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Robert Tulip
2018-Jan-14, 05:22 AM
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 (https://forum.cosmoquest.org/attachment.php?attachmentid=22892&d=1515907005), 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 (https://forum.cosmoquest.org/attachment.php?attachmentid=22893&d=1515907035) 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.

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/showthread.php?80362-Spiral-Model-of-Solar-System&p=2057269#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

grapes
2018-Jan-14, 07:17 AM
You're contrasting your value of 178.86 years with his value of 178.7 years, and your granularity is .27 years?

Robert Tulip
2018-Jan-14, 08:05 AM
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.

grapes
2018-Jan-14, 07:15 PM
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.

Robert Tulip
2018-Jan-14, 10:37 PM
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.

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.

Hornblower
2018-Jan-14, 11:21 PM
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.

Robert Tulip
2018-Jan-14, 11:51 PM
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.
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.
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.
After all, the planets' periods are not small integer multiples of one anotherThe 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.
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.

Hornblower
2018-Jan-15, 03:39 AM
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.

Robert Tulip
2018-Jan-15, 04:09 AM
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 (https://forum.cosmoquest.org/attachment.php?attachmentid=22897&stc=1&d=1515989188) 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.

profloater
2018-Jan-15, 09:06 AM
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.

Hornblower
2018-Jan-15, 05:42 PM
Here is a diagram of the SSB wave function (https://forum.cosmoquest.org/attachment.php?attachmentid=22897&stc=1&d=1515989188) 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?

profloater
2018-Jan-15, 05:54 PM
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.

Hornblower
2018-Jan-15, 05:59 PM
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.

Robert Tulip
2018-Jan-15, 08:26 PM
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.

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.
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.

tusenfem
2018-Jan-17, 12:27 PM
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] (https://forum.cosmoquest.org/showthread.php?167716-Tidal-forces-on-the-Sun-extracted-from-Sun-and-Barycentre-Period&p=2436402#post2436402).

grapes
2018-Jan-17, 05:12 PM
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.

grapes
2018-Jan-17, 05:40 PM
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.

profloater
2018-Jan-17, 09:56 PM
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.

Robert Tulip
2018-Jan-18, 01:29 PM
the usual signal processing approach would be autocorrelation. Yes, autocorrelation is precisely what I am looking at.

From Wikipedia (https://en.wikipedia.org/wiki/Autocorrelation): “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 (https://forum.cosmoquest.org/showthread.php?80362-Spiral-Model-of-Solar-System&p=2057269#post2057269) and this spreadsheet with the details of the FFT data (https://forum.cosmoquest.org/showthread.php?80362-Spiral-Model-of-Solar-System&p=2057688#post2057688).

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.

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.

grapes
2018-Jan-18, 04:06 PM
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 (https://en.wikipedia.org/wiki/Autocorrelation): “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.

profloater
2018-Jan-18, 05:49 PM
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.

Robert Tulip
2018-Jan-19, 05:39 AM
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.

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.

profloater
2018-Jan-19, 09:51 AM
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?

Robert Tulip
2018-Jan-19, 10:28 AM
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.

Robert Tulip
2018-Jan-19, 10:33 AM
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.

profloater
2018-Jan-19, 10:52 AM

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?

Robert Tulip
2018-Jan-20, 01:48 AM
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.

Hornblower
2018-Jan-20, 04:18 AM
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"?

Robert Tulip
2018-Jan-20, 07:13 AM
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.

profloater
2018-Jan-20, 10:18 AM
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

grapes
2018-Jan-20, 11:01 AM
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.

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.

profloater
2018-Jan-20, 02:05 PM
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.

profloater
2018-Jan-20, 02:10 PM
this is a screen shot, maybe easier to read.
22906

grapes
2018-Jan-20, 03:14 PM
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.

Hornblower
2018-Jan-22, 11:15 PM
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.

Robert Tulip
2018-Jan-27, 10:41 AM
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.
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 (http://www.sciencedirect.com/science/article/pii/0019103582901348?via%3Dihub), (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.

Hornblower
2018-Jan-27, 02:11 PM
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.

Hornblower
2018-Jan-27, 02:37 PM
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.

Robert Tulip
2018-Jan-27, 08:29 PM
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.

grapes
2018-Jan-27, 09:48 PM
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.

Robert Tulip
2018-Jan-27, 09:55 PM
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.

grapes
2018-Jan-31, 09:55 AM
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?

Robert Tulip
2018-Feb-03, 09:26 PM
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.
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.

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.

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.

grapes
2018-Feb-04, 04:39 PM
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.

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?

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.

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?

Hornblower
2018-Feb-05, 05:45 PM
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.

grapes
2018-Feb-05, 06:24 PM
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. :)

Robert Tulip
2018-Feb-05, 09:50 PM
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.

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 (https://forum.cosmoquest.org/showthread.php?80362-Spiral-Model-of-Solar-System&p=2059466#post2059466) “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.

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 (http://www.real-statistics.com/time-series-analysis/stochastic-processes/autocorrelation-function/): “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?

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.

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.

grapes
2018-Feb-08, 06:52 PM
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 (https://forum.cosmoquest.org/showthread.php?80362-Spiral-Model-of-Solar-System&p=2059466#post2059466) “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 (http://www.real-statistics.com/time-series-analysis/stochastic-processes/autocorrelation-function/): “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.

profloater
2018-Feb-08, 09:19 PM
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?

grapes
2018-Feb-09, 12:28 AM
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.

profloater
2018-Feb-09, 04:20 AM
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.?

Robert Tulip
2018-Feb-09, 08:13 AM
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.

Robert Tulip
2018-Feb-09, 08:58 AM
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.

grapes
2018-Feb-14, 03:15 PM
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.