A Direct Connection Between the Venus, Earth and Jupiter Tidal-Torquing Cycles (a Proposed Driver of Solar Activity) and the Long-Term Strength of Perigean Spring Tides

IMPORTANT CLAIMS:

1. The Synodic (phase) cycle of the Moon precisely re-synchronises with the times of the Extreme Perigean Spring tides (EPST) once every 574.60 topical years.

2. Jupiter precisely re-synchronises itself in a frame of reference that is rotating with the Earth-Venus-Sun line once every 575.52 tropical years.

3. The orientation of Jupiter to the Earth-Venus-Sun line produce the tidal torques that act upon the base of the convective layers of the Sun which are thought to be responsible for the periodic changes in the level of magnetic activity on the surface of the Sun (i.e. the Solar Cycle).

4. The period of time required for Jupiter to precisely re-align with the Earth-Venus-Sun line in a reference frame that is fixed with respect to the stars is 4 x 575.52 = 2302 years. This is the Hallstatt cycle that is intimately associated with the planetary configurations that are driving the VEJ Tidal-Torquing model for solar activity.

5. Hence, the repetition period for strongest of the Extreme Perigean Spring tides appears to match that of the planetary tidal-torquing forces that are thought to be responsible for driving the Solar sunspot cycle.

6. The Venus–Earth–Jupiter (VEJ) tidal-torquing model is based on the idea that the planet that applies the dominant gravitational force upon the outer convective layers of the Sun is Jupiter, and after Jupiter, the planets that apply the dominant tidal forces upon the outer convective layers of the Sun are Venus and the Earth. Periodic alignments of Venus and the Earth on the same or opposite sides of the Sun, once every 0.7993 sidereal Earth years, produce temporary tidal bulges on the opposite sides of the Sun’s surface. Whenever these temporary tidal bulges occur, Jupiter’s gravitational force tugs upon the tidally induced asymmetries and either slows down or speeds-up the rotation rate of plasma near the base of the convective layers of the Sun. The VEJ tidal-torquing model proposes that it is the variations in the rotation rate of the plasma in Sun’s lower convective layer, produced by the torque applied by Jupiter upon the periodic Venus–Earth (VE) tidal bulges that modulate the Babcock–Leighton solar dynamo. Hence, the model asserts that it is the modulating effects of the planetary tidal-torquing that are primarily responsible for the observed long-term changes in the overall level of solar activity.

What makes this simple VEJ tidal-torquing model so intriguing is the time period over which the Jupiter’s gravitational force speeds up and slows down the rotation rate of the Sun’s outer layers. Jupiter’s movement of 13.00 deg. per 1.5987 yr with respect to closest tidal bulge means that Jupiter will increase the rotation speed of the lower layers of the Sun's convective zone for 11.07 yrs. This is almost the same amount of time as to average length of the Schwabe sunspot cycle (11.1 ± 1.2 yrs, Wilson, 2011).

In addition, for the next 11.07 yrs, Jupiter will start to lag behind the closest tidal bulge by 13.00 deg. every 1.5987 yrs, and so its gravitational force will pull on the tidal bulges in such a way as to slow down the rotation rate of the outer convective layers of the Sun. Hence, the basic unit of change in the Sun’s rotation rate (i.e. an increase followed by a decrease in rotation rate) is 2 × 11.07 = 22.14 yrs. This is essentially equal to the mean length of the Hale magnetic sunspot cycle of the Sun, which is 22.1 ± 2.0 yrs (Wilson, 2011).

It is important to note that, the actual torques that are applied by Jupiter to the temporary tidal bulges induced by alignments of Venus and the Earth, vary in-phase with the observed 11 year sunspot cycle.

ARTICLE:

A. The 574.6 Year Cycle in Extreme Perigean Spring Tides

     Extreme Perigean Spring tides (EPST) occur when a New moon occurs at time when the Perigee of the lunar orbit points directly at the Sun or when a Full Moon occurs when the Perigee of the lunar orbit points directly away from the Sun (the latter are often called Extreme Super Moons). Figure 1 shows a schematic diagram an EPST occurring at a New Moon.

Figure 1.      

     EPST at New Moon re-occur once every 18 Full Moon Cycles (FMC) = 20.2937 tropical years (where one tropical year = 365.242189 days).

[Note: A FMC (= 411.78443029 days epoch J2000.0) is the the time required for the Sun (as seen from the Earth) to complete one revolution with respect to the Perigee of the Lunar orbit. In other words, it is the time between repeat occurrences of the Perigee of the lunar orbit pointing at the Sun. This value for the FMC is based upon a Synodic month = 29.53058885 days, an anomalistic month = 27.55454988 days - Epoch J2000.0.]  

     Figure 2, below, has as its initial starting point (T = 0.0 tropical years), a New Moon taking place at the precise time that the Perigee of the lunar orbit points directly at the Sun. In addition, this figure shows the number of days to (negative values on the y-axis) or from (positive values on the y-axis) a New/Full Moon for each of the EPST's that occur over the next 618.4 tropical years.

     Figure 2 shows that the point representing the New Moon at T = 0.0 tropical years is part of a triplet of points with the other two points occurring at  (-1.1274 tropical years, 1.64 days) and (+1.1274 tropical years, -1.64 days). Hence, a point starting at (-1.1274 tropical years, 1.64 days), reaches the x-axis at (573.4727 topical years, 0.0 days), leading to an overall repetition cycle of 574.600 tropical years.
   
Figure 2.

B. The Venus–Earth–Jupiter (VEJ) Tidal-Torquing Model 
     (A Proposed Driver of Solar Activity)

Quote from: Wilson, I.R.G.: The Venus–Earth–Jupiter spin–orbit coupling model, Pattern Recogn. Phys., 1, 147-158

http://www.pattern-recogn-phys.net/1/147/2013/prp-1-147-2013.html

     "The Venus–Earth–Jupiter (VEJ) tidal-torquing model is based on the idea that the planet that applies the dominant gravitational force upon the outer convective layers of the Sun is Jupiter, and after Jupiter, the planets that apply the dominant tidal forces upon the outer convective layers of the Sun are Venus and the Earth. Periodic alignments of Venus and the Earth on the same or opposite sides of the Sun, once every 0.7993 sidereal Earth years, produces temporary tidal bulges on the opposite sides of the Sun’s surface (Fig. 3 – red ellipse). 

Figure 3.

      Whenever these temporary tidal bulges occur, Jupiter’s gravitational force tugs upon the tidally induced asymmetries and either slows down or speeds-up the rotation rate of plasma near the base of the convective layers of the Sun. The VEJ tidal-torquing model proposes that it is the variations in the rotation rate of the plasma in Sun’s lower convective layer, produced by the torque applied by Jupiter upon the periodic Venus–Earth (VE) tidal bulges that modulate the Babcock–Leighton solar dynamo. Hence, the model asserts that it is the modulating effects of the planetary tidal-torquing that are primarily responsible for the observed long-term changes in the overall level of solar activity. 

      It is important to note that tidal bulges will be induced in the surface layers of the Sun when Venus and the Earth are aligned on the same side of the Sun (inferior conjunction), as well as when Venus and the Earth are aligned on opposite sides of the Sun (superior conjunction). This means that whenever the gravitational force of Jupiter increases/decreases the tangential rotation rate of the surface layer of the Sun at inferior conjunctions of the Earth and Venus, there will be a decrease/increase the tangential rotation rates by almost the same amount at the subsequent superior conjunction. 

     Intuitively, one might expect that the tangential torques of Jupiter at adjacent inferior and superior conjunctions should cancel each other out. However, this is not the case because of a peculiar property of the timing and positions of Venus– Earth alignments. Each inferior conjunction of the Earth and Venus (i.e. VE alignment) is separated from the previous one by the Venus–Earth synodic period (i.e. 1.5987 yr). This means that, on average, the Earth–Venus–Sun line moves by 144.482 degrees in the retrograde direction, once every VE alignment. Hence, the Earth–Venus–Sun line returns to almost the same orientation with respect to the stars after five VE alignments of almost exactly eight Earth (sidereal) years (actually 7.9933 yr). Thus, the position of the VE alignments trace out a five pointed star or pentagram once every 7.9933 yr that falls short of completing one full orbit of the Sun with respect to the stars by (360−(360×(7.9933− 7.0000))) = 2.412 degrees (fig. 4). 

Figure 4.

     In essence, the relative fixed orbital longitudes of the VE alignments means that, if we add together the tangential torque produced by Jupiter at one superior conjunction, with the tangential torque produced by Jupiter at the subsequent inferior conjunction, the net tangential torque is in a pro-grade/retrograde direction if the torque at the inferior conjunction is greater/less than that of the torque at the superior conjunction.

Figure 5.

     What makes this simple tidal-torquing model so intriguing is the time period over which the Jupiter’s gravitational force speeds up and slows down the rotation rate of the Sun’s outer layers. 

     Figure 5 shows Jupiter, Earth and Venus initially aligned on the same side of the Sun (position 0). In this configuration, Jupiter does not apply any tangential torque upon the tidal bulges (the position of the near-side bulge is shown by the black 0 just above the Sun’s surface). Each of the planets, 1.5987 yrs later, moves to their respective position 1's. At this time, Jupiter has moved 13.00 deg. ahead of the far-side tidal bulge (marked by the red 1 just above the Sun’s surface) and the component of its gravitational force that is tangential to the Sun’s surface tugs on the tidal bulges, slightly increasing the rotation rate of the Sun’s outer layers.

     After a second 1.5987 yrs, each of the planets moves to their respective position 2's. Now, Jupiter has moved 26.00 deg. ahead of the near-side tidal bulge (marked by the black 2 just above the Sun’s surface), increasing Sun’s rotation rate by roughly twice the amount that occurred at the last alignment. This pattern continues with Jupiter getting 13.00 deg. further ahead of the nearest tidal bulge, every 1.5987 yrs. Eventually, Jupiter will get 90 deg. ahead of the closest tidal bulge and it will no longer exert a net torque on these bulges that is tangential to the Sun’s surface and so it will stop increasing the Sun’s rotation rate. 

      Interestingly, Jupiter’s movement of 13.00 deg. per 1.5987 yr with respect to closest tidal bulge means that Jupiter will get 90 deg. ahead of the closest tidal bulge in 11.07 yrs. This is almost the same amount of time as to average length of the Schwabe sunspot cycle (11.1 ± 1.2 yrs, Wilson, 2011). In addition, for the next 11.07 yrs, Jupiter will start to lag behind the closest tidal bulge by 13.00 deg. every 1.5987 yrs, and so its gravitational force will pull on the tidal bulges in such a way as to slow down the rotation rate of the outer convective layers of the Sun. Hence, the basic unit of change in the Sun’s rotation rate (i.e. an increase followed by a decrease in rotation rate) is 2 × 11.07 = 22.14 yrs. This is essentially equal to the mean length of the Hale magnetic sunspot cycle of the Sun, which is 22.1 ± 2.0 yrs (Wilson, 2011)." 

C. The 575.52 year Realignment Cycle for Jupiter in a Reference Frame that     is  Rotating with the Earth-Venus-Sun Line

The Movement of Jupiter with Respect to the Tidal-Bulge that is Induced in the Convective Layers of the Sun by Periodic Alignments of Venus and the Earth.

     The slow revolution of the Earth-Venus-Sun alignment axis can be removed provided you place yourself in a framework that rotates by 215.5176 degrees in a pro-grade direction [with respect to the fixed stars] once every 1.59866 years. In this rotating framework, Jupiter moves in a pro-grade direction (with respect to the Earth-Venus-Sun line) by 12.9993 degrees per [inferior conjunction] VE alignment.

     Figure 6 shows the position of Jupiter every VE alignment (i.e. 1.59866 years) in reference frame that is rotating with the Earth-Venus-Sun alignment line. This keeps the Earth and Venus at the 12:00 o'clock position in this diagram whenever the number of VE aligns is even and at the 6:00 o'clock position whenever the number of VE aligns is odd. In contrast, Jupiter starts out at JO and moves 12.9993 degrees every 1.59866 years, taking 11.07 years to move exactly 90 degrees in the clockwise (pro-grade) direction and 11.19 years to the position marked J7 (at roughly 91 degrees).

Figure 6.

 Also shown on this diagram is the position of Jupiter after 27, 28 and 29 VE alignments. This tells us that Jupiter completes exactly one orbit in the VE reference frame once every 44.28 years (= 11.07 years x 4), with the nearest VE alignment taking place at 28 VE alignments (= 44.7625 years) when Jupiter has moved 3.9796 degrees past realignment with its original position at JO.

     The following table shows how Jupiter advances by one orbit + 3.9796 degrees every 28 VE alignments until the alignment of Jupiter with the Earth-Venus-Sun line progresses forward by   13 orbits in the VE reference frame plus 51.7345 degrees. This angle (see * in table) is almost exactly equal to the angle moved by Jupiter in 4 VE aligns (i.e. 4 x 12.99927 degrees = 51.9971 degrees).   

 VE_multiple______Angle of______Orbits_+__Degrees   of 
12.9993_______Jupiter_______________________degrees

28_________363.9796_______1__+___3.9796____
56_________727.9592_______2__+___7.9592____
84________1091.9387_______3__+__11.9387___
112________1455.9183_______4__+__15.9183___
140________1819.8979_______5__+__19.8979___
168________2183.8775_______6__+__23.8775___
196________2547.8571_______7__+__27.8571___
224________2911.8366_______8__+__31.8366___
252________3275.8162_______9__+__35.8162___
280________3639.7958______10__+__39.7958___
308________4003.7754______11__+__43.7754___
336________4367.7550______12__+__47.7550___
364________4731.7345______13__+__51.7345__*

This means that Jupiter returns to almost exact re-alignment with the Earth-Venus-Sun line after:

(364 - 4) VE aligns = 360 VE aligns = 575.52 years 

[i.e. 12.9993 orbits of Jupiter in a retro-grade direction in the VE reference frame, falling 0.2625 degrees short of exactly 13 full orbits]

APPENDIX

The Planetary Connection to the 2300 Hallstatt Cycle

      It has long been recognised that there is a prominent 208 year de Vries (or Suess) cycle in the level of solar activity. The following blog post shows that the there is a 208.0 year de Vries cycle in the alignment between the times that Perigee of the Lunar orbit points directly at the Sun and the Earth's seasons provided that you measure the alignment in a reference frame that is fixed with respect to the Perihelion of the Earth's orbit:   

http://astroclimateconnection.blogspot.com.au/2016/05/there-is-natural-208-year-de-vries-like.html   

Its appearance, however, is intermittent. Careful analysis of the Be10 and C14 ice-core records show that the de Vries cycle is most prominent during epochs that are separated by about 2300 years (Vasiliev and Dergachev, 2002).  This longer modulation period in the level of solar activity is known as the Hallstatt cycle (Vitinsky et al., 1986; Damon and Sonett, 1991; Vasiliev and Dergachev, 2002).

  

Jupiter in a Reference Frame that is Fixed with Respect to the Stars

     Figure_A1 shows the orbital position of Jupiter, starting at (0,1), every 0.79933 years, over a period of 35.9699 years [i.e. just over three orbits of the Sun]. It is clear from this diagram that, in a reference frame that is fixed with respect to the stars,  the symmetry pattern perfectly re-aligns after moves roughly 24.26 degrees in a clockwise (pro-grade) direction. It takes Jupiter 71.9397 years (i.e. just over six orbits of the Sun or 45 VE aligns) to move 23.30 degrees in a clockwise (pro-grade) direction, to approach with one degree of producing a re-alignment of rotational symmetry.

Figure_A1

Re-aligning the Movement of Jupiter in the Rotating VE Reference Frame with its Movement in the Reference Frame that is Fixed with the Stars

    Figure_A2 shows the precise alignments Jupiter with the Earth-Venus-Sun line at 575.5176 years (360 VE aligns) and 1151.0352 years (720 VE aligns) in a frame of reference that is fixed with respect to the stars. Jupiter lags behind the VE alignments by 0.2654 degrees and 0.5251 degrees, respectively.

Figure_A2

  Figure_A3 shows the precise alignments of Jupiter with the Earth-Venus-Sun line at 1726.5528 years (1080 VE aligns) and 2302.0704 years (1440 VE aligns) in a frame of reference that is fixed with respect to the stars. Jupiter lags behind the VE alignments by 0.7876 degrees and 1.0502 degrees, respectively.

Figure_A3

  The important point to note is that after four precise Jupiter alignments of 575.5176 years (i.e. 4 x 575.5176 = 2302.07 years), the position of Jupiter advances from its initial position at JO (see figure 6 and figure_A1 above) by 24.2983 degrees. This angle is almost exactly the same as 24.26 degrees of rotation that is required to produce a re-alignment of the rotational symmetry of Jupiter, in the reference frame that is fixed with respect to the stars.

     Hence, the period of time required for Jupiter to precisely re-align with the Earth-Venus-Sun line in a reference frame that is fixed with respect to the stars is 2302 years. This is the Hallstatt-like cycle that is naturally found in the planetary configurations that are driving the VEJ Tidal-Torquing model for solar activity. 

References

Damon, P.E. and Sonett, C.P., 1991, “Solar and terrestrial components of the atmospheric 14C variation spectrum”, in The Sun in Time, (Eds.) Sonett, C.P., Giampapa, M.S., Matthews, M.S., pp. 360–388, University of Arizona Press, Tucson.

Vasiliev, S.S. and Dergachev, V.A., 2002, “The ∼2400-year cycle in atmospheric radiocarbon concentration: bispectrum of ¹⁴C data over the last 8000 years”, Ann. Geophys., 20, 115–120.
http://www.ann-geophys.net/20/115/2002/

Vitinsky, Y.I., Kopecky, M. and Kuklin, G.V., 1986, Statistics of Sunspot Activity (in Russian), Nauka, Moscow

  

Changes to the Earth's albedo appear to lead the SOI Index by approximately 6 months

Figures 1a shows the mean monthly apparent albedo anomalies from December 1998 to December 2014 as measured by ground-based earth-shine observations. The anomalies are calculated over the mean of the full period and positive anomalies are shown in red and negative in blue. The averaged standard deviation (error) of the monthly data is also indicated in the lower right corner.

Ref:
Palle, E., et al. (2016), Earth’s albedo variations 1998–2014 as measured
from ground-based earth-shine observations, Geophys. Res. Lett., 43, 
doi:10.1002/2016GL068025

Figure 1a and 1b

Figure 1b shows the monthly Southern Oscillation Index (SOI) published by the Australian Bureau of Meterology (BOM) at:

ftp://ftp.bom.gov.au/anon/home/ncc/www/sco/soi/soiplaintext.html

The SOI has be shifted backward in time by 6 months.

Not withstanding the large error bars associated with the mean monthly apparent albedo anomalies, and the gap in the albedo anomaly data between June 2005 and December 2006, there appears to be rough correlation between the retarded SOI and the monthly apparent albedo anomaly.

If this correlation has any validity then I would predict that the Earth's mean monthly albedo anomaly will remain in negative territory from late 2014 till the end of 2015. 

The next few of years of data from the Earth-shine project should be very interesting if it does. 

Moderate to strong El Nino events are triggered by the inter-annual variability in the lunar tides.

Moderate to strong El Nino events are triggered by long-term (i.e. inter-annual) variability in the lunar tides. Specifically, the timing of these events is directly related to 31/62 year Perigee/Syzygy lunar tidal cycle.

I do not have all the answers as to how this actually happens but the best answer that I can come up with is that slow forcings applied to the Earth by the lunar tides influences the formation and subsequent propagation of Madden-Julian Oscillations (MJO) along the Equatorial Indian Ocean and Pacific Oceans.

A MJO consists of a large-scale coupling between the atmospheric circulation and atmospheric deep convection. When a MJO is at its strongest, between the western Indian and western Pacific Oceans, it exhibits characteristics that approximate those of a hybrid-cross between a convectively-coupled Kelvin wave and an Equatorial Rossby wave. When a MJO moves from the western Indian Ocean into the western Pacific Ocean, it generally accelerates, becomes less strongly coupled to convection, and transitions into a convectively de-coupled (i.e. dry) Kelvin wave.

Periodically (i.e. roughly once every 4.5 years), the precise alignments of the lunar tidal forcings produce the right conditions that result an upsurge in the number and magnitude of what I call Pacific Penetrating MJO. These are MJO events that travel from the Eastern equatorial Indian Ocean, along the Equator, all the way into the Western Pacific Ocean, where they initiate Westerly Wind Bursts (WWB’s).

The spawning of these WWB’s takes place as the MJO event is transitioning from a hybrid-cross between, a convectively-coupled Kelvin wave and an Equatorial Rossby wave, and a convectively de-coupled (i.e. dry) Kelvin wave. The spawning of the WWB’s occurs in the Western Equatorial Pacific Ocean, somewhere between 60 deg E and 150 deg W longitude. The actual process involves the formation of a typhoon/cyclone pair straddling the equator which produces an intense WWB between the two intense low pressure cells.

The onset of El Nino event are marked by the weakening of the easterly trade winds associated with the Walker circulation. The actual drop off in easterly trade wind strength is always preceded by a marked increase in WWB’s in the western equatorial Pacific Ocean. The WWB’s help initiate an El Nino event by creating downwelling Kelvin waves in the western Pacific that propagate towards the eastern Pacific, where they produce intense localized warming, as well as by generating easterly moving equatorial surface currents which transport warm water from the warm pool region into the central Pacific.

The net result of the Moon’s involvement in the initiation of El Nino events means that:

El Niño events in New Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Solstices.

El Niño events in the Full Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Equinoxes.

http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are.html

For a full description of the meaning of Full and New Moon Epochs please read:

http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are_13.html

Are we looking in the wrong place for the connection between solar insolation and the world's mean temperature?

I propose that it is the lunar tidal modulation of the seasonal variations in the solar flux, coupled with the hemispherical asymmetry of the Earth’s surface properties (i.e. Nth Hemisphere – dominated by continents, St Hemisphere – dominated by oceans) that is responsible for setting the world's mean temperature.

On inter-annual time scales:

There are periodic slow downs in the Earth’s rotation rate every 13.66 days. These slows downs are caused by the passage of the lunar tidal bulge across the Earth’s equator once every half lunar tropical month = 13. 66 days. The ratio in the magnitude of the increase in Length Of Day (LOD) at one crossing with respect to the magnitude of the increase in LOD at the next is primarily governed by the orientation of the lunar line-of-apse with respect to the seasonal cycle as marked by the solstices and equinoxes (there is also a secondary effect caused by the 5 degree tilt of lunar obit with respect to the ecliptic). Please see:

http://astroclimateconnection.blogspot.com.au/2016/03/there-is-natural-gleissberg-like-cycle.html

On decadal time scales:

The climate variation is driven by the ratio in strength and frequency of El Nino to La Nina events – This is dominated by the 31/62 year lunar tidal cycle. For 31 years, El Ninos start in years when lunar line-of-apse is pointed at the Sun near the Winter/Summer solstices, then for next 31 years, El Ninos start in years when lunar line-of-apse is pointed at the Sun near the Vernal/Autumnal equinoxes.

http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are.html

On centennial to millennial time scales:

The climate variation appear to be correlated with variations in the overall strength of the Sun’s magnetic field as indicated by Be10 and C14 proxies. These primarily occur at 88.5 years (Gleissberg cycle), 208 years (de Vries Cycle), 354 years, 510 years, 708 years, 980 years (Eddy Cycle) and 2300 years (Hallstatt Cycle). It just so happens that these cycles in the Sun’s magnetic field strength are matched by the times at which the lunar line-of-apse points at the Sun at either the solstices or equinoxes of the Earth’s seasonal calendar (in a reference frame that is fixed with respect to the Earth’s orbit).

This produces a long term 21,000 year climate forcing which when coupled with the Milankovitch orbital forcing and the formation and melting of ice sheets at the Earth’s poles, produces the ice-age cycles.

http://astroclimateconnection.blogspot.com.au/2016/05/there-is-natural-208-year-de-vries-like.html

There is a natural 208 year de Vries-like cycle in the Lunar Tidal Forces acting upon the Earth

1. The Defacto 13 year Lunar tidal cycle

There is a defacto 13 year lunar tidal cycle created by the difference 

between 31 perigee/syzygy cycle and the 18 year Saros cycle, such that:

13 years = 31 – 18 years

Now the reason for the 18.03 sidereal year Saros cycle is:

223 Synodic months______= 18.02931 sidereal years
239 anomalistic months___ = 18.02990 sidereal years
242 Draconic months______= 18.02941 sidereal years
[with closest alignment between Synodic and Draconic cycles,
though the anomalistic cycle is not far off]

while the reason for the 31 year cycle is:

383.5 Synodic months______= 31.005568 sidereal years
411.0 anomalistic months___ = 31.005401 sidereal years
416.0 Draconic months_____= 30.992708 sidereal years
[with closest alignment between Synodic and anomalistic cycles]

hence, the defacto 13 year cycle possibly comes about because:

160.5 Synodic months______= 12.976254 sidereal years
172.0 anomalistic months___= 12.9754963 sidereal years
174.0 Draconic months_____= 12.9632963 sidereal years
[with closest alignment between Synodic and anomalistic cycles]

2. The 208 year de Vries Cycle

Now 

16 x 13 years = 208 years

Thus, this would indicate that a possible reason for the ~ 208 de Vries cycle is:

16 x 160.5 = 2568.0 Synodic cycles________= 207.6200718 sidereal years

16 x 172.0 = 2752.0 anomalistic cycles_____= 207.6079414 sidereal years 

16 x 174.0 = 2784.0 Draconic cycles_______= 207.4127406 sidereal years

or with a drift of 3.0 Draconic cycles in roughly 208 years you get:

2787.0 Draconic cycles___= 207.6362457 sidereal years 

[with closest alignment between Synodic and anomalistic cycles]

Finally, if you allow for a slight drift of 4.5 Synodic cycles and 5.0 anomalistic and

Draconic cycles you get:

2572.5 Synodic cycles___= 207.98389 sidereal yrs_____= 207.99196 tropical yrs

2757.0 anomalistic cycles_= 207.98514 sidereal yrs____= 207.99321 tropical yrs

2792.0 Draconic cycles___= 208.00875 sidereal yrs____= 208.01682 tropical yrs

Of course, the drift required to realign the sidereal/tropical reference frame 

with the seasonal year of 4.5 synodic = 5.0 anomalistic = 5.0 Draconic cycles 

over 208 tropical years is not arbitrary since this is equivalent to:

132.887 days in 75970.375 days = 0.0017492 of a full cycle in 208 tropical years.

which for the Earth’s orbit is 0.6297133 degrees in 208.0 tropical years

or 10.90 ~ 11 arc second per tropical year!

This is just the (pro-grade) rate of precession of the perihelion of the Earth’s orbit 

which is currently about:

11.45 arc seconds per year – theoretical

11.62 arc seconds per year – observed epoch 2000.

CONCLUSION 

Hence, If we look at times where the perigee of the lunar orbit points at the 

Sun, they will realign with the seasons in (almost) precisely 208.0 tropical 

years or one de Vries Cycle, if you measure the alignment in a reference 

frame that is fixed with the Earth’s orbit (i.e. a frame that is tracking the 

perihelion precession of the Earth’s orbit).

There is a natural Gleissberg-like Cycle in the Lunar tidal stresses placed upon the Earth

Preamble

1. There is a lunar tidal cycle that synchronizes the slow precession of the lunar line-of-apse with the seasons and the Synodic cycle (i.e. the Moon's phases). 

The tidal cycle is called the 31/62 year Perigee-Syzygy Cycle. This tidal cycle is the time required for a full (or new moon) at Perigee to re-occur at or very near to the same point in the seasonal calendar.

It is highly recommended that readers go to the following link to get a fuller understanding of the parameters that are used to define the lunar orbit as well a better understanding of the 31/62 year Perigee-Syzygy tidal cycle, before proceeding with this post.

II. Seasonal Peak Tides - The 31/62 year Perigee-Syzygy  Tidal Cycle.

http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are_11.html

2. The current post needs to be read in the light of the fact that a previous post at:

http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are_13.html

claimed that:

El Niño events in New Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Solstices..

El Niño events in the Full Moon epochs preferentially occur near times when the lunar line-of-apse aligns with the Sun at the times of the Equinoxes. 

CURRENT POST

The Changing Aspect of the Lunar Orbit & its Impact Upon the Earth's Length of Day.

a. Inter-Annual Changes in the Earth's LOD

The blue curves in figures 1a, 1b, and 1c (below) show the Earth's LOD over a six year period from January 1966 through to December 1971.  These plots use daily LOD values that are available online from the International Rotation and Earth Reference System Service (IERS) covering the period from January 1962 until the present.

This data can downloaded at: http://datacenter.iers.org/eop/-/somos/5Rgv/latest/214

1a   LOD - 1966 to 1968

1b   LOD – 1968 to 1970

1c   LOD – 1970 to 1972

It is evident from these three figures that there are abrupt periodic slow downs in the Earth's rotation rate (corresponding to an increase in LOD ~ 1 msec) once every 13.66 days (blue curve)* that are accompanied by much smoother longer-term changes in LOD that are associated with the annual seasonal cycle (red curves).

The smoother longer-term seasonal variations in LOD are primarily the result of changes in the angular momentum of the Earth that are a response to the slow (north-south) seasonal movement of the Earth's atmosphere and its wind patterns.

The green LOD curve is a crude seasonally de-trended version of the blue LOD curve.

[Note: Half of a lunar tropical month = 27.32158 /2 = 13.66079 days.*]

b. Reason for the Peaks in the Earth's LOD

A more detailed investigation show that the spikes in LOD (in the blue and green curves) occur

within a day or two of the time that the Moon crosses the Earth's Equator.

This tells you that the slow down in the rotation rate is a direct result of the lunar tidal bulge in the

Earth's oceans (and atmosphere) passing across the Earth's Equator.

The slow down occurs for much the same reason that a twirling ice-skater slows down their rate of

spin by extending their arms i.e. by the conservation of angular momentum.

c. The Change in the Ratio of Consecutive Peaks in LOD

In early 1966 (figure 1a) the peaks in LOD associated with transits of the Moon across 

the Equator from the northern to the southern hemisphere, are roughly twice as large

as the next peaks in LOD (13.66 days later) that are associated with transits of the

Moon across the Equator from the southern to the northern hemisphere.

By early 1969 (figure 1b), the consecutive peaks in LOD are almost equal in size. 

By late 1971 (figure 1c), the peaks in LOD that are associated with transits of the

Moon across the Equator from the southern to the northern hemisphere, are

roughly twice as large as the next peaks in LOD (13.66 days later) that are associated

with transits of the Moon across the Equator from the northern to the southern

hemisphere.

2. 

Figure 2 shows that the absolute size of the slow down in the Earth’s rotation rate is

determined by the proximity of the Moon as its crosses the Earth’s Equator 

3.

Figure 3 shows the ratio of consecutive peaks in LOD versus lunar distance (in kilometres) for the

numerator of the ratio, for the years from 1966 to 1971.

Figures 2 and 3 indicate that:

Whenever the ratio of consecutive peaks in LOD is close to 1.0, the distance of the

Moon from the Earth at consecutive transit crossings of the Equator are close to the

Moon's average distance from the Earth of approximately 380,000 km.

However, whenever the ratio of consecutive peaks in LOD is far from 1.0 (i.e. either

2.0 or 0.5), the distance of the Moon from the Earth at one transit crossing is at the

distance of closest approach (i.e. the distance of lunar perigee = 356,000 km), and the

distance of the Moon at the other transit crossing is at its furthest from the Earth

(i.e. the distance of lunar apogee = 407,000 km).

4. 

Figure 4 shows the difference in lunar distance for consecutive transits of the Earth’s

Equator from 1962 to 1976.

Figure 4 confirms that whenever the perigee of the lunar orbit is pointed at Sun at the time of the

Summer or Winter solstices, the difference in lunar distance for consecutive transits of the Earth’s

equator is near zero kilometres i.e. the ratio of consecutive peaks in LOD are ~ 1.0 because the lunar

 distances at consecutive crossings are both close to the average lunar distance of 380,000 km. 

Similarly, figure 4 confirms that whenever the perigee of the lunar orbit is pointed at Sun at the time

of the Vernal or Autumnal equinoxes, the difference in lunar distance for consecutive transits of the

Earth’s equator approaches the maximum 50,000 km i.e. the ratio of consecutive peaks in LOD are

far from 1.0 because the Moon is near perigee and apogee at consecutive crossings.

d. Reason for the Change in the Ratio of Consecutive Peaks.

5. Lunar Perigee pointing at the Sun near Summer or Winter Solstices

The yellow tilted elliptical orbits in figure 5 above, represent the apparent movement of the Sun about
the sky as seen from the Earth. The Sun takes a full tropical year (365.242189 days) to move once
about the yellow orbit, crossing the Earth’s equatorial plane (the grey plane) once every
six months at the Spring and Autumnal (Fall) equinox, respectively.

The red tilted elliptical orbits above, represent the apparent movement of the Moon about the sky

as seen from the Earth. The Moon takes a full tropical month (27.32158 days) to move once about

the red orbit, crossing the Earth’s equatorial plane roughly once every 13.66 days where the red

orbit crosses the black line [N.B. the ~ 5 degree tilt of the lunar orbit with respect to the ecliptic is
ignored as a second order effect at this stage of the argument.] 

Clearly, if the perigee of the lunar orbit points at the Sun at either the Winter (i.e. the top diagram)

or Summer Solstice (i.e. the bottom diagram), the Moon will be roughly at or near its average
distance from the Earth (i.e. ~ 380,000 km). This means that when it crosses the Earth’s equatorial
plane at consecutive transits of the Equator (i.e. the intersection of the red orbit and the black line),
the difference in lunar distance for consecutive transits will approach zero (i.e. the ratio of
consecutive peaks in LOD will be close to 1.0) 

6. Lunar Perigee pointing at the Sun near Vernal or Autumnal Equinox

   

The yellow tilted elliptical orbits in figure 6 above represent the apparent movement of the Sun about
the sky as seen from the Earth. The Sun takes a full tropical year (365.242189 days) to move once
about the yellow orbit, crossing the Earth’s equatorial plane (the grey plane) once every six
months at the Spring and Autumnal (Fall) equinox, respectively.

The red tilted elliptical orbits above, represent the apparent movement of the Moon about the sky

as seen from the Earth. The Moon takes a full tropical month (27.32158 days) to move once about

the red orbit, crossing the Earth’s equatorial plane roughly once every 13.66 days where the red

orbit crosses the black line.

Clearly, if the perigee of the lunar orbit points at the Sun at either the Vernal (i.e. the bottom
diagram) or Autumnal Equinox (i.e. the top diagram), the Moon will be at or near perigee and apogee
at consecutive transits of the equatorial plane (i.e. where the red orbit crosses the black line).

This means that when it crosses the Earth’s equatorial plane at consecutive transits, the difference in

lunar distance for consecutive transits will approach its maximum value of 50,000 km (i.e. the ratio

of consecutive peaks in LOD will be as far from 1.0 as possible).

Hence, figure 4 tells us that the perigee moves from pointing at the Sun at a Solstice(/Equinox)
to pointing at the Sun at the following Equinox(/Solstice) in the seasonal calendar once every  
2.0 Full Moon Cycles (FMC) = 2.0 x 411.78444836 days = 2.2547695 sidereal years = 2.2548570
tropical years

e. The 9.019 Tropical Year Cycle

7. 

Figure 7 shows the ratio of the consecutive 13.66 day peaks in LOD from 1962 to 1988.

It is evident from this plot that the long-term variation in the ratio of consecutive peaks is dominated

by a periodicity of ~ 9.0 years. In addition, there is an approximate 18.0 year periodicity that
modulates the ~ 9 year periodicity.  

The ~ 9.0 periodicity results from the fact that 4.0 x 2 FMC = 9.019428 tropical years  is the
time required for slowly drifting perigee of the lunar orbit to return to pointing at the Sun at the same
Solstice or Equinox (since it takes 2.2548570 topical years for the alignment of the perigee with the
Sun at a Solstice/Equinox to move to the following Equinox/Solstice in the seasonal calendar.

(N.B. The ~  9.0 period is close to but not necessarily the same as the 8.85 years that it takes the

lunar line-of-apse to precess once around the Earth with respect to the star. In addition, the
~ 18.0 periodic modulation of the 9.0 year period is close to but not necessarily the same as the 18.6
year period that it takes the lunar line-of-nodes to precess once around the Earth with respect to the
stars. The 18.6 year period is caused by the slowly changing tilt of the Moon’s orbit with respect to
the Earth’s equator caused by precession of the lunar-line-of-nodes - Please see the Addendum at the
end of this post about the possible long-term interaction of these two lunar cycles).

f. A Gleissberg Cycle in the Ratio of Consecutive Peaks in LOD.

The slow pro-grade precession of the perigee of the lunar orbit through the seasonal calendar leads to

the perigee moving from pointing at the Sun at one Solstice(/Equinox) to pointing at the Sun at the
following Equinox(/Solstice) once every 2.0 Full Moon Cycles (FMC) = 2.0 x 411.78445750
days = 2.2547695 sidereal years = 2.2548570 topical years.

However, since 2.0 FMC is longer than 2.00 sidereal years (by 0.2547695 sidereal years), the perigee
of the lunar orbit will slowly drift from pointing at the Sun at a given point in the seasonal calendar,
only re-synchronizing with the seasonal calendar after:
  

(2.0000000 x 2.2547695) / (2.2547695 - 2.0000000) ≈ 17.70046823 sidereal years 

This comes about because there are 8.850234 lots of 2.00 sidereal year cycles in 17.70046823
sidereal years and 7.850234 lots of 2.2547695 sidereal year cycles in 17.70046823 sidereal years.

In effect, what this means is that there will be a precise realignment between when the lunar perigee
points at the Sun at a given Solstice/Equinox and when it does so again at the same point in the
seasonal calendar (i.e. the same Solstice/Equinox), once every 354.000 years:    

157 x 2.0 FMC = 353.9988071 ≈ 354.00 sidereal years

Of course, it would take half of this time i.e. 177.0 sidereal years, if we broaden our criterion to
include the cases where the lunar Perigee points directly away from the Sun:

157 x 1.0 FMC = 176.9999404 ≈  177.000 sidereal years

And it would take half of this time again i.e. 88.5 years, if we only make the constraint that the

Perigee of the lunar orbit move from one Solstice/Equinox to the next, rather than go through the full

seasonal calendar:

157 x 0.5 FMC = 88.499702 ≈  88.500 sidereal years 

Hence, the long-term variations of the ratio of the strength of the consecutive (13.66 day) slow

downs in the Earth’s LOD that are caused by the Moon transiting across the Earth’s Equator,
have a natural long term repetition cycle with respect to the seasons that matches that of the:

88 year Gleissberg Cycle 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Addendum 1 - A Possible 2340 Year Hallstatt-like Cycle 

In this blog post we have established that there is a quasi 9.0 year periodicity in the ratio of
consecutive increases in the Earth’s LOD that result from transits of the Moon across the Earth’s
Equatorial plane every 13.66 days.

There is a possibility that the quasi 9.0 periodicity could be the harmonic mean of the two factors in
figure 7 that are influencing the long-term variations in the ratio of consecutive increases in the
Earth’s LOD  i.e. the 8.8505 tropical year precession of the lunar line-of-apse (i.e. the Lunar
Anomalistic Cycle - LAC) and the 9.3001 (= 18.6002/2.0) tropical year half cycle for the precession
of the lunar-line of nodes (i.e. the half Lunar Nodical Cycle - LNC) such that:

2.0 x (9.3001 x 8.8505) / (9.3001 + 8.8505) = 9.0697(3) tropical years

Since 9.0697(3) tropical years is slightly longer than 9.00 tropical years, it slowly drifts by 0.0697(3)
tropical years once every 9.06973 years, resulting in a forward shift by
one full tropical year once every:

9.06973 / (9.06973 - 9.00000) = 9.06973 / 0.06973 ≈ 130.069267 tropical years

In addition, the beat period between 9.0697(3) tropical year and 9.00000 tropical year gives:

9.00 x 9.06973 / (9.06973 – 9.00) = 1170.623 tropical year  ≈  9.0 x 130.069267 tropical years

Which is half of a Hallstatt-like cycle of 2341.247 tropical years. 

Hence, the interaction between the LAC with LNC naturally produces a Hallstatt-like cycle.

Addendum 2 - Some More Information on the 31 Year Perigee-Syzygy Lunar Tidal Cycle

A1

Figure A1 shows the offset in days from a New/Full Moon at each instant where the Perigee of the
lunar orbit points either towards or away from the Sun - up to 27.5 FMC = 31.00308 sidereal years.
This figure shows us that phase of the Moon goes from:

New --- Full --- New --- Full    every

0.0 --- 9.00 --- 18.00 --- 27.00 FMC's

0.0 --- 10.146463 --- 20.292925 --- 30.439388 sidereal years

with the Moon being less than one day past Full Moon at 27.5 FMC = 31.00308 sidereal years.

A2

Figure A2 shows the offset of the Moon from the lunar line-of-apse at each instant where the Perigee
of the lunar orbit points either towards or away from the the Sun - up to 27.5 FMC = 31.00308
sidereal years (N.B. the Perigee alternates between point directly at the Sun to pointing directly away
from the Sun once every 0.5 FMC).

Hence

New Perigee --- Full Apogee --- New Perigee --- Full Apogee    every

0.0 --- 9.00 --- 18.00 --- 27.00 FMC's

0.0 --- 10.146463 --- 20.292925 --- 30.439388 sidereal years

with the Moon returning to perigee, less than one day past Full Moon, at 27.5 FMC = 31.00308

sidereal years.