Now we’ve entered the minimum between solar cycles 24 and 25, this seems like a good moment to recap what we’ve discovered about the Sun and the planetary system that revolves around it here on the Talkshop during the last decade. The idea that the Sun’s activity cycles were somehow linked to the motion of the planets didn’t begin here of course. In fact, the idea goes all the way back to Rudolf Wolf, the Swiss astronomer who in the 1800s collated the old, and continued adding new sunspot observations. He was convinced that the orbit of Jupiter modulated sunspot numbers.
Wolf was an admirer of the work of Heinrich Schwabe, who was the first to discover an approximately decadal cyclic variation in sunspot numbers. Wolf refined and extended the observations and found that while some solar cycles were a little over ten years long, others were much closer to Jupiter’s orbital period of just under twelve years. The long term average was found to be around 11.1 years.
In the late 1990s, Finnish solar observer Timo Niroma made a careful study of the historic solar cycle lengths from one minimum to the next and illustrated his findings with this probability distribution diagram on his website. For each solar cycle the central estimate gets 4 x marks. at a tenth of a year either side, 3 x marks, at two tenths either side, 2 x marks and at three tenths of a year either side, 1 x mark. This procedure has the effect of smoothing the data so we can see the emergent pattern more clearly. The tentative data for cycle zero uses 0’s instead of x’s
Study of these data reveals a few important observations. Firstly, the solar cycle length is rarely its long term average of ~11.1 years, but tends to cluster around two attractor periods near 10.3 and 11.9 years.
Secondly, the difference between these two attractor periods is ~1.6 years, which is close to the length of the synodic conjunction period of Earth and Venus. This clue leads us to realise that the two attractors are 6.5 and 7.5 times the 1.5987 year E-V period respectively.
Finally, we can see that over the sunspot record, the shorter ~10.38 year period has occurred more frequently than the longer ~11.99 year period. The ratio is 4:3.
To calculate an accurate figure for the average solar cycle length then, we simply multiply the 10.38 year period by 4, and the 11.99 year period by 3, sum the results, and divide by the total number of cycles, which is 7. This gives us the longer term average of 11.07 years, which agrees with most modern studies of Schwabe cycle length.
Planetary alignment indices have been constructed by researchers Jean Pierre Desmoulins, Ching Cheh Hung (NASA), and Roy Martin to further understand these relationships. A more recent treatment has been made by astrophysicist Ian Wilson in his 2013 PRP paper The Venus–Earth–Jupiter spin–orbit coupling model.
This advances the concept that Jupiter and the terrestrial planets, specifically Earth and Venus, can influence bulk motions in the convective layers of the Sun, and thus the solar cycle itself. In section 2 of the paper (V-E-J tidal torquing model), we learn that Jupiter advances 13 degrees relative to the alignment line of each Venus-Earth (V-E) conjunction. After 7 V-E in 11.1909 years Jupiter has made 91 degrees of advancement, therefore the time taken for 90 degrees is 90/91 of 11.1909 = 11.068 years, very close to the widely accepted mean length of a solar cycle. For full details refer to section 2, and for a summary of the paper see section 4 – Conclusions.
Quoting from the PRP paper (the period in question is 360 Venus-Earth conjunctions):
It takes Jupiter 575.518 yr to re-synchronize itself with the penta-synodic Venus–Earth alignment cycle. In addition, it takes two 575.518 yr periods (= 1151.0 yr) for Jupiter to resynchronize itself with the penta-synodic Venus–Earth alignment cycle and also with respect to the stars (Wilson, 2013).
via Tallbloke’s Talkshop
May 11, 2020 at 01:12PM
Iowa Climate Science Education 