Quote:
Originally Posted by Jim
Fair question, and I see now the six decimal points on the title of this thread, while empirically derived, are less useful than a moving average. I don't think the argument is that your nine significant figure number is "less useful" but that it is far too precise considering how it was derived. I'm not even sure your five significant figure numbers are appropriately precise; they are based on data that is 500 years old and/or extrapolated into the future. Remember that you should not claim a level of precision for your calculation that is greater than the level of precision of the data being used. If you can show that x significant figures is appropriate for the least precise data point, then your result should not exceed x significant figures. I'd suggest three significant figures is appropriate given the source of the data points. So, the SSB for your first period is 179; the SSB for your second period is 179.
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Jim, Thanks for this comment. Because my numbers are derived solely from gravitational calculations they are more appropriately precise than you say.
The underlying planetary composition of the SSB 179 year period is the interactions of the Sun with Jupiter, Saturn, Uranus and Neptune (J-S-U-N). Using the C = 1/(1/A - 1/B) formula provided by
Hornblower at
this post gives the following correlations between outer planetary cycles and the great year (GY) estimated at 25764 years:
- Jupiter-Saturn: 9 cycles = 178.65 years: 178.65/GY/144-1 = -0.145%
- Jupiter-Uranus: 13 cycles = 179.4 years: 179.4/GY/144-1 = 0.27%
- Jupiter-Neptune: 14 cycles = 178.9034 years: 178.9034/GY/144-1 = 0.007%
- Saturn-Uranus: 4 cycles = 181.1 years: 181.1/GY/144-1 = 1.217 %
- Saturn-Neptune: 5 cycles = 179.35 years: 179.35/GY/144-1 = 0.241%
- Uranus-Neptune: 1 cycle = 172.7 years: 172.7/GY/144-1 = -3.483%
(Note: these numbers are from the formula and have small errors. Also, the GY is variously cited as 25764 and 25765 years – consistent with the slowing trend I have found here.)
My question is how planetary cycles interact with each other to produce a main stable pattern in the SSB. My finding is that using the SSB moving average reduces the GY phase errors in this list to 0.001%.
Over any given period the six cycles listed will produce SSB-POS radius peaks with average period around 179 years. This average can be decomposed to find more significant decimal places. This method is entirely scientific. From the data I have presented here, it appears the speed of the SSB has slightly slowed from 178.83 to 178.92 years per cycle over the last 500 years. I would like to obtain a much longer dataset to analyse cyclic periodicity in the SSB period.
A further point about the main cycle observed in my OP chart, mainly produced by the Jupiter-Saturn 19.7 year cycle. J-S have a 178.7 year period, slightly shorter than the cycle I am claiming to have found. The reason for this gap is that all the other cycles listed, with notable exception of Uranus-Neptune, are slightly more than 178.9. Hence, the J-S cycle, with discrepancy of 0.2 years, should also produce a longer wavelength that precesses against the SSB wave pattern about every 1000 cycles. This is just what I predict can be seen in the J-S shape as discussed at the OP and at Post 5 point 4 above. We can see this feature much more clearly in the main SSB secondary wave pattern which I understand is a function of the U-N 172 year pattern. The point is that there is an underlying wave pattern of the movement of the sun which requires five significant figures (ie 178.83 to 178.92) to see the trend. And, the fifth significant figure puts the current value into exact phase with lunisolar precession, a correlation which I hope to show is significant.
I debated some of these issues
here with
RTomes. My view is that the sun itself has a regular 179 year cycle, and Ray’s claim that the U-N factor produces cycles of fluctuating wavelength is very hard to conceptualise.