588 solar Carrington rotations (CarRots) = 587 lunar sidereal months
We’ll call this the HW cycle, about 43.91 years.
‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured relative to the stars, but because the Earth is orbiting the Sun, we see this period as 27.2753 days.’ – Wikipedia
Picking this ball up and running with it, we find there are 308 CarRots (27.2753 d) per 331 solar sidereal days (25.38 d) in 23 years (331 – 308). This period, or a multiple of it, can be found in certain identified solar-planetary cycles (as discussed below).
To connect these two observations, we first break them down.
308 = 11 x 28 CarRots
588 = 21 x 28 CarRots
5 x 11 x 28 = 55 x 28 CarRots = 23 years x 5 = 115 years
So 1 HW cycle x phi² (or 55/21) = 115 years
11 HW cycles = 483 years = 23y x 21
115 years will be at or very near a whole number of:
* Carrington rotations (1540 = 55 x 28 or 308 x 5)
* Solar sidereal days (1655 = 1540 + 115 or 331 x 5)
It’s also about 5 days short of 13 lunar apsidal cycles and 2 days more than 102 (34×3) full moon cycles. These periods (56 of them per 339 Metonic-year cycle) are analysed in more detail in the ‘quarter precession’ post :
So here we have a close correlation between solar, lunar and Earth periods with multiples of Fibonacci numbers (3, 13, 34, 55) to the fore.
If we increase the 115 year period by a factor of 5 to 575 years, the Jupiter-Saturn axial period is in play.
J+S axial = (J x S) orbit periods / (J + S) = 8.4561455 years
(In this context the axial is a period where the sum of the number of orbits of each planet in that time is 1. Or: half the harmonic mean.)
575y / 8.4561455 = 67.997883 J+S = ~68 (99.997% match)
68 = 34 x 2 (both Fibonacci numbers)
Turning to the possible significance of some of these periods:
‘Multi-scale harmonic model’ [etc.] – Nicola Scafetta
Scafetta identifies the 115-year period:
‘The major beat periods occur at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years.’
‘The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium such as the Oort, Wolf, Spörer, Maunder and Dalton minima as well as the seventeen ~115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years.’
‘The model forecasts a new prolonged solar minimum during 2020–2040, which is stressed by the minima of both the 61 and 115-year reconstructed cycles.’
Chinese scientists have also found this period:
Periodic oscillations in millennial global-mean temperature and their causes
‘The three long-term periods of the Medieval Warm Period (MWP), Little Ice Age (LIA) and recent Global Warming Period (GWP) were distinct in the temperature series. 21-year, 65-year, 115-year and 200-year oscillations were derived from the temperature series after removing three long-term climatic temperatures.’
Ian Wilson often refers to the Hallstatt cycle, thought to be around 2300 years, in his science papers and blog posts.
(2300 = 115y x 20 or 23y x 100)
‘The VEJ Tidal Torquing Model can explain many of the long-term changes in the level of solar activity.’ – Ian Wilson
II. The 2300 year Hallstatt Cycle
‘Solar activity levels in 2100’ – Clilverd et al
‘The residue 14C is then seen to oscillate about zero with an apparent period known as the Hallstatt cycle (Damon and Jirikowic 1992). The lower panel shows a sine wave with a Hallstatt period of 2300 years (solid line). The times of minima in the Hallstatt cycle (indicated by arrows) appear to coincide with significant solar activity minima such as the Maunder Minimum of around 1700. Century-scale oscillations during these periods have been linked to solar activity (Damon and Jirikowic 1992). It is thus possible that the recovery of solar activity from significant minima such as the Maunder Minimum is repeatable over time scales of about 2300 years.’
For how long will the current grand maximum of solar activity persist?
Authors: J. A. Abreu, J. Beer, F. Steinhilber, S. M. Tobias, N. O. Weiss
This paper says: ‘It is apparent that there are many grand minima and maxima in this record. Frequency analysis reveals the presence of a number of significant periodicities, namely around 200 years (de Vries) and 2300 years (Hallstatt) [Tobias et al., 2004].’
Note: 23 x 21 x 5 = 2415 = 115 years more than the 2300 year sine wave period.
‘The ∼ 2400-year cycle in atmospheric radiocarbon concentration:
bispectrum of 14C data over the last 8000 years’
S. S. Vasiliev and V. A. Dergachev
The authors say: ‘The epochs of fluctuations with high amplitude are repeated each 2300–2500 years.’ [see fig. 2]