Does the Planetary Torque on the Oblate Spinning Sun Affect Solar Activity?
Robert M. Wood
Scientists for centuries have noted that there is an 11-year cycle of solar activity and have been largely unsuccessful in either predicting future solar activity or correlating it to the influence of planets. Present consensus among solar physicists is that the influence of the planets on the Sun, though very real, is too small to make a difference, citing the fact that the height of the tide caused by the planets is only a few millimeters and is therefore inconsequential. Furthermore, they have shown that the planetary influence on tides, though small, does not have a repetitive timing consistent with any solar activity. Furthermore, having the planets influence our lives through solar activity seems close to what astrology would claim to perform, and it is a rare astronomer who claims interest in astrology.
Surprisingly, there seem to be no references to or calculations of the torque caused by the planets. Nearly everyone understands that the planets are essentially in the plane of the ecliptic (Earth’s plane) and so is the plane of rotation of the Sun. Therefore, any one planet as it goes around the Sun, except when it happens to be in the plane of the solar equator, will produce a torque on the Sun because the Sun is spinning and therefore is an oblate spheroid. Thus, the gravitational pull by a planet is larger on the “bulge” closest to it than it is on the one farther away. This causes a torque on the spinning Sun, which is so dense in the center than it has been suggested that it acts like a solid body. If this were so, there will be precession; and if it is a fluid, a more complex influence on solar motion.
The torque has therefore been computed with reasonable accuracy using Newtonian physics and known equations for elliptical orbits. Since the torque depends on the cube of the distance from the planet (as do tidal terms), the torque can be calculated to a good accuracy by considering only the planets Mercury, Venus, Earth, and Jupiter. All others are less than 1% of these. The geometry is actually quite complex, since the torque from any one planet depends both on the orbit inclination angle to the solar equator and also on the ascending node location with respect to the Sun. Furthermore, torque is a vector and needs to be broken down into x and y components. The torque in the direction of the axis of the sun might even affect the rotation rate.
Both the time history of the torque on the Sun and the frequency spectrum are shown for representative times. Some comparison with solar activity will be shown, and estimate will be made of the significance of the correlation with the gravitational planetary torque.