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Originally Posted by Carl_Smith
OK, having followed the thread and looked at the graphs, there are a few things that come to mind:
1) there is no obvious direct connection between the Z-axis position of the SSB and sunspots, or with the differences taken to 3 levels (velocity, acceleration, and delta-acceleration).
2) we can rule out a direct link between SSB and sunspots.
3) the SSB cycles and sunspot cycle are similar timewise but have a phase shift.
4) we cannot at this stage rule out a less direct link if as Ray says the sunspots are internally driven by solar dynamic oscillations of unknown origin while torque impulses from the SSB only influence solar dynamics at times - and perhaps only when a threshold is exceeded - to rule this in or out would require a far more sophisticated analysis and perhaps hundreds of years more sunspot observations.
5) I have no idea how to implement Ray's 'displacement' in a spreadsheet or simple program - I have never studied calculus, but am quite capable of implementing quite sophisticated equations at a practical level if I understand the formulae and what they actually do, which can be learned quite easily from examining implementations of them and playing in a spreadsheet - perhaps some clues might help?
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The Z measurement is directly proportional to the displacement, so nothing more needs to be done there.
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BTW, I am an old dog now, and have neither the time nor the inclination to take on any advanced maths or physics classes, and I am not likely to be writing any scientific papers in the near future - I will leave that to those with the necessary education and skills - but I will continue to potter around the edges poking at things and examining them to see what makes them tick
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Great.
Unfortunately my computer died and I had to buy another one today. I lost a lot of time that I had hoped to put into taking this a bit further, which is to develop the regression equation from the Z axis displacement to produce the sunspot numbers (with a correlation of at least 0.66). There is still a small chance of this, but in 1.5 days from now I will be away until the thread closes. So I will at least outline what is involved to make this final link, because it also gives big hints as to what would need to happen in a solar model to close the gap between the baycentre z movement and the actual sunspot numbers. It is clear though that you cannot get a bunch of periods the same in each if there is not some causal connection.
Most spreadsheets have a regression equation in them. What is needed is to make a equations that accomplish this...
Let d(t) be the z axis displacement at time t, and probably annually is often enough at least initially.
Let s(t) be the sunspot number for time t.
There then needs to be the solar oscillator with period close to 10.5 years, but we want the period to be a variable so that we can optimize it, say p. Also we need a Q factor for the resonance of that oscillator, call it q.
Then we must determine p and q so that the series d(t) will most accurately estimate s(t). Because the q factor will be reasonably high, we need a reasonably long run in period for d(t) before we can expect to get s(t) out. That is not a problem because we can get data on d(t) going back much further than s(t).
There might be a better way than this, but the way that I started to do it before my computer died is to have a sine and a cosine component of the oscillator (or you can use phase and amplitude equivalently) which is updated each period by advancing the proportion of the oscillator period and decaying by the proportion of the q factor and then adding in the new d(t) value. Then moving onto to the following d(t) and so on, producing the amplitude of the oscillator at each point in time. The correlation of this with s(t) is then examined and the values of p and q adjusted until a maximum correlation is achieved. There is no very complex maths involved. It can all be done in a spreadsheet and actually this way doesn't use regression at all.