Reposted for discussion from Ian Wilson’s blog Astro-Climate Connection
Direct instrumental observations of the Sun since 1610 have shown that the level of sunspot activity on the Sun has a mean periodicity of 22.3 years, known as the Hale cycle. In addition, these observations of the Sun have shown that there are longer-term periodicities present in the level of solar activity.
One of the most prominent long-term cycles that have been identified is the ~210 year de Vries (Suess) cycle. However, because of the limited time over which instrumental observations have been available, the confirmation of the de Vries cycle  has required the use of proxies such as de-trended δC14 from tree rings [2,3], Be10 levels in the GRIP ice cores [4,5,6], and dust profiles in GISP2 ice cores . These proxy observations have indicated that:
a) the de Vries cycle amplitude varies with a period of about 2200 years . In other words, its appearance is intermittent in nature.
b) the largest amplitude of the de Vries cycle are found near Hallstatt cycle minima centered at 8,200, 5,500, 2,500 and 800 B.P .
c) grand solar minima occur preferentially at minima of the Hallstatt cycle that are characterized by large de Vries cycle amplitudes .
d) the cycle length is somewhere in the range 205 – 210 years, with the more precise estimates being in the range 207-208 years.
Abreu et al. (2012)  have identify a 208 year period in a 9400 year reconstruction of the solar modulation potential that is derived from C14 and Be10 observations taken from ice cores. The solar modulation potential is thought to be a good indicator the strength of the solar magnetic field that is responsible for the deflection of cosmic ray, and so a good proxy of the overall level of past solar magnetic activity. Abreu et al. (2012)  also show that there is a 208 year period in the planetary induced torques that could act upon any asymmetric structure in the boundary layer known as the solar tachocline. These authors propose that it these planetary induced torques that could be responsible for modulating the long-term solar magnetic activity on the Sun.
Abreu et al. (2012)  do not identify the specific physical mechanism that is responsible for producing the 208 year period in the planetary torques, although it is reasonable to assume that it must be linked in some way with the synodic interactions between orbital period of Jupiter [the main source of planetary torque] and one or more of the other planets.
However, it can be shown that there is a natural 208 year periodicity associated with the position of the Earth in its orbit when it is observed at intervals separated by half the precession cycle of the Lunar line-of-apse, in a reference frame that is fixed with respect to the stars.
The following diagram shows the angle that the Earth in its orbit about the Sun forms with a fixed direction in a sidereal reference frame, at time steps of half the precession period of the lunar line-of-apse (= 4.42558131 sidereal years for 2000.0). This angle is plotted as a function of time measured in sidereal years.
A: The lunar line-of-apse is a line passing through the centre of the Earth that connects the perigee and apogee of the lunar orbit.
B: The lunar line-of-apse precesses about the Earth once every 8.85116364 sidereal years, when measured with respect to the fixed stars.
C: The reference direction in the sidereal frame that was used (as T = 0 years) is that of the Earth on January 1st 2000.0 at 00:00 UT.
D: The following values for the Anomalistic month = 27.554549878-(0.00000001039*T) and the Sidereal month = 27.321661547+(0.000000001857*T) were used for all calculations, where T is the number of sidereal years since 2000.0.]
Interestingly, the Earth/Venus pentagram alignment pattern resets itself with respect to the Sun and the fixed stars once every 149.5 VE alignments (of 1.59866 years) = 238.9996251 years ( with an error of 0.134964 degrees).
[see the updated and corrected blog post at:
http://astroclimateconnection.blogspot.com.au/2013/08/the-vej-tidal-torquing-model-can.html and extensive discussion at the talkshop here: https://tallbloke.wordpress.com/2013/08/12/ian-wilson-the-vej-tidal-torquing-model-can-explain-many-of-the-long-term-changes-in-the-level-of-solar-activity-part-2]
Similarly, the relative position of the Moon in its orbit about the Earth compared to the Lunar line-of-apse reset themselves with respect to the Sun and the fixed stars almost exactly once every 31.0 sidereal years (actually closer to 31.0 sidereal years + 2 days). This comes about because:
31.0 sidereal years _________= 11322.94725312 days
383.5 synodic lunar months ___= 11324.980825 days
411.0 anomalistic lunar months _= 11324.92000 days
27.5 Full Moon Cycles _______= 11324.071833 days
This means that that if you have a New Moon at closest perigee, 31.00 sidereal years (+ 2 days) later, you will have a Full Moon at closest perigee, on almost the same day of the calender year.
Now, it seems quite remarkable that:
a) The position of the Earth in its orbit, as seen once every half precession cycle of the Lunar line-of-apse (= 4.42558131 sidereal years for 2000.0), resets itself with respect to the stars once every 208.0 sidereal years.
b) The relative position of the Moon in its orbit about the Earth compared to the Lunar line-of-apse reset themselves with respect to the Sun and the fixed stars almost exactly once every 31.0 sidereal years.
c) 208.0 sidereal years + 31.0 sidereal years = 239.0 sidereal years
d) the Earth/Venus pentagram alignment pattern resets itself with respect to the Sun and the fixed stars once every 149.5 VE alignments (of 1.59866 years) = 238.9996251 years.
One is left with the feeling that this is more than just a coincidence.
1. Rogers, M. L., Richards, M.T. and Richards, D. St. P. (2006), Long-term variability in the length of the solar cycle, preprint, arXiv: astro-ph/0606426v3
2. Peristykh, A.N. and Damon, P.E. (2003) Persistence of the gleissberg 88-year solar cycle over the last ~12,00 years: Evidence from cosmogenic isotopes. Journal of Geophysical Research 108, 1003.
3. Stuiver, M. and Braziunas, T.F. (1993) Sun, ocean, climate and atmospheric CO2: An evaluation of causal and spectral relationships. Holocene 3, 289-305
4. Wagner, G., Beer, J., Masarik, J., Muscheler, R., Kubik, P. W., Mende, W., Laj, C., Raisbeck, G.M. and Yiou, F., (2001), Presence of the Solar deVries cycle (≈205 years) during the last ice age, Geophysical Research Letters 28 (2), 303-306
5. Abreu J. A., Beer J., Ferriz-Mas A., McCracken K.G., and Steinhilber F., (2012), Is there a planetary influence on solar activity?, A&A 548, A88.
6. Steinhilber F., et al., (2012), 9,400 years of cosmic radiation and solar activity from ice cores and tree rings, PNAS, vol. 109, no. 16, 5967–5971
7. Ram, M. and Stolz, M. R. (1999) Possible solar influences on the dust profile of the GISP2 ice core from Central Greenland, Geophysical Research Letters, 26 (8), 1043-1046