Quote:
Originally Posted by Carl_Smith
I made a graph of the continuous series of Daily Sunspot Numbers (i.e. since late Dec 1848) with the Solar Latitude of the Solar System Barycentre (SSB) as well as Jupiter, Saturn, Uranus, and Neptune continued a little way into the future (click image for larger version):
The horizontal scale is in 11 year intervals since 1845, the vertical scale for the planets and SSB is 0.2 radians per faint line from the centre line through the curves, and for sunspot numbers is 100 per faint line from the bottom.
One thing this shows clearly is how closely the SSB latitude is tied to Jupiter, and how the contribution from other planets also perturbing the Sun periodically causes the SSB to move away from Jupiter's latitude and back again, with some quite sharp deviations at times.
Perhaps rtomes could explain what his ideas say regarding the relationships graphed above?
Data sources for graph:
Daily sunspot data from SIDC.
Daily solar latitudes of the SSB and all planets calculated by the NASA JPL Horizons online ephemeris. |
Hi Carl Smith
Thank you for presenting this data. Checking the actual results is always a good approach.
I originally used a longer data series, but of course the sunspot data gets less reliable as we go back further. However it might be necessary to use more data to confirm what I am saying.
I would like to check one thing also as it is very important. Is the latitude that you are using for the barycentre measured from the ecliptic or from the Sun's equatorial plane? If it is from the ecliptic then it is not the right measure, it must be from the Sun's rotational axis plane. As far as I can remember, the Sun's rotational axis plane is titled about 7.1 degrees to the ecliptic with an ascending node at 74 degrees longitude.
If your data is based on the Sun's rotational axis (or if you now get data that it is) then these are the steps to follow to replicate my study. I would also recommend using a longer period of time (even though the sunspot data is less reliable) because the resonance that I say must exist at about 10.5 years has a high
Q factor and so is difficult to determine from a shorter data period. It also takes a while for the correct resonance amplitude and phase to get established at the start of the time period so having less accurate data there is not so serious.
You are then trying to explain the SS cycle based on the barycentre motion after putting it through a resonance function with period near 10.5 years and have to determine two variables by a regression equation (which is available in most spreadsheets). The variables are the period of the resonance and the Q factor.
It is not the actual barycentre displacement that has the ultimate effect as that is only the acceleration component and we want the displacement component of the solar core. That means integrating the barycentre displacement twice with respect to time. That also develops two integration constants which are unknown but can be set so that over a long period of time the solar core is wandering off out of the Sun. This is another reason why a longer series for the planetary forces is useful.
Of course the resulting solar core displacement is moving both sides of the solar equator, and each extreme is causing the same effect, so it is necessary to also allow for that by taking either the absolute value of the displacement or the square of it, to make both extremes have the same sign. Finally that value can be used as the predictor into the regression equation.
I do think that this is a most worthwhile exercise to produce a spreadsheet with the data, calculations, regression equations and graphs.
Ray