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.

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.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

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