these, why postulate "cosmic waves [...] tending to cause cycles to come into tune with them"?

According to this ATM idea, what should this graph look like if a completely different set of astronomical data (frequencies) had been used as input? For example, one in which Newtonian gravity was not the dominant force.

It doesn't fit the strong harmonics.

I guess that we have to await a more accurate Hubble constant to see if the typical spacing of other galaxies do.

You probably noticed that some parts of the range of cycles are better populated than others. The range from 10,000 to 10,000,000 years was a bit sparse so I used things in that range that would not have been used in the 0.1 to 10,000 year range.

The only point of doing all of that was to try and get a fix on the longest cycle. There is no point in doing that if the theory is not seen to be useful first. To that end I suggest concentrating on the known cycles in the range 3 to 160 minutes and 25 days to 100 years, because there is much more data in that range and the results will be easier to demonstrate. I think that would should be clear in those ranges is that there are many cycles linked by ratios that can be seen to be integers within a small margin, and that as many of these steps are taken the errors do not accumulate as they would if the ratios were chance ones. By that I mean that all of the periods can be calculated within small margins from a single value and a set of exact integer ratios.

Furthermore, the ratios over a largish interval (the years ones is large enough) will show mostly ratios of 2 and a lesser number of 3s with just a few other primes, like 5, 7 and 13.

The planets concerned are the four gas giants. These account for the vast bulk of angular momentum of the solar system. There are several theories that make that significant, although there are arguments against some of these.

The elements concerned are the longitudes. You can get these from any ephemeris, but we are interested in the groupings. The planets come into configurations either all on one side of the Sun which is important in the C.O.M hypothesis (and some others) or stretched in a line on both sides which is important in tidal forces theories. However tidal force theories also make Venus, Earth and Mercury important. Both groups of theories have shown that there are correlations with solar behaviour but the theories do not seem to be complete. All the same, almost all of the many periods found in the sunspots are accounted for by these theories. There are many papers on each of these theories in peer review journals starting with Wood in Nature in the ~1970. They are not worth us going into though. This is just background.

A reference eon some of the things like the great Jupiter Saturn inequality and various resonances and stuff. It has a lot of maths but not a lot of explanation: http://www.cyclesresearchinstitute/ladma/cycles.htm

What is the relationship between the plot in post #65 and that in #80?

Specifically, how do the two x-axes relate to each other? How do the two y-axes relate to each other?

Why not trawl through the billions (trillions?) of values in the various online astronomy databases until you find one that is as close to what you are looking for as you like?

Having found it, I imagine it would be the work of but seconds to come up with a plausible-sounding a posterori reason why it has significance. After all, if you chose 2.22 million light years to include in analyses that involve periods (frequencies), surely it doesn't much matter what it is, does it?

Better still, I'm sure there is a combination of historical units of length* that you could apply to any arbitrary astronomical datum and so derive 2.22 million. And if not length, then perhaps volume, or energy, or ...

re the part I bolded above: I'm afraid I still don't get the acceptability of "within a small margin". If the predicted - exact - value lies >3 σ from the mean value determined by good, reproducible experiments or observations, how can the hypothesis not be rejected? And if 5 σ (say) is acceptable, why not 2.22 million σ?

Further, independent of these acceptability criteria, what value (scientifically) does the kind of a posterori statistical analysis that you seem to be engaging in have anyway?

*Something to do with cubits perhaps, or furlongs, or stadia.

The plot in #65 has period in years on a log scale on the x axis.
It has number of cycles in a narrow % range in an index of cycles from FSC on the y axis. I played no part in assembling that data, it was done in the 1980s by an executive director of FSC based on Cycles publications in the past and before I knew about FSC.

The plot in #80 has period in years on a log scale on the x axis.
It has a measure of commutation on the y axis for the "test period". This is based on Kotov's method, which I will describe below. I have inverted the scale compared to Kotov's calculation because people are used to peaks in the spectrum meaning that the cycle is stronger. The data for this was the mean daily motion for all satellites in the solar system known at the time I did the analysis which was June 2005. Although I used motion data for the planets from the NASA web site, but in the graph converted these to periods in years. If I had used periods the result would be identical.

Example of Kotov's method.

The data are the planets motions in "/century. I used planets for the example because the satellite list is too long. The test value for this printout is 1559715"/century. As you can see, this value commutes with most of the planets motions. The motions are near to integer multiplies or divisors for all except Mars and Saturn. The sum of the deviations is randomly expected to be 0.25 per item in the table because deviations can be between 0 and 0.5 from the nearest integer. So in this case 0.25*9=2.25 but the actual is only 0.56 because the test period commutes strongly with the data. In a graph like #80, test values are calculated at tiny steps apart and a graph made of this result but inverted so that small sums of deviations appear as peaks. In each case in #80 the larger peaks are labeled with the period that gave the minimum deviation or maximum peak.

Century motion Relation to Deviation
of Planet " Test value from integer

538101628.29 *344.999970052221 .000029
210664136.06 *135.065788339536 .065788
129597740.63 *83.0906547862911 .090654
68905103.78 *44.1780093029816 .178009
10925078.35 *7.00453502723254 .004535
4401052.95 *2.82170329194757 .178296
1542547.79 /1.01112912683243 .011129
786449.21 /1.98323678143182 .016763
522747.9 /2.98368486989618 .016315

Test value 1559715
Sum of deviations 0.561522

A test value of 1559715"/day motion corresponds to 83.092 years.

As a note, it makes no difference if you use daily motions or orbital periods because they are inversely related. The * and / simply flip over in the table and the answer is the inverse.

I should have mentioned that as #65 and #80 graphs were derived from pretty much entirely different data, the similarity in the periods at which peaks occur must be due to some all pervading cause that affects astronomical and terrestrial oscillations alike.

IOW the 'log(years)' were binned, with bins being of equal size ... right?Motions wrt an observer located where?

Earlier in this post you called them "mean daily motion" - how was the "mean" determined?

Which "NASA web site" did you get the "motion data" from?What is the scale of the y axis?

Why use absolute value of the difference ("deviations"), and not (as is standard) the square of the difference?What are the increments of log(years) ("steps") used to produce the post #80 plot?

Alternatively, all it may show is the strength of the degeneracy in the input data, or selection biases, or some rather odd features of the data reduction methods, or ....

The lack of a null test seriously weakens the scientific validity of any conclusions you may seek to draw from these.

What happens when you use the second billion digits in the decimal expression of pi (for example) to generate pseudo cycle input data?