The VEJ Tidal Torquing Model

As with any new idea there are many people who have contributed to its overall development. Listed here are just a few people who  have contributed to the evolution of the VEJ Tidal Model over the years:

J. P. Desmoulins
Ulric Lyons
Ching-Cheh Hung
Ian Wilson
Ray Tomes
P. A. Semi
Roy Martin
Roger "Tallbloke" Tattersall
Paul Vaughan

However the first reference that we can find to this model [hat tip to Paul Vaughan) is that of:

Bollinger, C.J. (1952). A 44.77 year Jupiter-Earth-Venus configuration Sun-tide period in solar-climate cycles. Academy of Science for 1952 – Proceedings of the Oklahoma 307-311.

http://digital.library.okstate.edu/oas/oas_pdf/v33/v307_311.pdf

who  illustrated the ~22 year JEV cycle  over 60 years ago — see the configurations illustrated in Table 1 on p.308.

The Venus-Earth-Jupiter (VEJ) Tidal-Torquing Model is based upon the following set of simple principles [1]: 

• The dominant planetary gravitational force acting upon the outer convective layer of the Sun is that produced by Jupiter.

•  Other than Jupiter, the two planets that apply the greatest tidal forces upon the outer   convective layer 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 0.7997 sidereal Earth years, produces temporary tidal bulges on opposite sides of the Sun's surface layers (red ellipse in the schematic diagram above).

• Whenever these temporary tidal-bulges occur, Jupiter’s gravitational force tugs upon these tidally-induced asymmetries and either slows down or speed-up the rotation rate of plasma near the base of the convective layers of the Sun.

• It is proposed that it is the resultant variations in the rotation rate of the Sun’s lower convective layer, produced by the planetary tidal torquing of Venus, the Earth and Jupiter, that modulate the Babcock-Leighton solar dynamo.  Hence, we claim that it is this modulation mechanism that is responsible for the observed long-term changes in the overall level of solar activity. In addition, this mechanism may be responsible for the torsional oscillations that are observed in the Sun's convective layer, as well.

The VEJ Tidal-Torqueing Model exhibits the following properties that closely match the observed properties of the Sun’s long-term magnetic activity cycle:

•  It naturally produces a net increase in the rate of rotation of the outer layers of the Sun that lasts for 11.07 years (i.e. equivalent to the Schwabe cycle), followed by a net decrease in the rate of rotation of the outer layers of the Sun, also lasting 11.07 years [1], [2].

• Hence, the net torque of Jupiter acting on the V-E tidal bulge has a natural 22.14 year periodicity that closely matches the 22 year Hale (magnetic) cycle of solar activity [1], [2], [3].

• The equatorial convective layers of the Sun are sped-up during ODD numbered solar cycles and slowed-down during EVEN numbered solar cycles [2]. This  provides a  logical explanation for the Gnevyshev−Ohl (G−O) Rule for the Sun [4].

• This model naturally produces systematic changes in the rotation rate of the outer layers of the Sun that result in an apparent synchronization with the Bary-centric motion of the Sun about the centre-of-mass of the Solar System, as observed by Wilson et al. (2008) [5].

• In all but two cases between 1750 and 2030, the time for solar minimum is tightly synchronized with the times where the Jupiter's net torque (acting on the V-E tidal bulge) is zero (i.e. it changes direction with respect the Sun's rotation axis) [6], [7].

• If you consider the torque of Jupiter upon the V-E tidal bulge at each inferior and superior conjunction of Venus and Earth (rather than their consecutive sum = net torque), the actual magnitude of Jupiter's torque is greatest at the times that are at or near solar minimum. Even though Jupiter's torque are a maximum at these times, the consecutive torques at the inferior and superior conjunctions of Venus and the Earth almost exactly cancel each other out.

• Remarkably, if the first minimum of Solar Cycle 25 occurs in 2021 ± 2 years, it will indicate a re-synchronization of the solar minima with a VEJ cycle length of 11.07 +/- 0.05 years over a 410 year period [6].

• On these two occasions where the synchronization was disrupted (i.e. minima prior to the onset of cycle 4 (1784.7) and Cycle 23 (1996.5), the timing of the sunspot minimum quickly re-synchronizes with the timing of the minimum  change in Jupiter's tangential force acting upon Venus-Earth tidal bulge [6].

•  If the time frame is extended back to 1610, then the four occasions where the synchronization is significantly disrupted  closely correspond to the four major changes in the level of solar activity over the last 410 years i.e. the minima prior to the onset of cycle -11 (1618/19), marking the start of the Maunder Minimum, the minimum prior to cycle -4 (1698), marking the end of the Maunder Minimum or the restart of the solar sunspot cycle after a 60 year hiatus, the minimum prior to cycle 4 (1784.7), marking the onset of the Dalton Minimum and minimum prior to cycle 23 (1996.5), marking the onset of the upcoming Landscheidt Minimum [7].

•  The main factors that influence the level of tidal torquing of Jupiter, Venus and the Earth upon the outer layers of the Sun are the 3.3 degree tilt in the heliocentric latitude of Venus' orbit and the mean distance of Jupiter from the Sun. At times when the tidal torquing of Jupiter, Venus and the Earth reach its 11 year maximum, the long-term tidal-torquing is weakest when Venus is at its greatest positive (most northerly) heliocentric latitude and Jupiter is at its greatest distance from the Sun (≈ 5.44 A.U) [4].

• Since 1000 A.D., every time the long-term peak planetary tidal torquing forces are at their weakest there has been a period of low solar activity know as a Grand Solar minimum [4]. 

• The one exception to this rule, was a period of weak planetary tidal peaks centered on 1150 A.D. that spanned the first half of the Medieval Maximum from 1090−1180 A.D. The reason for this discrepancy is unknown, although it could be explained if there was another countervailing factor present during this period that was working against the planetary tidal effects [4].

• The VEJ Tidal-Torquing Model has natural periodicities that match the ~ 90 year Gleissberg Cycle, the ~ 208 year de Vries Cycle, and the ~ 2300 Hallstatt Cycle [1].

References

[1] http://astroclimateconnection.blogspot.com.au/2012/03/planetary-spin-orbit-coupling-model-for.html

[2] http://astroclimateconnection.blogspot.com.au/2012/11/v-e-j-tidal-torquing-model.html

[3] http://astroclimateconnection.blogspot.com.au/2012/03/short-comings-of-planetary-spin-orbit.html

[4]  Ian R. G. Wilson, Do Periodic Peaks in the Planetary Tidal Forces Acting Upon the Sun Influence the Sunspot Cycle? The General Science Journal, 2010. 

      http://www.wbabin.net/Science-Journals/Research%20Papers-Astrophysics/Download/3812

[5] Wilson, I.R.G., Carter, B.D., and Waite, I.A., Does a Spin-Orbit Coupling Between the Sun and the Jovian Planets Govern the Solar Cycle?, 

      Publications of the Astronomical Society of Australia,  2008, 25, 85 – 93.

      http://www.publish.csiro.au/paper/AS06018.htm

[6] http://astroclimateconnection.blogspot.com.au/2012/04/why-does-solar-cycle-keep-re.html

[7] http://astroclimateconnection.blogspot.com.au/2012/04/v-e-j-tidal-torquing-model-maunder.html

Why the VEJ Tidal-Torquing Model?

If you are unfamiliar with the Tidal-Torquing Model go to: 

http://astroclimateconnection.blogspot.com.au/2012/03/planetary-spin-orbit-coupling-model-for.html

Set out below is a general description of the evolution of my ideas on the topic of planetary  motion and Solar activity over the last eight years. 

Note: If you are kind enough to read the following in full you, might want to do so in light of the fact that at every revelation, twist and turn along my journey of discovery, I found that there were others before me who had independently come to the same or similar realizations and/or conclusions.

and SIM = Solar Intertial Motion 

THE EARLY YEARS – Linking SIM and Solar Activity [2005 - 2007]

In 2005-6, when I first started this research, I believed that solar activity was (somehow) being modulated/influenced by the Sun’s SIM (i.e. Barycentric) motion. Since, the Sun’s Barycentric motion is primary controlled by the Jovian planets (dominated by Jupiter and Saturn), I argued that there was a link between the orbital motion of the Sun about the Barycentre (represented by the moment-arm of Jupiter upon the Sun as it moved about the Barycentre) and the rotation rate of the outer layers of the Sun. We called this link a SPIN-ORBIT COUPLING because it appeared that the rotation rate of the surface layers of the Sun [i.e. the SPIN] was linked the orbital motion of the Sun about the Barycentre [i.e the ORBIT]. Unfortunately we could not provide a valid physical mechanism to explain this link. All we had was an observational link [see figure 8 of the paper cited directly below] however this was strong enough for our paper to get through peer-review, after a messy two year battle with the editors of three different journals.

Wilson, I.R.G., Carter, B.D., and Waite, I.A., Does a Spin-Orbit Coupling Between the Sun and the Jovian Planets Govern the Solar Cycle?, Publications of the Astronomical Society of Australia, 2008, 25, 85 – 93.

http://www.publish.csiro.au/paper/AS06018.htm

http://eprints.usq.edu.au/4795/

ITS HAS GOT TO BE THE TIDES [2008 - 2010]

It soon became apparent to me (around 2008) that there was no viable physical mechanism to directly link SIM with changes in the level of solar activity. Einsteins Principle of Equivalence had to be violated if there was such a connection.

However, I still firmly believed that there must be a connection between the motion of the planets and the level of solar activity. This meant that it must have something to do with the planetary tides – even if their weakness made them an unlikely candidate.

http://astroclimateconnection.blogspot.com.au/2010/05/mechanism-for-amplifying-planetary.html

This created a dilemma. The strongest planetary tides acting upon the Sun were those of Jupiter, Venus and the Earth, while the dominant direct gravitational influence on the Sun’s SIM was that produced by Jupiter and Saturn.

Given that I knew that there was an observation link between the rotation rate of the surface layers of the Sun and the SIM of the Sun, and the fact that I believed that it was the changes in solar rotation that were moderating the level of solar activity – I could come to only one conclusion.

The tidal forces of the planets [i.e. Jupiter, Venus, and/or Earth] which were most likely responsible for the changes in the Sun’s rotation rate via tidal torquing had to be somehow linked with the gravitational forces that were producing the Sun’s SIM [i.e. Jupiter and Saturn].

This is when I discovered that the synodic and orbital periods of the Terrestrial and Jovian planets were link through a remarkable series of near resonances. [Note: while the discovery was made independently, there were others who had already gone down this path]:

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation Rate Externally Driven and Do They Affect Climate? The General Science Journal, Dec 2011, 3811. [first published in 2010]
http://gsjournal.net/Science-Journals/Essays/View/3811

To me, this explained the APPARENT link between the Sun’s orbital motion about the Barycentre (i.e SIM) and it’s equatorial rotation rate. The train of logic went something like this:

Orbital Periods of Jovian Planets —> SIM

Orbital Periods of Jovian Planets —-> Orbital Periods of Terrestrial Planets —> Solar Tides —> Tidal Torquing —> Equatorial Solar Rotation Rate —> Level of Solar Activity

I published this idea in:

Wilson, I.R.G., 2011, Do Periodic peaks in the Planetary Tidal Forces Acting Upon the Sun Influence the Sunspot Cycle? The General Science Journal, Dec 2011, 3812. [first published in 2010]
http://gsjournal.net/Science-Journals/Essays/View/3812

Although I did not fully appreciate the role that tidal-torquing played in this model, preferring to believe that it was peaks in the strength of the planetary tides caused by alignments between Jupiter, Venus and the Earth that were responsible for modulating solar activity.

THE VEJ TIDAL-TORQUING MODEL [2011-2013]

Some time in 2011, I finally realized that in order to produce large enough changes in the rotation rate of the outer (equatorial) layers of the Sun, you need to have the strongest gravitational force acting upon the Sun [i.e. Jupiter] acting upon the biggest possible tidal bulge that could be produced by the remaining planets [i.e. alignments of Venus and the Earth].

This slowing down and speeding up of the outer layers of the Sun could only be accomplished by a TIDAL-TORQUING mechanism similar to the mechanism by which the Moon slowed down the Earth’s Rotation through its GRAVITATIONAL action upon the Earth’s oceans via the TIDAL BULGES.

However, in the case of the Sun, Jupiter provides the GRAVITATIONAL FORCE that slows and speeds up the Sun’s rotation rate, while alignments of VENUS and EARTH produced the tidal bulges.

This VEJ TIDAL-TORQUING MODEL slightly modified the train of logic so that it became:

Orbital Periods of Jovian Planets —> SIM

Orbital Periods of Jovian Planets (Primarily Jupiter) —-> Orbital Periods of Terrestrial Planets (Primarily Venus and Earth) —> Solar Tides in the base of the Convective Zone of the Sun near the Tachocline —> Tidal Torquing (via the VEJ TIDAL TORQUING MODEL) —> Equatorial Solar Rotation Rate —> Level of Solar Activity

So, from about 2008, on-wards, I have been arguing that the connection between SIM and solar activity is an ILLUSION.

It wasn’t until 2011, that I finally realized that this ILLUSION was created by the logic train cited directly above.

Hence, it is important that a context or model is developed to show how the gravitational and tidal forces of planets act upon the Sun to influence the general level of solar activity. 

I believe that I have provided one possible MODEL which does just that:

The VEJ TIDAL-TORQUING MODEL

Do you think that Moon might have something to do with the onset of El Ninos?

Update: 18/02/2013

And could this connection be the result of the fact that if you plot the rate of change of the Earth's Length of Day (LOD) [with the atmospheric component removed] against time [starting in 1962] you find that there is a ~ 6 year periodicity that is phase-locked with the 6 year period that it takes the lunar line-of-nodes aligns to re-align with the lunar line-of-apse.?

[Note that in this case the line-of-nodes and line-of-apse are just re-aligning with each other. They do not necessarily realign with the Sun]

 

Scientific Publications & Presentations

                         UPDATED 16/04/2013

The following is a list of my recent scientific publications
and presentations. I am placing the list on my blog so that
others can have easy access.

2006

Wilson, I. R. G., 2006, Possible Evidence of the 

De Vries, Gleissberg and Hale Cycles in the Sun’s 

Barycentric Motion, Australian Institute of Physics 17^th

National Congress 2006, Brisbane, 3^rd -8^th December 

2006 (No longer available on the web)

2008

Wilson, I.R.G., Carter, B.D., and Waite, I.A., 2008, 

Does a Spin-Orbit Coupling Between the Sun and the 

Jovian Planets Govern the Solar Cycle?,
Publications of the Astronomical Society of Australia, 

2008, 25, 85 – 93.

http://www.publish.csiro.au/paper/AS06018.htm

http://eprints.usq.edu.au/4795/

  

N.S. Sidorenkov, Ian Wilson. The decadal fluctuations 

in the Earth’s rotation and in the climate characteristics. 

In: Proceedings of the "Journees 2008 Systemes de reference 

spatio-temporels", M. Soffel and N. Capitaine (eds.), 

Lohrmann-Observatorium and Observatoire de Paris. 

2009, pp. 174-177 

  

http://syrte.obspm.fr/jsr/journees2008/ProcJournees2008.pdf

http://syrte.obspm.fr/jsr/journees2008/Sidorenkov.pdf

Which Came First? - The Chicken or the Egg?

A Presentation to the 2008 Annual General Meeting of the
Lavoisier Society by Ian Wilson

http://www.lavoisier.com.au/articles/greenhouse-science/solar-cycles/IanwilsonForum2008.pdf

2009

Wilson, Ian R.G., 2009, Can We Predict the Next Indian 

Mega-Famine?, Energy and Environment, Vol 20, 

Numbers 1-2, pp. 11-24.

http://multi-science.metapress.com/content/a15v07801838k763/

El Ninos and Extreme Proxigean Spring Tides

A lecture by Ian Wilson at the Natural Climate Change
Symposium in Melbourne on June 17th 2009.

http://www.naturalclimatechange.info/?q=node/10

2010

N. Sidorenkov, I.R.G. Wilson and A.I. Kchlystov, 2009, The 

decadal variations in the geophysical processes and the 

asymmetries in the solar motion about the barycentre. 

Geophysical Research Abstracts Vol. 12, EGU2010-9559, 

2010. EGU General Assembly 2010 © Author(s) 2010

http://meetingorganizer.copernicus.org/EGU2010/EGU2010-9559.pdf

2011

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation 

Rate Externally Driven and Do They Affect Climate? 

The General Science Journal, Dec 2011, 3811.

http://gsjournal.net/Science-Journals/Essays/View/3811

Wilson, I.R.G., 2011, Do Periodic peaks in the Planetary Tidal 
Forces Acting Upon the Sun Influence the Sunspot Cycle? 
The General Science Journal, Dec 2011, 3812.

http://gsjournal.net/Science-Journals/Essays/View/3812

[Note: This paper was actually written by October-November 2007 and submitted to the New Astronomy (peer-reviewed) Journal in early 2008 where it was rejected for publication. It was resubmitted to the (peer-reviewed) PASP Journal in 2009 where it was rejected again. It was eventually published in the (non-peer reviewed) General Science Journal in 2010.]

2012

Wilson, I.R.G., Lunar Tides and the Long-Term Variation 

of the Peak Latitude Anomaly of the Summer Sub-Tropical 

High Pressure Ridge over Eastern Australia

The Open Atmospheric Science Journal, 2012, 6, 49-60

http://www.benthamscience.com/open/toascj/articles/V006/49TOASCJ.pdf

Wilson, I.R.G., Changes in the Earth's Rotation in relation 

to the Barycenter and climatic effect.  Recent Global Changes 

of the Natural Environment. Vol. 3, Factors of Recent 

Global Changes. – M.: Scientific World, 2012. – 78 p. [In Russian].

This paper is the Russian translation of my 2011 paper
Are Changes in the Earth’s Rotation Rate Externally 
Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811. 

V-E-J Tidal-Torquing Model

See the bottom of this post for essential background 
reading if you knowledge of the formulation and 
evolution of the V-E_J Tidal-Torquing Model is 
not up-to-date :


THE UPDATED V-E-J TIDAL TORQUING MODEL

The problem with the collective blog postings about the 

Spin-Orbit Coupling or Tidal-Torquing Model that are described 

at the end of this post is that they only look at the tidal-torquing 
(i.e. the pushing and pulling of Jupiter upon the Venus-Earth 
tidal bulge in the Solar convective zone) when Venus and Earth 
are inferior conjunction (i.e. when Venus and Earth are on the 
same side of the Sun). However, a tidal bulge is also produced  

when Venus and the Earth align on opposites sides of the Sun, 

as well (i.e  at superior conjunction).

This means that in the real world, tidal bulges are induced in 

the convective layer of the Sun once every 0.8 years rather 
than every 1.6 years, as assumed in the original basic model. 

This is achieved by a sequence of alternating conjunctions 

of Venus and the Earth:

IC --> SC --> IC --> SC --> IC --> etc.. 

[where IC = Inferior conjunction & SC = Superior conjunction]  

Unfortunately, logic tells you the gravitational pushing/pulling 

of Jupiter on the V-E tidal bulge at a given inferior conjunction 

will be roughly equal opposite to the pushing/pulling that occurs

at the next superior conjunction. At first glance, this would seem 

to destroy any chance for the gravitational force of Jupiter (acting 

on the V-E tidal bulge) to produce any nett spin in the outer 

convective layers of the Sun. However, it turns out that the 

gravitational tugging of Jupiter at inferior V-E conjunction is

not completely cancelled by the tugging at the next superior 

V-E conjunction. This lack of cancellation is primarily related 

to the changing orientation and tilts of the respective orbits 

of Venus and Jupiter.

The diagram immediately below shows sunspot number 

(SSN) for solar cycles 0 through  to 9. Plotted below the

sunspot number curve in this figure is the net tangential torque

of Jupiter acting the V-E tidal bulge, where Jupiter's tangential 

torque at one V-E inferior conjunction is added to Jupiter's

 tangential torque at the next V-E superior conjunction to 

get the nett tangential torque. In this diagram, a positive 

nett torque means that the rotational speed of the Sun's

equatorial convective layer is sped-up and a negative 

nett torque means that the equatorial convective layer 

is slowed-down.

[N.B. The nett torque curve has been smoother with a 

5th and 7th order binomial filter to isolate low frequency 

changes]       

  

Some important things to note are:

a) The nett torque of Jupiter acting on the V-E tidal bulge
     has a natural 22 year peridocity which matches the 22
     year hale (magnetic) cycle of solar activity.

b) the equatorial convective layers of the Sun are sped-up
    during ODD solar cycles and slowed-down during EVEN
    solar cycles.


These two points provide a logical explanation for the
Gnevyshev−Ohl (G−O) Rule for the Sun.

This rule states that if you sum up the mean annual Wolf
sunspot number over an 11 year solar cycle, you find
that the sum for a given even numbered sunspot cycle is
usually less than that for the following odd numbered
sunspot cycle (Gnevyshev and Ohl 1948). The physical
significance of the G−O rule is that the fundamental activity
cycle of the Sun is the 22 year magnetic Hale cycle, which
consists of two 11 year Schwabe cycles, the first of
which is an even number cycle (Obridko 1995). While
this empirical rule generally holds, there are occasional
exceptions such as cycle 23 which was noticeably weaker
than cycle 22.


These two points are also in agreement with the results of
Wilson et al. 2008.


Does a Spin–Orbit Coupling Between the Sun and the Jovian Planets Govern the Solar Cycle? 

I. R. G. Wilson, B. D. Carter, and I. A. Waite

Publications of the Astronomical Society of 

Australia, 2008, 25, 85–93.

Figure 8 from Wilson et al. 2008 (above) shows the moment arm
of the torque for the quadrature Jupiter and Saturn nearest the
maximum for a given solar cycle, plotted against the change in the
average equatorial (spin) angular velocity of the Sun since the previous
solar cycle (measured in μrad s−1). The equatorial (≤±15 deg)
angular velocities published by Javaraiah (2003) for cycles
12 to 23 have been used to determine the changes in the
Sun’s angular velocity (since the previous cycle) for cycles
13 to 23.


What this graph clearly shows is that the Sun's equatorial
angular velocity increases in ODD solar cycles and decreases
in EVEN solar cycles, in agreement with the V-E-J
Tidal-Torquing model.

c) The 11 year solar sunspot cycle cycle constantly tries to
    synchronize itself with the Jupiter's nett tidal torque.

The original figure plotted at the top of this blog post is
reproduced here with superimpose blue and red vertical
lines showing the times where the Jupiter's nett torque
(acting on the V-E tidal bulge) changes sign (i.e. direction
with respect the axis of the Sun's rotation). The points
of sign change in Jupter's nett torque that occur just
before solar sunspot minimum are marked by blue lines
while the points that occur after solar minimum are
marked by red lines. The figure below shows that

i) Normally their is a phase-lock between the time of sign
    change in Jupiter's torque and solar minimum.

ii) As soon as this phase-lock is broken (i.e. around about 1777)
    22 years later (i.e. one Hale cycle) after the loss of lock, there is
     a collapse in the strength of the solar sunspot cycle.

The graph below shows if you plot the torque of Jupiter upon
the V-E tidal bulge at each inferior and superior conjunction of
Venus and Earth (rather than their consecutive sum), the actual
magnitude of Jupiter's torque is greatest at the times that are at
or near solar minimum. However, even though Jupiter's torque
are a maximum at these times, the consecutive torques at the
inferior and superior conjunctions of Venus and the Earth almost
exactly cancel each other out.

It is interesting to speculate whether the rapid fluctuations at
times when Jupiter's torque is strongest could explain why the
solar magnetic cycle is driven to synchronize with the Jupiter's
tidal torquing force.

References:

1. Gnevyshev, M. N. and Ohl, A. I., 1948, Astron. Zh., 25, 18
2. Obridko, V.N., 1995, Solar Phys., 156, 179
3. Javaraiah, J., 2003, SoPh, 212, 23
4. Wilson I.R.G, Carter B.D, and Waite I.A., 2008, 

     Publications of the Astronomical Society of 

     Australia, 25, 85–93.

5. Wilson, I. R. G., 2010, General Science Journal
    http://www.gsjournal.net/h/papers_view.php?id=3812


Essential background reading if you knowledge of
the evolution of this model is not up-to-date :

Does a Spin–Orbit Coupling Between the Sun and the Jovian Planets Govern the Solar Cycle?

I. R. G. Wilson, B. D. Carter, and I. A. Waite

Publications of the Astronomical Society of 

Australia, 2008, 25, 85–93.

Do Periodic Peaks in the Planetary Tidal Forces Acting Upon the Sun Influence the Sunspot Cycle?

I.R.G. Wilson

A free download of the paper is available in the General 

Science Journal were it was published in 2010 

Two blog entries that give a basic explanation of the 

V-E-J Tidal-Torquing Model

A Planetary Spin-Orbit Coupling Model for Solar Activity

Shortcomings of the Planetary Spin-Orbit Coupling Model

Six blog entries that investigate the properties of the  

V-E-J Tidal-Torquing Model

A mechanism for amplifying planetary tidal forces in the Sun's outer convective zone

The V-E-J Tidal Torquing Model & Solar Maxima

The V-E-J Tidal Torquing Model & The Maunder Minimum

Why does the solar cycle keep re-synchronizing itself with the gravitational force of Jupiter that is tangentially pushing and pulling upon the Venus-Earth tidal bulge in the Sun's convective layer?

Recent grand minima in solar activity and the orbits of Venus and Jupiter

Why are the even and odd sunspot cycle maxima synchronized with the position angle of Jupiter at the time of Earth-Venus alignments?