# Thread: Sun and Barycentre Period

1. ## Sun and Barycentre Period

A paper on the sun’s motion http://adsabs.harvard.edu/full/1965AJ.....70..193J by Paul D. Jose published in 1965 in the Astronomical Journal states “the variation in the motion of the sun around the center of mass of the solar system has a periodicity of 178.7 years.”

In researching this topic, I have found indication of a possible small error in Jose’s calculation, with a strong periodicity at 178.86 years in the NASA JPL Horizons calculations of the distance of the sun from the barycentre over 6000 years. I am interested to seek comment on my method for deriving this figure, and help in explaining the 0.16 year difference from Jose’s figure.

My attached charts show my results. The first chart, showing Solar System Barycentre Variance in Solar Distance, compares the change in solar distance to the SSB over different time periods, ranging from one year to 244 years. The resulting line has a clear minimum at 179 years, and a clear axis of symmetry at 89.5 years, indicating periodicity at 179 years. It shows that after 179 years, the variance in distance is 7% of the peak variance. The oscillation in the chart matches the Jupiter-Saturn 20 year cycle, with variance greatest at points separated by 10, 30, 50 etc years and smallest at points separated by 20, 40, 60 etc years.

The 179 year minimum occurs when Jupiter, Saturn and Neptune are at the same relative position, which makes sense since these three planets have the biggest effect on the SSB. The very clear axis of symmetry in the graph at 89.5 years reflects the fact that if these three planets come together every 179 years, their ‘outward’ and ‘inward’ journeys on that cycle will be close to mirror images.

In seeking finer resolution of the observed 179 year period, my second chart indicates a minimum, and therefore an average periodicity, at 178.86 years. My method for this calculation was to use the JPL data with granularity 0.27 years to find the average difference for periods from 177 to 194 years, producing the following table.

Code:
```Average Variance in Distance from Sun to SSB (Solar Radii)	Years
0.252923908	177.1379
0.216642582	177.4112
0.179511942	177.683
0.141957922	177.9549
0.104649252	178.2349
0.070030527	178.5054
0.047409704	178.78
0.052477895	179.0573
0.081795385	179.3306
0.118153163	179.6024
0.155814897	179.8743
0.193518583	180.1489
0.230623183	180.4221
0.266936145	180.694
0.302168912	180.9658
0.336327244	181.2445
0.455907453	194.9303```
The minimum at this level of detail is 178.78. Plotting the data and extending the arms of the curve gives a minimum of 178.86, which also matches my previous research calculating the period from the difference between turning points in the JPL graph.

I would be grateful for advice on best mathematical method to calculate the exact minimum of the curve that best fits to the above data. I tried this using the following websites but could not get a close enough curve. https://mycurvefit.com/ https://www.derivative-calculator.net/https://www.symbolab.com/solver/step-by-step/

My reason for thinking that 178.86 is more likely than Jose's 178.7 is based on my previous analysis of the spectral power. Decomposing the JPL data by Fourier Transform shows that components with period multiples just slightly more than 179 provide 33% of the wave power, balancing the 41% of the wave power from the multiple of the Jupiter-Saturn cycle at 178.67 years.

I posted on this a few years ago at https://forum.cosmoquest.org/showthr...69#post2057269 and am now posting again because this new research validates and expands my observation of a stable 178.86 year SSB wave function.

Robert Tulip

2. You're contrasting your value of 178.86 years with his value of 178.7 years, and your granularity is .27 years?

3. Originally Posted by grapes
You're contrasting your value of 178.86 years with his value of 178.7 years, and your granularity is .27 years?
Yes. The input data produces curve points separated by 0.27 years, synthesising 6000 years of the NASA calculation. The minimum point on the curve can be calculated to a far more precise value than this range.

It is like if you have a parabola with points (-3,9), (-1,1), (8,64), you can calculate the minimum point (0,0).

I had another go at fitting the curve, and came up with the attached, showing how 178.7 is well short of the turning point, which is clearly between 178.85 and 178.9, as the two arrows indicate. My calculation from two separate methods was 178.86 as shown, at the turning point of this curve just using visual inspection.

4. I see how you're determining the end-of-cycle point, but how did you determine the starting point? The graph starts out so much lower.

O, I see. You've taken your higher Fourier components and combined them into a synthetic curve, which then essentially starts with all the planets together on the same side of the sun. That's your "zero" point. Then you determine your period by the distance (time) to the next extreme low point (which you have interpolated).

ETA: However, that distance is going to change over time. Run it out ten or twenty more iterations--you just have to calculate the values around the suspected low points, maybe 4000 years from now. I suspect that the average value will tend towards a multiple of the period of the Jupiter-Saturn component, since that is clearly the dominant one. Probably the value that appeared in the article was derived from the periods of Jupiter and Saturn. Using ( https://nssdc.gsfc.nasa.gov/planetary/factsheet/ ) Jupiter period of 4331 days and Saturn period of 10747, we get 10747*4331/(10747-4331), 7254.56 days, or divided by 365.242 times nine periods (very close to 165 years, the period of Neptune) is 178.76 years. Looking at the article, it seems they use 178.77, so maybe that's how they got it.

OK, looking at that NASA chart I linked to above, those periods are tropical not sidereal, these webpages ( https://nssdc.gsfc.nasa.gov/planetary/planetfact.html ) from the same website make the distinction, and the sidereal values are 4332.589 and 10759.22, and the calculation is 10759.22*4332.589*/(10759.22-4332.589), 7253.455 days, times nine periods is 178.73 years.
Last edited by grapes; 2018-Jan-14 at 10:12 PM. Reason: ETA

5. ## Calculation Method

Originally Posted by grapes
I see how you're determining the end-of-cycle point, but how did you determine the starting point? The graph starts out so much lower.
Assuming you are speaking about the first graph, with file name SSB Variance 179 yr.png, and showing Solar System Barycentre Variance in Solar Distance over 244 years.

My method for producing this graph was as follows.
1. Obtain 22,000 data points from NASA JPL Horizons showing calculated distance from the sun to the SSB over 6000 years from 3000 BC to 3000 AD.
2. Extract from this 4096 annual data points, noting that the SSB-sun vector change over one year is smooth and regular.
3. Tabulate every difference in vector over a specified time gap. At points separated by 0 years the difference is 0, which is why the graph starts at 0. At points separated by one year, the difference is calculated by averaging the differences between all data points separated by one year, giving a result of 0.14 solar radii.
4. This process is repeated iteratively for every annual gap, 2, 3, … 244 years. For example at the observed chart minimum point (not counting zero), 179 years, the difference is calculated by averaging the differences between all data points separated by 179 years. This figure is 0.046 solar radii by my calculation. So any two sun-SSB vectors separated by 179 years will on average differ by 0.046 solar radii, one third the difference between points separated by one year, and 7% of the maximum average difference of 0.7 radii.
5. Redo the above using all 22000 data points to calculate the average vector between 177 and 181 years (with 194 as outlier) with granularity 0.27 years to produce second graph.
6. Interpolate the minimum point of this second graph as the axis of symmetry between its arms.

It is very interesting to me that the first curve, with annual data to 244 years, shows the change in SSB vector as such a smooth and symmetrical pattern with strong periodicity driven by the gas giant planets.

The difference between my calculation of the SSB period, 178.86 years, and Jose’s 178.7 years, is 365.25 x 0.16 = 58.44 days.
Originally Posted by grapes
O, I see. You've taken your higher Fourier components and combined them into a synthetic curve, which then essentially starts with all the planets together on the same side of the sun. That's your "zero" point. Then you determine your period by the distance (time) to the next extreme low point (which you have interpolated).
No, it is not Fourier components. It is just average differences in distance. It doesn’t start with all the planets together, which would pull the SSB more than a solar radius out of the sun, but just starts at the difference between any point and itself, zero, as explained above.

There is no interpolation in this initial chart. But in the second chart, file name SSB variance 178.86 years.png, I interpolate the theoretical minimum point of the curve of best fit, which I then show again at the Fit My Curve picture in my second post.

6. If Jose was using a different data set, I would say the results are in remarkably good agreement, when you consider that the waveform only roughly repeats from one cycle to the next. After all, the planets' periods are not small integer multiples of one another and the orbits have significant eccentricity.

7. Originally Posted by Hornblower
If Jose was using a different data set,
That looks likely since his paper is from 1965 and the JPL analysis of the SSB is more recent.
Originally Posted by Hornblower
I would say the results are in remarkably good agreement,
Yes true, which means this is a revision. I have not been able to find any other references except false ATM claims that there is no regular SSB cycle at all. It seems the main interest in Jose’s paper was just in relation to prediction of sunspot cycles.
Originally Posted by Hornblower
when you consider that the waveform only roughly repeats from one cycle to the next.
Not true that the repetition is only rough. The repetition from one 179 year cycle to the next is very close, with only a slow drift in the shape of the wave at period of about 1000 years.
Originally Posted by Hornblower
After all, the planets' periods are not small integer multiples of one another
The integer multiples occur around the 179 year point, which is within 0.5 years of 9 x JS, 5 x SN, 14 x JN and 13 x JU.
Originally Posted by Hornblower
and the orbits have significant eccentricity.
Yes, that is a very good point to raise. I am sure eccentricity is a factor in the millennial drift of the wave form, but doubt it makes much difference at the 179 year comparison between successive periods.

8. Originally Posted by Robert Tulip
That looks likely since his paper is from 1965 and the JPL analysis of the SSB is more recent. Yes true, which means this is a revision. I have not been able to find any other references except false ATM claims that there is no regular SSB cycle at all. It seems the main interest in Jose’s paper was just in relation to prediction of sunspot cycles. Not true that the repetition is only rough. The repetition from one 179 year cycle to the next is very close, with only a slow drift in the shape of the wave at period of about 1000 years.The integer multiples occur around the 179 year point, which is within 0.5 years of 9 x JS, 5 x SN, 14 x JN and 13 x JU. Yes, that is a very good point to raise. I am sure eccentricity is a factor in the millennial drift of the wave form, but doubt it makes much difference at the 179 year comparison between successive periods.
Very close but not exact, with changing shape from one cycle to the next. Multiples close to but not exactly small integers. That is my idea of being roughly periodic. You and I appear to have different ideas of what roughly means. So be it.

9. Originally Posted by Hornblower
Very close but not exact, with changing shape from one cycle to the next. Multiples close to but not exactly small integers. That is my idea of being roughly periodic. You and I appear to have different ideas of what roughly means. So be it.
Here is a diagram of the SSB wave function showing how close the shape is from one 179 year SSB cycle to the next. There are almost no visible gaps between successive lines. The drift in shape occurs over much longer time.

10. Why are you not looking at a circular plot as posted in the other thread or compare it with the planets which separates out the effects of Jupiter and Saturn and the lesser effects of all the other planets? You seem to be finding the effect of Neptune's orbit for example which lines up with Jupiter, Saturn about every 170 years ( that's an approximation from memory) it is also messed up a bit by pluto's weird orbit.

11. Originally Posted by Robert Tulip
Here is a diagram of the SSB wave function showing how close the shape is from one 179 year SSB cycle to the next. There are almost no visible gaps between successive lines. The drift in shape occurs over much longer time.
At that image scale with no coordinate grid lines I cannot read the interval between successive crests with any certainty.

Is there some variation from one cycle to the next in the interval between successive crests? If not, then why jump through a lot of curve fitting hoops to get a period?

12. This is silly in my opinion, the biggest drivers are Jupiter and Saturn and they conjunction every 11 years or so and then a lesser driver is Neptune with a slower orbit which sometimes also conjunction Jupiter and Saturn. All predictable and so no surprise that you find an extreme point depending on how many years you take into account. What point are you seeking? The regular periods are altered as you would expect by the other planets. Either with or opposing the big ones.

13. Originally Posted by profloater
This is silly in my opinion, the biggest drivers are Jupiter and Saturn and they conjunction every 11 years or so and then a lesser driver is Neptune with a slower orbit which sometimes also conjunction Jupiter and Saturn. All predictable and so no surprise that you find an extreme point depending on how many years you take into account. What point are you seeking? The regular periods are altered as you would expect by the other planets. Either with or opposing the big ones.
And don't forget Uranus.

14. Originally Posted by Hornblower
At that image scale with no coordinate grid lines I cannot read the interval between successive crests with any certainty.
The method to produce this diagram was to take the NASA Sun-SSB data over 6000 years, divide it into 178.9 year segments, and stack these segments on top of each other. This form of presentation came from the late Carl Smith. It is a way to show the speed of drift in the SSB wave form. When there is no white space between two lines, the interval between successive crests, defined as the variance in solar vector over 178.9 years, is negligible. White points between lines appear when the shape of the curve is changing over centuries from a local concavity to convexity. However, the small number of these white points illustrates the stability of the wave, and that its pattern is regular rather than rough. My interpretation of the data is that the stability comes from the interaction of Jupiter, Saturn and Neptune as the main drivers of the SSB position with respect to the sun in its repeating 178.9 year pattern, while the occasional faster periods of change shown by the few white points between the lines may come from the influence of the planet Uranus.
The purpose of this thread is to quantify the interval between successive crests, so I appreciate your putting the problem in those terms. As per the explanation in the opening post, overall the variance between the vertically connected points in this graph of 6000 years of data is actually 7% of the random difference between the length of any two SSB-sun vectors. While 7% may seem a lot, it is only enough to produce the slow millennial drift seen in the wave form, which overall has a strong orderly stability. Its nine subpeaks are caused by the Jupiter-Saturn 20 year cycle and each successive line is strongly similar to the preceding and succeeding wave forms.
Originally Posted by Hornblower
Is there some variation from one cycle to the next in the interval between successive crests?
Yes, as per my opening post, this variation is 7% of random, ie very small. In addition, this 7% variation is itself orderly, reflecting directional patterns that cause the gradual change of the shape of the wave over thousands of years.
Originally Posted by Hornblower
If not, then why jump through a lot of curve fitting hoops to get a period?
The curve fitting exercise in my second post was purely designed to illustrate the method to quantify the exact SSB period and to explain how the data granularity can produce a more exact result. As I use the curve fit to show, supporting the initial method of analysing the axis of symmetry around 179 years, the 1965 close estimate by Jose of 178.7 years was out by two months, and the best estimate of the actual SSB wave period is 178.86 years.

15. You may notice that there are some posts missing.
Keep this thread on the barycentre of the solar system only.
For the discussion of tidal forces that are playing, see the new thread Tidal forces on the Sun [extracted from Sun and Barycentre Period].

16. Originally Posted by Robert Tulip
Assuming you are speaking about the first graph, with file name SSB Variance 179 yr.png, and showing Solar System Barycentre Variance in Solar Distance over 244 years.

My method for producing this graph was as follows.
1. Obtain 22,000 data points from NASA JPL Horizons showing calculated distance from the sun to the SSB over 6000 years from 3000 BC to 3000 AD.
2. Extract from this 4096 annual data points, noting that the SSB-sun vector change over one year is smooth and regular.
3. Tabulate every difference in vector over a specified time gap. At points separated by 0 years the difference is 0, which is why the graph starts at 0. At points separated by one year, the difference is calculated by averaging the differences between all data points separated by one year, giving a result of 0.14 solar radii.
4. This process is repeated iteratively for every annual gap, 2, 3, … 244 years. For example at the observed chart minimum point (not counting zero), 179 years, the difference is calculated by averaging the differences between all data points separated by 179 years. This figure is 0.046 solar radii by my calculation. So any two sun-SSB vectors separated by 179 years will on average differ by 0.046 solar radii, one third the difference between points separated by one year, and 7% of the maximum average difference of 0.7 radii.
5. Redo the above using all 22000 data points to calculate the average vector between 177 and 181 years (with 194 as outlier) with granularity 0.27 years to produce second graph.
6. Interpolate the minimum point of this second graph as the axis of symmetry between its arms.

It is very interesting to me that the first curve, with annual data to 244 years, shows the change in SSB vector as such a smooth and symmetrical pattern with strong periodicity driven by the gas giant planets.

The difference between my calculation of the SSB period, 178.86 years, and Jose’s 178.7 years, is 365.25 x 0.16 = 58.44 days.
I see. I think the usual signal processing approach would be autocorrelation. You'd get similar results, but where your method gives lows or zeros at the period, autocorrelation would give highs, or 1.
No, it is not Fourier components. It is just average differences in distance. It doesn’t start with all the planets together, which would pull the SSB more than a solar radius out of the sun, but just starts at the difference between any point and itself, zero, as explained above.

There is no interpolation in this initial chart. But in the second chart, file name SSB variance 178.86 years.png, I interpolate the theoretical minimum point of the curve of best fit, which I then show again at the Fit My Curve picture in my second post.
One "easy" way would be to take the points and feed them to wolframalpha.com

0, 0.216642582), (1, 0.179511942), (2, 0.141957922), (3, 0.104649252), (4, 0.070030527), (5, 0.047409704), (6, 0.052477895), (7, 0.081795385), (8, 0.118153163), (9, 0.155814897), (10, 0.193518583)

I changed the x-component values to simple integers, since they're evenly spaced in time anyway. (And I had number-of-characters limitation, accessing the website on my phone!) If you copy them into wolfram, you can precede them with "Fit" or "Fit curve" and it'll give you an equation.

17. Originally Posted by Robert Tulip
As I use the curve fit to show, supporting the initial method of analysing the axis of symmetry around 179 years, the 1965 close estimate by Jose of 178.7 years was out by two months, and the best estimate of the actual SSB wave period is 178.86 years.
I doubt it.

As near as I can tell from your graphs, the main influences are Jupiter, Saturn, and Neptune. In order for there to be any semblance of regularity in the signal, the excursions due to Jupiter/Saturn conjunction have to align. That means the period has to be an integer multiple of their synodic period--and that's the value that Paul Jose uses. It's just nine times that synodic period, and the 9x is as close as possible to the period of Neptune (164.8 years), the solar system body with the next size effect (ETA: or, the synodic period of Uranus and Neptune, which Paul Jose has as 171.4 years, even closer to that 178). Unless those values change over time.

Regardless, you have the whole signal, reconstructed, back thousands of years ago, why not use the entire signal for cross correlating data sets? There will be effects from orbit ellipticity after all, as has been mentioned.
Last edited by grapes; 2018-Jan-18 at 11:24 AM. Reason: ETA

18. It may be interesting that the barycentre passes close to the sun centre every time saturn is on the opposite side from Jupiter and very close every other such opposition. in other words the planetary line up to bring the barycentre to the sun centre is a 39 year cycle twice the jupiter saturn cycle. the two most recent years were 1951 and 1990.

19. Originally Posted by grapes
the usual signal processing approach would be autocorrelation.
Yes, autocorrelation is precisely what I am looking at.

From Wikipedia: “Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.”

Considering the Sun-SSB vector as a signal, I have analysed its correlation with delayed copies and found stable repeating patterns.

In my previous work on the Fourier Transform of this data, I produced this SSB FFT chart and this spreadsheet with the details of the FFT data.

We see here the barycentric frequencies of the solar system in peak order, with their planetary drivers.

I have added in the power of each peak, as can be readily seen against the chart, with the percentages of each peak against the sum of these 11 peaks, and the actual orbital periods, which match the peaks as shown. The unknown peaks are 8% of the total power.

Code:
```Cycle	FFT Peak in years	A	B	Power	%	Actual Period
1	19.85	Jupiter	Saturn	983	40.9%	19.85
2	12.8	Jupiter	Neptune	419	17.4%	12.78
3	13.8	Jupiter	Uranus	190	7.9%	13.81
4	35.9	Saturn	Neptune	189	7.9%	35.87
5	11.9	Jupiter	Cycle	137	5.7%	11.86
6	7.8	unknown		128	5.3%
7	45.5	Saturn	Uranus	96	4.0%	45.37
8	9.9	Jupiter	Saturn?	75	3.1%	9.93
9	8.2	unknown		72	3.0%
10	29.5	Saturn	cycle	59	2.5%	29.46
11	171	Uranus	Neptune	57	2.4%	171.37
2405	100.0%```
It is interesting that the Jupiter-Neptune peak is double the power of the Jupiter-Uranus peak. Neptune is so much further away that it 'pulls' the barycenter more than Uranus does.

Looking at this analysis against the autocorrelation framework, it appears that the autocorrelation identifies the missing fundamental frequency of 178.9 years in a signal implied by its harmonic frequencies, defined by the spectral peaks in the fourier transform, equating mainly to the main planetary pairs.

20. Originally Posted by Robert Tulip
Yes, autocorrelation is precisely what I am looking at.
Not precisely.

I've read through the other thread, and Paul Jose's old article. Interesting stuff.
From Wikipedia: “Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.”
Autocorrelation, as I mentioned before, produces correlation values from -1 to 1, with high values when there is a match, whereas you're producing low values when there is a match. I'm not implying that the answer will be any different, with a different method.

But I don't see how you are not getting the 9xJS value, either. That doesn't make sense to me.

21. did you see that ancient paper which introduced the concepts of acceleration and jerk which is rate of change of acceleration of the barycentre, and the fascinating thing there was the correlation of jerk to the 11.8 year average sunspot cycle?. I cannot find any figures for how that jerk was calculated. If it was sinusoidal there is no jerk but if it involves a combination of the faster inner planets I suppose there could be a rate of change of acceleration. Or it's nonsense.

22. Originally Posted by grapes
Not precisely. I've read through the other thread, and Paul Jose's old article. Interesting stuff. Autocorrelation, as I mentioned before, produces correlation values from -1 to 1, with high values when there is a match, whereas you're producing low values when there is a match. I'm not implying that the answer will be any different, with a different method. But I don't see how you are not getting the 9xJS value, either. That doesn't make sense to me.
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.
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.

23. I find now that I need more explanation of what that spreadsheet does. I can see in the first column the period in years of the conjunctions of planets given in the next column. But after that I need more explanation of the calculations For example you have "spectral power" 983 etc. But then there is a 9.9 also given as Jupiter Satrun, what is that?

24. Originally Posted by profloater
This is silly in my opinion, the biggest drivers are Jupiter and Saturn and they conjunction every 11 years or so and then a lesser driver is Neptune with a slower orbit which sometimes also conjunction Jupiter and Saturn. All predictable and so no surprise that you find an extreme point depending on how many years you take into account. What point are you seeking? The regular periods are altered as you would expect by the other planets. Either with or opposing the big ones.
Hi Profloater, I wasn't quite sure what you thought was "silly", but I wanted to note for the record that your statement that Jupiter and Saturn "conjunction every 11 years or so" is false. I would not want other readers thinking your comment was correct. The Jupiter-Saturn conjunction period is 19.85 years, not 11 years. I have found your comments in this thread hard to follow, as it does not seem you have read my posts very carefully. If you think it is "all predictable" then you should be able to explain the difference between my calculations and those of Jose that I asked about. On your question "what point are you seeking?", hopefully readers should be able to see fairly clearly that the point is to analyse the wave function of the solar system barycentre. And your statement "with or without the big ones" seems to wrongly imply that the terrestrial planets have significant effect on the barycentre. My understanding is that the terrestrial planets are too small and close to have significant effect, as I outlined in the spectral analysis.

25. Originally Posted by profloater
9.9 also given as Jupiter Satrun, what is that?
I suspect that Hornblower was correct that the eccentricity of the gas giant orbits is important, as this seems to be a possible explanation of the distinct spectral peak at 9.9 years, as half of the JS conjunction period. These figures reflect the peaks linked in the graph of the Fourier Spectrum analysis of the SSB wave.

26. Originally Posted by Robert Tulip
Hi Profloater, I wasn't quite sure what you thought was "silly", but I wanted to note for the record that your statement that Jupiter and Saturn "conjunction every 11 years or so" is false. I would not want other readers thinking your comment was correct. The Jupiter-Saturn conjunction period is 19.85 years, not 11 years. I have found your comments in this thread hard to follow, as it does not seem you have read my posts very carefully. If you think it is "all predictable" then you should be able to explain the difference between my calculations and those of Jose that I asked about. On your question "what point are you seeking?", hopefully readers should be able to see fairly clearly that the point is to analyse the wave function of the solar system barycentre. And your statement "with or without the big ones" seems to wrongly imply that the terrestrial planets have significant effect on the barycentre. My understanding is that the terrestrial planets are too small and close to have significant effect, as I outlined in the spectral analysis.
You are quite right I typed too fast and used the approximate Jupiter period, my mistake. I did not see early on any link to a sunspot analysis which interests me. Now I made that comment because it seemed to me you were analysing the sun to barycentre distance as a frequency without realising it must be due to the positions of all the planets. Therefore the positions and orbits of the planets are the cause and predictable without going backwards from the reported barycentre from a paper.

My take was that the barycentre is a mass balance whereas the gravitational effect is a distance squared or distance cubed effect. So when I was looking at sunspots and the jupiter eccentricity and saturn effects I used Newtons gravity but still had a forcing frequency going out of phase with the sunspot record.

In other words the sun does not feel the barycentre (mass times distance) it feels the gravity of the planets mass divided by distance squared and distance cubed depending on what you are looking for. That's why I think the barycentre analysis will miss the point.

When I say what point are you seeking I was expecting you to say sunspots. So are we at cross purposes?

27. Originally Posted by profloater
When I say what point are you seeking I was expecting you to say sunspots. So are we at cross purposes?
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.

28. 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.
What is "structure of time"?

29. Originally Posted by Hornblower
What is "structure of time"?
I am using structure of time to mean an orderly stable repeating encompassing pattern that characterises the physical system of the sun and its orbiting objects.

30. this table compares the mass times distance with the mass divided by distance squared:

mass kg x10^ sun dist x10^ mass/dist^2 orbit years massXdist 10^
km kg/m^2 kgkm
mercury 3.3 23 57.9 6 98.44 0.24 19.107 30
venus 4.86 24 108.2 6 415.13 0.62 525.852 30
earth 6 24 149.6 6 268.09 1.00 897.6 30
mars 6.41 23 227.9 6 12.34 1.88 146.0839 30
jupiter 1.898 27 778.5 6 3,131.69 11.86 1477.593 33
saturn 5.683 26 1.429 9 278.30 29.46 8.121007 35
uranus 8.681 25 2.871 9 10.53 84.01 24.92315 34
neptune 1.024 26 4.498 9 5.06 164.76 4.605952 35

I hope the formatting stays together, you can see how different the gravity effect is from the barycentre calculation
i show the exponential separately, that's the 10^ column Oh i see it didnt Ill try again