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Wednesday, May 19, 2010

A Mechanism for Amplifying Planetary Tidal Forces in the Sun's Outer Convective Zone

The image above is a cross-section of the Sun showing the rotational periods of a section of it's interior.
The rotation rates range from about 34.0 days near the poles to about 25.2 days in the Sun's equatorial convective zone. The dotted line that is located ~ 0.7 solar radii out from the centre of the Sun marks the positions the Solar Tachocline. This represents the boundary between the core of the Sun, were the main form of energy transport is by radiation, and the outer convective layer of the Sun, where the main form of energy transport is by convection.

The diagram shows that mean rotation period at a point just below the equatorial Tachocline is ~ 26.3 days, while the mean rotation period in the equatorial mid-convective layer is ~ 25.2 days.

Amazingly, if the rotation period of the point just below the equatorial Tachocline was in fact 26.3365 days, you would get an amplified resonance between the tides of the two dominant tidal forcing Terrestrial planets, Venus and Earth.

Consider the case where the Earth and Venus are aligned in their orbits about the Sun, roughly above the Equator of the Sun (note: these planets can be located up to +/- 7 degrees from the Sun's equator). Take a
point (A) just below the Tachocline boundary that is right on the Sun's equator, and a point (B) that is dierctly above it, at the mid (radial) point in the equatorial convective layer of the Sun. In this configuration, the tidal bulges produced by the combined gravitational forces of Venus and Earth upon the convective layer of the Sun would be superimposed upon one another.

Interestingly, however, you would find that it took 28.38305 days for point A to rotate once around the Sun and then catch up to advacing line connecting the centre of the Sun to the Earth, and 28.38315 days for point B to rotate once around the Sun and then catch up to the advancing line connecting the centre of the Sun to Venus. The net effect being, that rougly every 28.38310 days, the initial tidal bulges produced by the alignment of Venus and Earth would be reinforced by the Earth at the equatorial Tachocline boundary (i.e. point A) and by Venus at the mid-point in the Sun's equatorial convective layer (i.e. point B). More importantly, this reinforcement would repeat 103 times every 28.38310 days, until Venus and Earth again realigned themselves in roughly the same part of the sky roughly 8.0 sidereal years later, where the whole cycle would start all over again. This happens because:

102.9504 x 28.38310 days = 2922.05150 days = 8.0000016 sidereal years
110.9504 x 26.3365 days = 2922.04521 days = 7.9999844 sidereal years
115.9544 x 25.2 days = 2922.05088 days = 7.9999999 sidereal years

Note that Venus and Earth Align rougly once every 1.599 sidereal years and that five these alignments is:

5 x 1.599 sidereal years = 7.9950 sidereal years (difference from 8.0000 sidereal years =1.8256 days !)
Bottom line? This resonance may represent a way for the small tidal forces of Venus and Earth
acting on the convective layers of the Sun to be significantly amplified, so that they become influential in the dynamic process in the outer layers of the Sun.
It is interesting to note that:
4 x SVE = 6.3946 years SVE = synodic period of Venus and Earth
3 x SEM = 6.4059 years SEM = synodic period of Earth and Mars
7 x SVM = 6.3995 years SVM = synodic period of Venus and Mars
28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs
69 × SVJ = 44.770 yrs = synodic period of Venus & Jupiter
41 × SEJ = 44.774 yrs = synodic period of Earth & Jupiter
20 × SMJ = 44.704 yrs = synodic period of Mars & Jupiter
4 x 1.599 yrs = 6.396 yrs
(Repetition time for the alignment of Venus, Earth and Mars)
5 x 1.599 yrs = 7.995 yrs
(Repetition time for the amplification mechanism discussed above)
7 x 1.599 yrs = 11.193 yrs
(Solar Sunspot Schwabe cycle)
14 x 1.599 yrs = 22.386 yrs
(Solar Hale cycle)
28 x 1.599 yrs = 44.772 yrs
(Alignment synodic periods Jupiter with Venus, Earth & Mars)
56 x 1.599 yrs = 89.544 yr
(Solar Gleissberg cycle)
112 x 1.559 yrs = 179.088 yrs
(Jose cycle - overall repetotion cycle for Jovian planets)


Which means that:

345 x Synodic period Venus/Jupiiter = 223.85 yrs
205 x Synodic period Earth/Jupiter = 223.87 yrs
100 x Synodic period Mars/Jupiter = 223.52 yrs


and that for the rotation periods of point A and B in the Sun's outer convective layers:

2883 x 28.38310 days = 81828.4773 days = 224.03026 (sidereal) years
3107 x 26.3365 days = 81827.5055 days = 224.02759 (sidereal) years
3247 x 25.2 days = 81824.400 days = 224.01901 (sidereal) years

with realignment errors of 1 to 3 days.

This is absolutely amazing!


  1. Years ago I was working on a similar idea, trying to relate Jupiter-Venus-Earth cycles to solar effects through resonances that were near to the solar rotation period. During that exercise I discovered that the tidal approach would lead to a 5.5 year solar cycle not an 11 year one if rotational resonances were involved. It was this that got me thinking that there had to be a gravitational component (G/R^2 related) rather than tidal component (G/R^3 component) to get an 11 year cycle. I then realized that this existed in a GR force that was different on the solar interior to the surface. See and also my articles elsewhere (e.g. BAUT) on the calculations involved.

  2. Posted on behalf of Roger Tallbloke

    All the resonances and relationships you are finding will, I believe, lead us to an understanding of solar system dynamics which will turn conventional solar physics on it's head. More power to your elbow sir!

    The question I am puzzling over is this:
    Why does the sun's equatorial region rotate more quickly than the polar regions? I think it may have something to do with longitudinal flows creating a bulge which is flattened by the suns high surface gravity. Maybe these flows are induced by the angle betwen the solar equatorial plane and the plane of invariance? Your thoughts would be appreciated.

  3. That is interesting looking at resonance of solar rotation with synodic periods. I find a figure of 28.913 days fits very well with many synodic periods.