This is an extended re-write of the earlier post on this topic. The purpose is to explain the Jose cycle chart shown below (in blue).
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The Hale cycle is the time taken for solar magnetic polarity to return to its initial state (i.e. two ~11-year cycles: one north, one south), so the two reversals of polarity take around 22 years.
Estimates of mean solar (Hale) cycle length:
‘Finally, we recover a 22.14-year cycle of the solar dynamo in the framework of a reduced zero-dimensional a-s dynamo model.’
N. Scafetta re JEV: The 22.14 yr period is very close to the ~22 yr Hale solar magnetic cycle
I. Wilson (2012)
A Planetary Spin-Orbit Coupling Model for Solar Activity
Hence, the basic unit of change in the Sun’s rotation rate (i.e. an increase followed by a decrease) is 2 x 11.07 years = 22.14 years. This is essentially equal to the mean length of the Hale magnetic sunspot cycle of the Sun which is 22.1 +/- 2.0 yrs).
The aim here is to link the Hale cycle to the planetary movements of Jupiter and Saturn.
Planetary theory – from Abreu et al (2012):
Results. We find an excellent agreement between the long-term cycles in proxies of solar activity and the periodicities in the planetary torque and also that some periodicities remain phase-locked over 9400 years.
Conclusions. Based on these observations we put forward the idea that the long-term solar magnetic activity is modulated by planetary effects. If correct, our hypothesis has important implications for solar physics and the solar-terrestrial connection.
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In the Talkshop post Jupiter, Saturn and the de Vries cycle the graphic on the right showed the long-term orbital patterns in 14 Jose cycles ( = 14 x 9 = 126 Jupiter-Saturn conjunctions).
Note that 85 S = 211 J = 126 J-S.
Dividing by the number of Jose cycles in the period i.e. 14:
S = 6 x 14, +1
J = 15 x 14, +1
J-S = 9 x 14 (9 J-S = 1 Jose cycle)
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The Jose cycle chart (below, right) shows how the ‘components’ of the ~179-year Jose cycle fit together, using this data. Added in is the notional value of the number of mean Hale cycles expected in the period (8, + 1/14).
It’s a ‘model’ because not every 179 year period can be exactly the same, not least because solar cycles vary in length, within a range of roughly 11 +/- 3 years.
However over very long periods the numbers may average out as per the model. The Hale cycle would have a mean value of 22.15~years according to the model, i.e. a 99.95% match with the estimates above.
The idea of 15 plus 1/14th Jupiter orbits was once put forward by planetary cycles researcher Timo Niroma:
‘And one guess: the weak 179-year supercycle may bind the 9.9-year cycle with 15 1/14 Jovian years. This may have repercussions to the hypothesis that every 15th cycle among some others have the length of one Jupiter year.’
Chart – re S-H and J-H:
7 + 2 = 9 J-S conjunctions
7 – 2 = 5 = Landscheidt’s ‘pentadactyl hand’ (Lake Saki Varves paper – see Figs. 2 and 3)
[7 * 2 = 14]
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Landscheidt and the ‘pentadactyl hand’ [extract from link above]:
Lake Saki Varve Thickness and Impulses of the Torque
FIG. 2 : Smoothed 9-year running variance in the angular momentum of the sun’s motion about the center of mass of the solar system (v), for the period 700-1600. The cyclic pattern, formed by the curve, conveys the impression of five-fingered (pentadactyl) hands. [bold added]
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A complete five-fingered hand covers a period of 178.8 years, the fundamental cycle in the sun’s motion discovered by Jose (1965) and studied by Fairbridge, Sanders, and Shirley (Fairbridge and Sanders 1987; Fairbridge and Shirley 1987). Dansgaard (Dansgaard et al. 1969) has derived a cycle of just 180 years in climate from the Camp Century ice core drilled from the Greenland Ice Sheet. This correspondence begs for investigation of a possible relationship of climate features with the complex pattern of the five-fingered hand, which reflects both variations in impulses of the torque in the sun’s motion and secular sunspot activity.
The mean interval between fingers of the hand is 35.76 years.
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Re. the 179 year cycle:
Gerry Pease Links Improved and Updated Solar-Planetary paper – Gerry Pease and Gregory Glenn
Do the planets affect the sunspot cycle? – Ask the Astronomer [Dr. Sten Odenwald]
Prolonged minima and the 179-yr cycle of the solar inertial motion – Fairbridge and Shirley (1987)