1. Originally Posted by Robert Tulip
I have invented my own analysis method to find the correlation of the SSB signal with the delayed copy of itself as a function of delay, which is the definition of autocorrelation. I would be happy to reconfigure this into the standard methods used for autocorrelation.
What you're doing is not autocorrelation (which would produce values between -1 and 1), but I still wondered why you were coming up with the discrepancy. It turns out that you are not that far off from Jose--even though the abstract reports the period as 178.7 years, his calculation of the period of R, which corresponds to your calculation, is 178.81 years (see Table II), with a standard deviation of .32, so your value of 178.86 is not in disagreement.
From the table, the 9xJS value only provides 41% of the power of the signal. I did more work on this table to show the integer multiples of each subwave that are closest to 179, as follows.
Code:
```Fourier Spectrum Decomposition of Wave Function of Solar System Barycentre
Cycle	SSB Spectral Peak (Years)
A	First Planet
B	Second Planet
C	Spectral Power
D	% of total spectrum
E	Orbital Period
F	Cycle period close to 179 years
G	Cycles in 178.86 years
H	Rounded # of cycles
I	Absolute Variance from 178.86
J	Precession Ratio
K
1	19.85	Jupiter	Saturn	983	40.9%	19.85	178.67	9.010	9	0.11%	          144.24
2	12.8	Jupiter	Neptune	419	17.4%	12.78	178.92	13.996	14	0.03%	          144.04
3	13.8	Jupiter	Uranus	190	7.9%	13.81	179.52	12.952	13	0.37%	          143.55
4	35.9	Saturn	Neptune	189	7.9%	35.87	179.36	4.986	5	0.28%	          143.68
5	11.9	Jupiter	Cycle	137	5.7%	11.86	177.90	15.081	15	0.54%	          144.86
6	7.8	unknown		128	5.3%	7.80	179.40	22.931	23	0.30%	          143.65
7	45.5	Saturn	Uranus	96	4.0%	45.37	181.48	3.942	4	1.44%	          142.01
8	9.9	Jupiter	Saturn	75	3.1%	9.93	178.67	18.019	18	0.11%	          144.24
9	8.2	unknown		72	3.0%	8.20	180.40	21.812	22	0.85%	          142.86
10	29.5	Saturn	cycle	59	2.5%	29.46	176.76	6.071	6	1.19%	          145.80
11	171	Uranus	Neptune	57	2.4%	171.37	171.37	1.044	1	4.37%	          150.39

Source	Fourier Transform	E= D/SUM(D)	F =
1/(1/B - 1/C)	G=
F x I	H= 178.86/F	I= round(H)	J=
ABS(H/I-1)	K= 25771/G```
(Note due to the coding format the letters in the list at the top match to the text in the following line, eg % of total spectrum is explained by E in the notes at the bottom).

As I mentioned earlier, there are three subwaves , JN, JU and SN, which have integer multiples just above 179. With JS contributing 41%, and these three contributing 33%, it makes sense that the overall wave period would sit in between these main groups, as I found by the autocorrelation of the wave form.
Jose just combines all of the periods into a single estimate of 178.77--and noticing that that's essentially the period of 9xJS (which he calculates as 178.72), he rounds it off to 178.7. But his calculation is virtually identical to yours.

So why is it even that much greater than 178.73, the value we calculated for 9xJS. I suspect it is the influence of Neptune, and Uranus. The UN synodic period is 171.393, which is just shy of 178.73. Integrated over a complete cycle, the cross correlation should be zero, but you're integrating over 6000 years, just like Jose (which is why you get the same answer 178.86 as he does 178.81, both larger than 178.73). A complete JS/UN cycle would be complete in 178.73381/(178.73381-171.393)*178.73381 or 4351.8 years. Try re-doing your calculation with just the last 4352 years of data (or the first 4352, or any set of 4352 years inbetween), and see what value that you get.
Last edited by grapes; 2018-Jan-20 at 03:24 PM. Reason: ETA: any set of 4352 years

2. the eccentricity means the conjunctions are not correct to four figures. That will make the average just an average and dependent on how many cycles you consider.

3. this is a screen shot, maybe easier to read.
Screen Shot 2018-01-20 at 14.00.41.png

4. Originally Posted by profloater
the eccentricity means the conjunctions are not correct to four figures. That will make the average just an average and dependent on how many cycles you consider.
I'm pretty sure that's why Robert is integrating over thousands of years.

5. Originally Posted by Robert Tulip
Eventually my interest in this material is to explain the structure of time for the solar system. The SSB appears to me to be the integrating function of the solar system, or the 'centre of the world', as Newton put it. Then there is the question of how the earth is nested within this solar system orderly structure. I think it may be possible there is an entraining 1/144 resonance between the spin wobble of the earth and the SSB wave function, but that is a purely speculative idea with no empirical evidence for it.
Let's make sure we don't fall into a booby trap of letting the relatively large barycentric solar displacements caused by the outer planets make us think that their gravity could somehow lock the Earth's precession period at 144 times the average SSB pattern period. As I understand it, the gravitational torque from any given planet will be proportional to its mass and the inverse cube of its distance. As with the tides on the Sun as listed in the other thread, this makes the effects of the outermost planets really feeble in proportion to those of the inner planets and Jupiter.

I calculated how much the Moon's orbit would expand in an angular momentum exchange from a reduction of Earth's spin rate by 1%. The reduction of torque from the Moon's gravity was considerably more than that. The precession rate is proportional to the torque for any given spin rate, indicating that the precession rate would slow down. Thus I find the present ratio of precession to SSB pattern to be a transient coincidence.

6. Originally Posted by Hornblower
Let's make sure we don't fall into a booby trap of letting the relatively large barycentric solar displacements caused by the outer planets make us think that their gravity could somehow lock the Earth's precession period at 144 times the average SSB pattern period.
Agreed. I was not at all implying that any such “locking” mechanism could exist. Where I find this 1:144 ratio between the precession and SSB periods interesting is just in noting that the traditional concept of a zodiac age, as the period that the equinox takes on average to traverse one twelfth of the ecliptic, is also twelve times the SSB period. Perhaps that is just an artefact, and yet it also is a remarkable coincidence that our 60-base system of clock time is nested within the primary temporal structure of earth's relation to the whole solar system.
Originally Posted by Hornblower
I find the present ratio of precession to SSB pattern to be a transient coincidence.
“Transient” is an interesting phrase for something that exists for billions of years. The speed of change of both these variables is very slow. My understanding from the Newtonian mechanics is that there is not much change in the speed of precession. The only thing changing the speed is the slow increase in distance to the moon, but that is minimal over historical time frames. The figures at this scientific paper, (Comments on the long-term stability of the Earth's obliquity, Icarus, 1982, William R. Ward), indicate the precession period will only increase by 0.4 years per Great Year for the next billion years. Assuming that the orbital periods for the gas giants have similar tiny rate of change, it appears probable that this 1:144 ratio has been the closest whole number since the dawn of life on earth.

7. Are we looking at the same paper? In the abstract the author states that over a period of some 2 billion years the precession period will greatly increase. That reinforces my opinion that the present-day precession period is a transient feature over the very long term.

8. Originally Posted by Hornblower
Are we looking at the same paper? In the abstract the author states that over a period of some 2 billion years the precession period will greatly increase. That reinforces my opinion that the present-day precession period is a transient feature over the very long term.
Addendum: Let me stress that I am not arguing that it is a transient feature over human recorded history. These proportions are very much fixed as seen by anyone before modern times when precision observations can pick up slow changes.

9. Originally Posted by Hornblower
Are we looking at the same paper? In the abstract the author states that over a period of some 2 billion years the precession period will greatly increase. That reinforces my opinion that the present-day precession period is a transient feature over the very long term.
My mistake, you are correct. Sorry about that. Thank you for checking.

The periodic increase implied by Ward's abstract is 0.4 years per precession cycle of ~25.8KY, not over the whole two billion years he describes. That means the current period of 25771.4 years will increase to 25,771.8 years over the next 50,000 years.

That means the ~144 ratio lasts for millions of years, not billions. My calculation, assuming SSB periodic stability at 178.86 years, is that this ratio was exactly 144 one million years ago, and will reach 145 in ten million years.

10. Originally Posted by Robert Tulip
My mistake, you are correct. Sorry about that. Thank you for checking.

The periodic increase implied by Ward's abstract is 0.4 years per precession cycle of ~25.8KY, not over the whole two billion years he describes. That means the current period of 25771.4 years will increase to 25,771.8 years over the next 50,000 years.
Based on that, wouldn't it increase to 25,772.2 years?
That means the ~144 ratio lasts for millions of years, not billions. My calculation, assuming SSB periodic stability at 178.86 years, is that this ratio was exactly 144 one million years ago, and will reach 145 in ten million years.

11. Originally Posted by grapes
Based on that, wouldn't it increase to 25,772.2 years?
I was reading it (probably wrongly) as saying the current equinox sidereal position will return in 25,771.4 years, but if the current speed is one cycle per 25,771.4 years, then you are right, in 50,000 years the speed will be 25,772.2. Thanks.
Last edited by Robert Tulip; 2018-Jan-27 at 10:36 PM.

12. Originally Posted by grapes
Try re-doing your calculation with just the last 4352 years of data (or the first 4352, or any set of 4352 years inbetween), and see what value that you get.
Have you tried this yet?

13. Originally Posted by grapes
What you're doing is not autocorrelation (which would produce values between -1 and 1),
Thanks very much for these comments grapes, and sorry for delay in response. I agree that I have not used the conventional autocorrelation formula, as I just invented my own method to compare every part of the curve to every other part. But I think the result is the same as conventional autocorrelation, even if the values produced are different.
Originally Posted by grapes
but I still wondered why you were coming up with the discrepancy. It turns out that you are not that far off from Jose--even though the abstract reports the period as 178.7 years, his calculation of the period of R, which corresponds to your calculation, is 178.81 years (see Table II), with a standard deviation of .32, so your value of 178.86 is not in disagreement.
Yes, this closeness to Jose’s number illustrates that there is an actual wave function of the sun at around the 179 year period. The question then is how to calculate it more precisely. My suspicion is that Jose did not have access to the computing power that went into the NASA JPL figures integrating all the mass of the solar system.
Originally Posted by grapes

Jose just combines all of the periods into a single estimate of 178.77--and noticing that that's essentially the period of 9xJS (which he calculates as 178.72), he rounds it off to 178.7. But his calculation is virtually identical to yours.
As I showed in the diagram attached to an earlier post in this thread, there is a three month difference between Jose’s estimate and my calculation from the JPL data. When we are looking as something as fundamental as the period of the integrating wave function of the solar system, I think there is value in getting the number right rather than being happy with a rough estimate based on inaccurate data.
Originally Posted by grapes
So why is it even that much greater than 178.73, the value we calculated for 9xJS. I suspect it is the influence of Neptune, and Uranus. The UN synodic period is 171.393, which is just shy of 178.73. Integrated over a complete cycle, the cross correlation should be zero, but you're integrating over 6000 years, just like Jose (which is why you get the same answer 178.86 as he does 178.81, both larger than 178.73). A complete JS/UN cycle would be complete in 178.73381/(178.73381-171.393)*178.73381 or 4351.8 years. Try re-doing your calculation with just the last 4352 years of data (or the first 4352, or any set of 4352 years inbetween), and see what value that you get.
The way I have set up the excel spreadsheet with this data makes it easy for me to measure this wave function against any length of time of SSB radius data. I can send the spreadsheet to anyone who wants to look at it. The 178.86 year
period looks remarkably stable, even testing it against very short periods like ten years, let alone your suggestion of four thousand years. That stability fits with my hypothesis that it is caused by the balance between JS as the main component of the spectrum and the other main components (JN, JU, SN) which have multiples slightly higher than this integrating system value.
Last edited by Robert Tulip; 2018-Feb-03 at 09:34 PM.

14. Originally Posted by Robert Tulip
Originally Posted by grapes
What you're doing is not autocorrelation (which would produce values between -1 and 1),
Thanks very much for these comments grapes, and sorry for delay in response. I agree that I have not used the conventional autocorrelation formula, as I just invented my own method to compare every part of the curve to every other part. But I think the result is the same as conventional autocorrelation, even if the values produced are different.
Well, it's not an autocorrelation or correlation at all, just your own attempt at calculating a period. I'm not sure, but that "difference" approach may be susceptible to systemic errors. I'll look into it, there's probably analysis somewhere online.
Originally Posted by grapes
but I still wondered why you were coming up with the discrepancy. It turns out that you are not that far off from Jose--even though the abstract reports the period as 178.7 years, his calculation of the period of R, which corresponds to your calculation, is 178.81 years (see Table II), with a standard deviation of .32, so your value of 178.86 is not in disagreement.
Yes, this closeness to Jose’s number illustrates that there is an actual wave function of the sun at around the 179 year period. The question then is how to calculate it more precisely. My suspicion is that Jose did not have access to the computing power that went into the NASA JPL figures integrating all the mass of the solar system.
It looks like you were using similar simulated datasets, so there may be no real difference. But that's a good point, if you have access to the current technology, like the autocorrelation function, why not take advantage of it, rather than homegrowing your own?
Originally Posted by grapes

Jose just combines all of the periods into a single estimate of 178.77--and noticing that that's essentially the period of 9xJS (which he calculates as 178.72), he rounds it off to 178.7. But his calculation is virtually identical to yours.
As I showed in the diagram attached to an earlier post in this thread, there is a three month difference between Jose’s estimate and my calculation from the JPL data. When we are looking as something as fundamental as the period of the integrating wave function of the solar system, I think there is value in getting the number right rather than being happy with a rough estimate based on inaccurate data.
I highlighted the two figures in your quote of my post, above, his in red and yours in green. The difference, 178.86-178.81=.05 years, is 18 days, about half of the month intervals in the data you're analyzing.
Originally Posted by grapes
So why is it even that much greater than 178.73, the value we calculated for 9xJS. I suspect it is the influence of Neptune, and Uranus. The UN synodic period is 171.393, which is just shy of 178.73. Integrated over a complete cycle, the cross correlation should be zero, but you're integrating over 6000 years, just like Jose (which is why you get the same answer 178.86 as he does 178.81, both larger than 178.73). A complete JS/UN cycle would be complete in 178.73381/(178.73381-171.393)*178.73381 or 4351.8 years. Try re-doing your calculation with just the last 4352 years of data (or the first 4352, or any set of 4352 years inbetween), and see what value that you get.
The way I have set up the excel spreadsheet with this data makes it easy for me to measure this wave function against any length of time of SSB radius data. I can send the spreadsheet to anyone who wants to look at it. The 178.86 year
period looks remarkably stable, even testing it against very short periods like ten years, let alone your suggestion of four thousand years. That stability fits with my hypothesis that it is caused by the balance between JS as the main component of the spectrum and the other main components (JN, JU, SN) which have multiples slightly higher than this integrating system value.
Ten years? That's impossible. How are you trying to do that?
Last edited by grapes; 2018-Feb-04 at 05:53 PM. Reason: systemic red/green

15. The orbits of the planets appear to be stable over billions of years, so I would say it is rather unremarkable that the wave pattern of the sun's barycentric displacement as a function of time is stable. That is, unless Robert is using "stable" in some esoteric sense that I am not getting.

16. Originally Posted by Hornblower
The orbits of the planets appear to be stable over billions of years, so I would say it is rather unremarkable that the wave pattern of the sun's barycentric displacement as a function of time is stable. That is, unless Robert is using "stable" in some esoteric sense that I am not getting.
I think he agrees with this. He has repeated an analysis from 55 years ago. Both his and the original have a slightly longer period than Jupiter/Saturn synodic period and he thinks maybe he has improved the calculation. I think he's not done yet.

17. Originally Posted by grapes
Well, it's not an autocorrelation or correlation at all, just your own attempt at calculating a period. I'm not sure, but that "difference" approach may be susceptible to systemic errors. I'll look into it, there's probably analysis somewhere online.
Thanks again. As noted previously, autocorrelation is the correlation of a signal with a delayed copy of itself as a function of delay. In this case, I have established that the SSB signal correlates with its delayed copy to produce a simple orderly symmetrical wave function with period 178.86 years. While I have not used the established mathematical formula for autocorrelation, and have instead just added the differences of the wave amplitude over every range from zero to 244 years, this clearly establishes that the comparison over the delay of 178.86 years reveals autocorrelation in the similarity between observations as a function of the time lag between them. This matches to other aims of autocorrelation, such as finding a simple repeating pattern, the presence of a periodic signal obscured by noise, and identifying the missing fundamental frequency in the time domain signal.
Originally Posted by grapes
It looks like you were using similar simulated datasets, so there may be no real difference.
The simulation here is the JPL calculation of the SSB. NASA told me “the planetary ephemerides are not derived from a formula (in which periodicities might be "put in"). We are oblivious to periodicities when solving for planetary orbits. Instead, orbit solutions come from a numerical integration of 2nd order differential equations of relativistic gravitational motion in which periodicities are emergent properties of the physics and a fit to measurement data.”
There is a small real difference between my calculation and Jose’s.
Originally Posted by grapes
But that's a good point, if you have access to the current technology, like the autocorrelation function, why not take advantage of it, rather than homegrowing your own?
I am working in excel, and the autocorrelation function requires use of the covariance function with the formula as follows: “The autocorrelation function (ACF) at lag k, denoted ρk, of a stationary stochastic process is defined as ρk = γk/γ0 where γk = cov(yi, yi+k) for any i. Note that γ0 is the variance of the stochastic process.”

The measurement I did looks to achieve the same result, although it was laborious, requiring calculation separately for every annual lag from 1 to 244. Confirming using the above formula looks equally laborious. It seems that to produce an autocorrelation chart you need to manually calculate the correlation across sample lags in the expected range, which equates to what I did. Do you know if there is a simpler way?
Originally Posted by grapes
I highlighted the two figures in your quote of my post, above, his in red and yours in green. The difference, 178.86-178.81=.05 years, is 18 days, about half of the month intervals in the data you're analyzing.
Jose uses 178.77 in the first sentence of his abstract, combining the 178.81 defined as the mean period of the distance from the centre of mass to the sun with other factors listed in Table 2. He says his data covers the time from 1653 to 2060 over 407 years or about 2.25 SSB periods, using the 1951 publication Coordinates of the Five Outer Planets 1653-2060.

Thanks for drawing attention to the slightly higher number in this Table, but it still differs substantially from the period I found in the 6000 year JPL calculations. I have looked at the periodicity over the shorter more recent time period used by Jose and it does not change, indicating some difference between the 1951 calculations or methods and the JPL dataset.
Originally Posted by grapes
Ten years? That's impossible. How are you trying to do that?
I am comparing each data point to every subsequent year up to 244 years later, producing a smooth curve. My initial result compares the data for the entire 6000 year dataset, and the ten year comparison just looks at a ten year slice, giving the same result, as expected due to the stability of the orbits.

18. Originally Posted by Robert Tulip
Thanks again. As noted previously, autocorrelation is the correlation of a signal with a delayed copy of itself as a function of delay. In this case, I have established that the SSB signal correlates with its delayed copy to produce a simple orderly symmetrical wave function with period 178.86 years. While I have not used the established mathematical formula for autocorrelation, and have instead just added the differences of the wave amplitude over every range from zero to 244 years, this clearly establishes that the comparison over the delay of 178.86 years reveals autocorrelation in the similarity between observations as a function of the time lag between them. This matches to other aims of autocorrelation, such as finding a simple repeating pattern, the presence of a periodic signal obscured by noise, and identifying the missing fundamental frequency in the time domain signal.
I don't doubt that your approach comes up with an answer that is close. What I do suspect is that your technique exaggerates the same errors that Jose found in his analysis. By not using standard techniques, you certainly leave yourself open to that criticism from reviewers.
The simulation here is the JPL calculation of the SSB. NASA told me “the planetary ephemerides are not derived from a formula (in which periodicities might be "put in"). We are oblivious to periodicities when solving for planetary orbits. Instead, orbit solutions come from a numerical integration of 2nd order differential equations of relativistic gravitational motion in which periodicities are emergent properties of the physics and a fit to measurement data.”
There is a small real difference between my calculation and Jose’s.
You have not done near enough analysis to show that the difference is "real", that's the problem. Not using standard techniques is questionable anyway, but I suspect that your technique would show a different answer if applied to a different view of the data. I've given my reasons for that suspicion.
I am working in excel, and the autocorrelation function requires use of the covariance function with the formula as follows: “The autocorrelation function (ACF) at lag k, denoted ρk, of a stationary stochastic process is defined as ρk = γk/γ0 where γk = cov(yi, yi+k) for any i. Note that γ0 is the variance of the stochastic process.”

The measurement I did looks to achieve the same result, although it was laborious, requiring calculation separately for every annual lag from 1 to 244. Confirming using the above formula looks equally laborious. It seems that to produce an autocorrelation chart you need to manually calculate the correlation across sample lags in the expected range, which equates to what I did. Do you know if there is a simpler way?
Implementing signal processing algorithms in Excel has to be the worst way to go, probably.
Jose uses 178.77 in the first sentence of his abstract, combining the 178.81 defined as the mean period of the distance from the centre of mass to the sun with other factors listed in Table 2. He says his data covers the time from 1653 to 2060 over 407 years or about 2.25 SSB periods, using the 1951 publication Coordinates of the Five Outer Planets 1653-2060.

Thanks for drawing attention to the slightly higher number in this Table, but it still differs substantially from the period I found in the 6000 year JPL calculations.
I'm not sure that 18 days can be considered a substantial difference, given that the period measured is 180 years, especially since your sampling rate seems to be nearly twice that.
I have looked at the periodicity over the shorter more recent time period used by Jose and it does not change, indicating some difference between the 1951 calculations or methods and the JPL dataset.
I am comparing each data point to every subsequent year up to 244 years later, producing a smooth curve. My initial result compares the data for the entire 6000 year dataset, and the ten year comparison just looks at a ten year slice, giving the same result, as expected due to the stability of the orbits.
Ah, that makes the measurement over 254 years, not just 10. That was what I thought impossible.

I assume that ten year period calculation was the one to refine the data calculation? Would it be easy to repeat the calculation for another ten year period (similarly centered at S/J conjunction), from 2200 years ago? It wouldn't be as good as doing it for an entire cycle, but I would be interested in the results.

19. Is it valid to go back well beyond modern measurement evidence to investigate those periods? Surely all the ancient cycles are calculated backwards in time? The planet orbits may well be stable but for example the eccentricity of Jupiter might be greater or less in very ancient times and we do not have the evidence. It is thought there were massive perturbations in the early solar system if you consider billions of years. The evidence at a stretch goes into the chinese records a few thousand years, can we confirm both periods and eccentricities from those pre telescope days?

20. Originally Posted by profloater
Is it valid to go back well beyond modern measurement evidence to investigate those periods? Surely all the ancient cycles are calculated backwards in time? The planet orbits may well be stable but for example the eccentricity of Jupiter might be greater or less in very ancient times and we do not have the evidence. It is thought there were massive perturbations in the early solar system if you consider billions of years. The evidence at a stretch goes into the chinese records a few thousand years, can we confirm both periods and eccentricities from those pre telescope days?
I'm taking the analysis at face value, I think it is interesting to see what pitfalls there are in signal processing.

21. Ok well as I understand auto correlation it could find correlation independent of the planetary causes, since it looks at a result from a separate calculation derived from a double integration involving numerical analysis rather than assuming fixed periods. So I am not convinced about the data set. However I understand the interest in Roberts method versus autocorrelation. There are maybe lessons for error correction in mixed frequency signals.?

22. Originally Posted by profloater
the eccentricity of Jupiter might be greater or less in very ancient times and we do not have the evidence. It is thought there were massive perturbations in the early solar system if you consider billions of years.
Milankovitch climate analysis is based on the largely Newtonian celestial mechanics which incorporates variations in eccentricity of all the planets. These orbital patterns have been calculated with small error bars for thousands of years. The expulsion of Neptune from its early orbit at the time of the late heavy bombardment nearly four billion years ago is thought to have led to a stable solar system that has not appreciably changed over the million year framework discussed here, except for small factors such as the tiny outward drift of the moon discussed above.

23. Originally Posted by profloater
Ok well as I understand auto correlation it could find correlation independent of the planetary causes, since it looks at a result from a separate calculation derived from a double integration involving numerical analysis rather than assuming fixed periods. So I am not convinced about the data set. However I understand the interest in Roberts method versus autocorrelation. There are maybe lessons for error correction in mixed frequency signals.?
Profloater, unfortunately, none of your comment seems to make any sense. NASA’s method to calculate the SSB-sun distance, as I mentioned earlier, was integration rather than input of periodicities. But that does not in the slightest mean the wave function is “independent of the planetary causes”. The SSB-sun distance is mainly driven by planetary causes, so nothing about it, let alone its possible autocorrelation, can possibly be independent of planetary causes. That idea seems to introduce only confusion. My method confirmed Jose’s finding of autocorrelation in this dataset, while questioning its precise measurement, so again your description of my method as opposing autocorrelation is wrong. I cannot detect any meaning in your comment about error correction.

24. Originally Posted by Robert Tulip
Profloater, unfortunately, none of your comment seems to make any sense. NASA’s method to calculate the SSB-sun distance, as I mentioned earlier, was integration rather than input of periodicities. But that does not in the slightest mean the wave function is “independent of the planetary causes”. The SSB-sun distance is mainly driven by planetary causes, so nothing about it, let alone its possible autocorrelation, can possibly be independent of planetary causes. That idea seems to introduce only confusion. My method confirmed Jose’s finding of autocorrelation in this dataset, while questioning its precise measurement, so again your description of my method as opposing autocorrelation is wrong. I cannot detect any meaning in your comment about error correction.
The way I read it, prof is basically conceding the possibility of your attempt to find a period different from the planetary period. He goes on to say he now understands my interest in comparing your own result to others, that there may be something instructive to be found in the difference between your method and the actual autocorrelation method.

25. Dear all, and especially Grapes and Hornblower,

With apologies for a two year delay in reply, my underlying agenda in the above discussion was to support a broader analysis of the precessional structure of time. I self-published my paper on this topic at http://rtulip.net/yahoo_site_admin/a....110163331.pdf

I hesitated to share my essay here because it includes cultural analysis that sits uneasily with the astronomical parameters of Cosmoquest. However, the first part is mostly pure astronomy, including an explanation of the relation between precession and the wave function of the solar system, that I hope readers here will find of interest. I would warmly welcome discussion of the astronomy in this paper.

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Originally Posted by Robert Tulip
... However, the first part is mostly pure astronomy, including an explanation of the relation between precession and the wave function of the solar system, that I hope readers here will find of interest.
The first part is not purely astronomy, Robert Tulip. It is mostly astronomy but there is astrology irrelevancy. Addressing the science:
Precession of the equinoxes is merely the fact that the axial tilt of the Earth is caused by "the gravity of the sun, moon and planets tugging on the bulge around the earth’s equator" as in your PDF.
Milankovitch cycles are one of several drivers that can be causing ice ages. There are several issues with the Milankovitch cycles alone causing ice ages, e.g. marine isotope stage 5 began 10,000 years before the corresponding cycle forcing.
The solar system has a barycentre and that it obviously changes as planets collect on different sides of the Sun. You cite the HORIZONS Web-Interface with a graphic that shows a slightly irregular "wave" with a 179 year period for the distance of the Sun from the SSB from 3000 BC to 3000 AD. The axial tilt of the Earth and the SSB are related because they have a common cause - the tugging of the Sun and planets. The major influence will be the gas giants. So a precession period for the Earth being about 144 times the SSB "wave" is physics. Or maybe just a interesting, coincidental number like the Moon currently being able to provide total solar eclipses.

27. I am just as skeptical as ever about your idea that the 144:1 ratio of the precession period and the roughly recurring pattern of the giant planets is anything more than a coincidental numerical curiosity.

28. Thank you very much Reality Check and Hornblower. I appreciate your replies. I understand that astronomers hold a natural disdain for discussion of astrology, in view of its anti-scientific popular forms. I may have failed to adequately convey the underlying intent in my paper, which is to show the remarkable elegance of the main stable temporal structure of the solar system as a primary astronomical framework behind the cultural artifact of the concept of Zodiac Ages.
Originally Posted by Hornblower
I am just as skeptical as ever about your idea that the 144:1 ratio of the precession period and the roughly recurring pattern of the giant planets is anything more than a coincidental numerical curiosity.
Perhaps in dynamic astronomical terms of physical resonance between these stable temporal structures you are correct. What I am doing is preparatory to that hypothesis. The pattern linking the earth’s wobble and the periodicity of the wave function of the sun holds enough coincidental numerical curiosity to be worth describing. It is a little-known stable temporal pattern that encompasses our planet, providing a quantifiable feature of the popular concept of the zodiac age.

I explain in my paper that the pattern of the giant planets is not “rough”, as you assert, but has an elegant beauty that is remarkably stable. The key point is that Jupiter, Saturn and Neptune are always 30° on from their right ascension of 178.9 years before, with only minor drift, like the lunar Saros cycle. I prove that this stable JSN cycle forms the dominant planetary influence on the solar system centre of mass. The triple conjunction cycle of these planets therefore forms the main periodicity of the wave function of the sun against the galactic arc of the solar system.

That in itself is an interesting scientific discovery. The further coincidence that these triple conjunctions occur after exactly one twelfth of a zodiac age (2148 years) enables an astronomical definition of the Zodiac Age. With the main example of the Age of Pisces, this period has twelve ‘houses’ formed by the JSN triple conjunctions as they entered the twelve tropical signs in order from the first point of of Aries in 53 AD, Taurus in 232, Gemini in 411, etc, through to the current end of this Age of Pisces cycle as it enters its twelfth house around 2022.

A wide orb triple JSN conjunction is now approaching, beginning the ‘House of Pisces’ within the Age of Pisces. This final segment of the current zodiac age, just considered in this astronomical framing, begins with the JS conjunction this year and the JN and SN conjunctions between then and 2026. There is no need to speculate about any astrological meaning of this event to recognize it as a readily measurable astronomical fact that correlates with the concept of zodiac ages.
Originally Posted by Reality Check
The first part is not purely astronomy, Robert Tulip. It is mostly astronomy but there is astrology irrelevancy.
It can be difficult here to define the boundary between science and nonsense, given the pervasive tendency of astrology to sit on the nonsense side of that division. I am explaining that Zodiac Ages have a purely astronomical underpinning that has not been generally recognized. This stable pattern of division into twelve houses against the wave function of the solar system is its primary indicator. Some things that astronomers might assume are irrelevant can actually be scientific.
Originally Posted by Reality Check
Precession of the equinoxes is merely the fact that the axial tilt of the Earth is caused by "the gravity of the sun, moon and planets tugging on the bulge around the earth’s equator" as in your PDF.
Milankovitch cycles are one of several drivers that can be causing ice ages. There are several issues with the Milankovitch cycles alone causing ice ages, e.g. marine isotope stage 5 began 10,000 years before the corresponding cycle forcing.
Thanks for raising this fascinating problem of the orbital drivers of climate. I am currently reading A Farewell to Ice by Professor Peter Wadhams. He explains that the temperature of the earth only fell to a point that enabled orbital sensitivity to generate climate periodicity between about three and six million years ago, but the ice core data only enables measurement of these cycles back to about one million years. Other forcing factors such as CO2 and dust generate feedback amplifiers, but these are largely driven by the orbital patterns, of which precession is the main single factor.
Originally Posted by Reality Check
The solar system has a barycentre and that it obviously changes as planets collect on different sides of the Sun. You cite the HORIZONS Web-Interface with a graphic that shows a slightly irregular "wave" with a 179 year period for the distance of the Sun from the SSB from 3000 BC to 3000 AD. The axial tilt of the Earth and the SSB are related because they have a common cause - the tugging of the Sun and planets. The major influence will be the gas giants. So a precession period for the Earth being about 144 times the SSB "wave" is physics. Or maybe just a interesting, coincidental number like the Moon currently being able to provide total solar eclipses.
A few points here. The cause of the axial tilt period of the earth is mostly (99%) the gravity of the sun and moon, whereas the cause of the SSB wave is the balance of mass, with the sun on one end of the ‘seesaw’ and the other end producing the dominant wave function of the cycles of Jupiter, Saturn and Neptune. So your description of a “common cause of tugging” is an oversimplification, since the barycentre position is not caused by gravity.

The 144:1 ratio is just a temporary artifact as I explain in my paper, comparable to the eclipse coincidence you mention. What it means is that for the last million years or so, zodiac age have been divided into twelve equal sections marked by successive triple JSN conjunctions that occur in order at the twelve ‘hours of the clock’.

The Age of Pisces presents this structure very neatly, with the JSN patterns beginning at the March equinox aligning directly to the period when the equinox was in Pisces, and going progressively around the sky. The Age of Aquarius would begin in about 179 years from now if there were no drift in this pattern, but the situation is that there are overlapping families of JSN conjunctions, again like eclipse families. The Pisces family had its focal point in 769 AD, and is succeeded by families focused in 1523 and 2994 AD.

As I explain in my paper, “There were no close triple JSN conjunctions in the twentieth century. This cycle of the Age of Pisces is now reaching its slow end, while new JSN conjunction families emerge about every thousand years. The next family of JSN conjunctions is centred on a triple conjunction in 1523 AD in Pisces, and will include a triple conjunction in Gemini in 2060-61. This family group bridges the Ages of Pisces and Aquarius. The tightest triple conjunction of the Age of Aquarius is in 2994 AD in Aquarius, and then the equivalent event for the Age of Capricorn is in 4284 AD in Capricorn. The JSN family group for the Age of Aquarius has a broad triple JSN conjunction in Virgo and Libra in 2096-2100.”

Based on my definition of a zodiac age in terms of a period of twelve JSN conjunction cycles, this triple conjunction from 2096 presents a reasonable astronomical choice to define the dawn of the Age of Aquarius.

29. I feel two different concepts are being shoehorned together. The origins of myths and the precessional causes of climate change. I am not opposed to either as concepts. It was my interest in psychology and the richer language of astrology that led me to study the subject years ago, but there is I fear no astrological link to climate change, while there is considerable evidence of the influence on religion and politics. The long term history of the climate vis a vis ice ages, evolution of the solar system, impacts and volcanos is of course fascinating and our knowledge gradually progresses. If you look at the astrological view of comets, i.e. bad news, it is easy to postulate a link to actual experience of comets as impacts although tenuous in the known history of astrology, even chinese astrology, does not go back far enough. The aboriginal oral tradition of sea level rise, possibly or probably following a major impact, is a better correlation but astrology is not involved in that myth, at least not western or chinese astrology. Therefore I find your paper very interesting but I would be happier to see it as two different papers, one on myths and the other on climate.

30. Originally Posted by Robert Tulip
The 144:1 ratio is just a temporary artifact as I explain in my paper, comparable to the eclipse coincidence you mention.
You are acknowledging that the ratio is merely a transient coincidence. This is after years of posting in a manner which led me to infer that you really believed that there was a dynamic resonance. I think I can safely conclude that your line of thought is based primarily in mythology and has no credible basis in physics.