Explaining Planetary Alignments Relationship to the Sunspot Cycle
Rau Tomes, Auckland, NZ
First a bit of background before I put forward a new proposal. Well, it isn't strictly new as I worked this out about 1990 and shortly after.
In the 1960s and 1970s there were a number of proposals regarding how planetary alignments might influence the Sun and explain variations in Sunspot numbers. Actually the tidal proposal was made as early as the 1800s but seems to have been totally forgotten about. These proposals fall into three main categories and I give one main reference for each category.
1. The tidal hypothesis(1). We know that on Earth the moon and sun cause tides and that we get bigger tides at new moon and full moon when the sun and moon come together to cause the largest tides, so tides are reasonably well understood things. It is important to remember that there are two tides raised, on on the same side as the body and one on the opposite side. That is why the tides forming from two bodies are maximal both when they come together and when they are opposite each other. When it comes to the Sun, the planets which create the largest tides are Jupiter and Venus, with Earth and Mercury not to far back. However we can study the tidal effects due to any pair of planets by looking at the number of sunspots as a function of the position in the synodic cycle of those two planets. Because the inner planets plus Jupiter have the biggest tidal effects, the shorter periods predominate in the tidal hypothesis, although a study of syzygys(4) will show that more complex nearly repeating configurations get many things right about the sunspot cycle. The syzygy proposal has a number of successes because it predicts that the average sunspot period will be 11.07 years and it is actually 11.08, and that the distribution will be bimodal with periods clustered near 10.4 and 12.0 years which is also correct. These studies are based on correlations, and although we know how to calculate tides, we do not know what mechanisms might get from tides to sunspots.
2. The Sun's motion relative to the COM (Centre of Mass) of the solar system has been proposed(2) as an explanation of sunspots or at least of longer term sunspot modulations of the order of 180 years and others. Although it is perfectly true that the Sun does do loops in space as a result of the outer planet motions, it was never clear to me what physical effect this was supposed to have. Recently however I saw this described as the Sun moving through its own magnetic field which does sound plausible. The Sun does move about by distances of the order of its own size. This proposal has been popular with those studying climate cycles in the hundred to few thousand year range. The main planets in order of effect are Jupiter, Saturn, Neptune and Uranus.
3. The third mechanism was proposed by Bigg(3) who also gave explanations for Jupiter's activity based on its moons. As I remember it (not very well) his proposal depended on torques which set up convection currents.
4. My proposal, and the intended subject of this thread is that a previously ignored GR effect by planets on radiation and relativistic matter in the Sun's core causes slight convection cells in the solar interior leading to a varying amount of heat reaching the surface and to the production of magnetic fields.
I will deal with the treatment of this GR effect mathematically in a following post, simply outlining the general flow of effects in this post.
When Einstein first worked out GR, one early prediction that was proven correct and helped lead to GR being accepted was that light from stars that passed very close to the Sun (and could be observed during a Solar eclipse) would be bent twice as muchas predicted by the Newtonian theory. The fact that radiation is more strongly affected by gravity than ordinary matter at non-relativistic velocities is the basis of my proposal. I will show that actually over all random directions of motion of radiation in the solar core, the average effect is 5/3 times. For now, I will make the assumption that radiation in the solar core (as an ensemble of mass) is accelerated by 5/3 times as much as non-relativistic matter and that there is a similar effect on the relativistic component of matter in the Sun also. I think that there may be some controversy over this part of the proposal, but the rest follows in a manner that is much less likely to be debated. Even if you reject what I have just stated here, I ask you to consider the rest of the proposal. If you find that it does lead to interesting results then you might want to come back and see whether there is something in this part after all.
What would the consequence of such acceleration be?
Because there is a greater proportion of radiation and relativistic matter in the solar core than in the Sun's outer layers, any acceleration by the outer planets would be trying to move the core relative to the outside of the the sun. Naturally various factors would prevent the middle of the sun coming loose in this way, but at least a convection pattern would be set up with the central region traveling towards the accelerating object and the outer layers traveling away (relatively speaking). Of course the effect is quite a small one, but remember that the sun does move about due to planetary forces by about its own size, so that the radiation part would be trying to move about twice as much. Because the radiation and relativistic mass content is quite a small proportion of the sun's mass, the effect is correspondingly reduced.
When I first did the calculations for this I made the assumption that the most important forces were in the plane of the planets orbits and ignore the "z axis" or direction towards the poles. That was a big mistake which I realized after a year or so. To make sense of that mistake it is necessary to know that the sun's poles are tilted about 7 degrees to the main plane of the planets orbits. The planets are constantly pulling on the suns interior at a different rate to the outside, but this effect is being undone by the sun rotating. After 13 days or so, the forces are pulling that radiation that was pulled outwards back toward the centre again. Or are they? Allowing for the tilt of the sun's axis, all the components of the acceleration get canceled out by rotation except the component in the polar direction. That component continues to build up into a convection current that flows (at one time) northward in the interior and southward on the outside, and then reverses at some future time.
The important thing in this proposal is not the direction of the planets relative to the Sun, but how far they are north or south of the Sun's equator.
I have calculated the magnitude of this current taking account of the planets motions over several hundreds of years. A cycles analysis of those results shows that a number of specific periods are present generally being the same periods as in the COM hypothesis. Not only that but the total force is actually remarkably similar to the COM hypothesis due to several amazing coincidences, but there is also a difference.
First the coincidences. The four major planets have orbits near the same plane. That means that when they are at their greatest distance north of the sun's equator, they are all near the same longitude, and likewise for south. So we think alignment is important but it actually N-S distance relative to the Sun.
Second coincidence. The dependency of this effect is quite different to the COM dependency, but it turns out to be equivalent when Kepler's law about period and distance is applied! However it has one big difference here. If the planets align when they are at the N or S extremes of their orbits relative to the sun's equator then there is a strong effect, however if they align when they are on the suns equator then there is no effect at all. I explained this to a climatologist once who was working with 20, 60 and 180 year cycles (intimately connected with Jupiter and Saturn and other outer planets alignments) and said that it would mean that all those cycles are modulated by a 2300 year cycle relating to where the alignments happen. He told me that the 2300 year cycle (already known as a climate cycle) did indeed modulate these cycles and he could never work out why because he thought the COM was right.
Anyway I digressed, but it is important to establish which of these causes has effects in which cycle period ranges and how important each is.
The cycles periods that I predicted did match the cycles periods found in the sun over a similar period of time. However there was one big difference between the two and that was the amplitudes calculated and observed. The amplitudes of cycles near 10.5 years was high but those far from that period were low, with a typical resonance response curve easily fitted to the ratio of observed to expected amplitudes.
Clearly this means that this proposal works only if the Sun has some natural resonance of 10.5 years and all of these forces are activating that resonance. Based on that further assumption, I could calculate sunspot numbers over several centuries with a correlation of r=0.66 from the planetary forces.
Such a model can also explain such events as the Maunder minimum if the planetary forces happen to bring the resonance to almost a standstill. However it is clear that this is an unusual condition.
I think that this is long enough for my opening statement. I will post two additional explanations in the near future. One will be the table of planets periods and the sizes of their effects according to the various different proposals. The other will be how to calculate the GR effect of the planets on the Sun.
Incidentally this effect does not apply only to the Sun. All bodies are affected in similar ways if their interior is warmer than their exterior because there is then some relativistic mass content variation with depth. Because electrons generally move faster than other stuff (except radiation) they will be especially affected, and we might even consider that this is an explanation for the whole cause of magnetic fields.
In the case of the Earth, the magnetic field is generally stated to not have any periodicity present in the reversals. However that is misleading because we need to look at the amplitude of the field as well, and it is clear that there are two long periods that are easily visible in the Earth's magnetic field reversals, 1.11 million years and 9 million years.
For the Earth the proportion of time that the planets spend north and south of our equator is important. That depends on the relative motion of the orientation of the Earth' ellipse in space (as we spend more time at the far end of the ellipse from the Sun) with respect to the nodes of the orbital inclination relative to the invariant plane of the solar system.
Adequate accuracy exists in the earth's orbital calculations to now test this hypothesis. Calculations over 23 million years of the orbits of the solar system are now used for dating geological deposits based on the ~400,000 year Milankovich cycle. I do know that other long term calculations show a 1.11 million year cycle of energy exchange between Jupiter and Neptune, so it would not be at all surprising if that period should show up in the earth's orbital elements and be responsible for the Earth magnetic field reversal.
(1) Wood, R. M. & Wood, K. D. Nature 208, 129-131 (1965).
(2) Jose, P. D. Astr. J. 70, 193-200 (1965).
(3) Bigg, E. K. Astr. J. 72, 463-466 (1967).
(4) Jean-Pierre Desmoulins Sunspot cycles are they caused by Venus, Earth and Jupiter syzygies?
Last edited by rtomes : 10-April-2008 at 01:53 AM. Reason: references to bottom
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