Influence of Uranus on Solar Angular Momentum

Influence of Uranus on Solar Angular Momentum

Geoff Sharp has a published paper here http://arxiv.org/ftp/arxiv/papers/1005/1005.5303.pdf that gives a graph of solar angular momentum back to about 1200 BC. (I couldn’t open the url, but Geoff e-mailed me the paper). There is a strange regularity in the AM graphs that shows a pattern of taller and shorter peaks as - tall, short, tall short, tall, short, short, short, short, tall. (The 4 shorts in a row could be thought of as short, weak tall, short, weak tall, and then tall). The cycles average very close to 20 years, so by eyeball the pattern of tall peak intervals is 40,40,100 years, and this pattern repeats. At near 1000 year intervals there is some loss of clarity lasting near 100 years, and then the pattern resumes. Between about 230 AD and 810 BC the 40,40,100 pattern is much more apparent at the troughs, and there seems to be about 1.5 cycles lost in switching from peak to trough and back to peak at the two ends of this period. Perhaps some modulating driver is slowly drifting out of phase, and then jumps back into phase, losing the 1.5 cycles. There is a loss of the peak pattern clarity also at about 1260 to 1160 AD, but without the peak to trough switch. What could cause the 40,40,100 year pattern?

First, the approximately 20 year period mentioned above is actually about 19.85 years averaged over the 3000 year period analyzed, so must be the Jupiter/Saturn (J/S) synodic cycle. Not knowing any better I am assuming that the orbital travel of Uranus can affect the angular momentum (A/M) of J/S. Uranus has a slightly elliptical orbit and will accelerate when travelling from major axis intercept to minor axis intercept and decelerate from minor to major. The alternating acceleration and deceleration could drive the alternating high and low AM peaks. If the distance covered by Uranus around its orbit in each 20 year period is 80 degrees, then starting with a tall peak at the major axis intercept the first 20 year period will be 100% acceleration, the second will be 12.5% acceleration and 87.5% deceleration, then the acceleration periods will be 75% , 50%, 62.5%, 87.5% and back to 100%. The 87.5/100/75% sequence with decelerations between gives us the 40,40 and the following low,low,low,low (accelerations less than 75% are assumed to be low) gives us the 100. This pattern repeats perfectly.

The loss of a short due to the 80 degree travel segments spread around 90 degree orbital quarters noted in the paragraph above supports this conjecture. When the 40,40,100 pattern is most visible, looking at the peaks, there are 5 troughs between high peaks for the 100 year segment. The center trough is least affected, (least deceleration) and therefore should have the shortest excursion. When the 40,40,100 is most visible looking at the troughs, the center peak of the 100 year stretch should have the least excursion. This pattern largely holds, which would also supports the Uranus ellipse hypothesis.

Unfortunately, Uranus travels 85 degrees during each 19.85 years J/S period, which generates a pattern that doesn’t match at all.

If the Uranus major axis also rotates 5 degrees during the J/S period, then Uranus would travel 80 degrees relative to its major axis for each cycle, and the pattern would hold. That would be a rotation of 0.252 degrees per year, which is almost imperceptible. A slightly different rotation rate (0.28 degrees per year?) might also generate the near 1000 year resynch pattern.

I think this analysis confirms beyond question that Jupiter, Saturn and Uranus are the primary drivers of the sun’s peculiar orbit relative to the SSB.

Questions:
Does the Uranus orbital ellipse slowly rotate, and if so why, and at what rate?.

When the peaks show the 40,40,100 pattern most clearly, peaks reach 4.5E+47, and when troughs are most useful max. peaks only reach 4.0E47. Similarly troughs are farther from or nearer zero. Something is pulling the SSB farther from and nearer to the sun at a long period cycle. Could it be the maximum eccentricities and minimum eccentricities of Jupiter, Saturn and Uranus (or maybe only Jupiter and Saturn as they have by far the highest gravitational pull) going into and out of alignment? How would that cycle be determined? What is the time for maximum eccentricities for each of Jupiter and Saturn, and for those maxima to be aligned?
Note: Neptune’s orbit is almost perfectly circular, so it wouldn’t have a similar effect