Saturday, March 17, 2012

A Planetary Spin-Orbit Coupling Model for Solar Activity

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

A free download of the paper is available in the General 
Science Journal were it was published in 2010 

The General Science Journal paper (above) was written in 
order to further investigate the main conclusion of the Wilson 
et al. (2008) paper that the Sun's level of solar activity is 
driven by a spin-orbit coupling mechanism between the Sun 
and the Jovian planets:  

Publications of the Astronomical Society of Australia, 2008, 
25, 85–93.
Does a Spin–Orbit Coupling Between the Sun and 
the Jovian Planets Govern the Solar Cycle?

The spin-orbit coupling mechanism investigated in the 
General Science Journal paper is based on the idea that the 
planet that applies the most dominant gravitational force upon 
the Sun is Jupiter, and that after Jupiter, the planets that apply 
the most dominant tidal forces upon the Sun are Venus and 
the Earth.

The spin-orbit coupling mechanism is based upon the idea that 
periodic alignments of Venus and the Earth (once every 1.5993 
years) produce temporary tidal bulges along the Earth-Venus
-Sun line, on opposite sides of the Sun. When these temporary
tidal bulges occur, Jupiter's gravitational force tugs on these 
bulges and either slows down or speeds up the Sun's rotation.

What makes this particular spin-orbit coupling mechanism
intriguing, is the time period over which the Jupiter's
gravitational pull speeds up and slows down the Sun rotation 
as Jupiter tugs on the tidal bulges.

[N.B. In the above diagram the planets are revolving in a
clock-wise direction and the Sun is rotating in a clock-wise
direction. Also, when near-side and far-side tidal bulges on
the Sun's surface are referred to, it is with respect to the
aligned planets Earth and Venus.]

The diagram above shows Jupiter, Earth and Venus initially 
aligned on the same side of the Sun (position 0). In this 
configuration, Jupiter does not apply any lateral torque upon 
the tidal bulges (The position of the near side bulge is shown by 
the black 0 just above the Sun's surface).  

1.5993 years later, each of the planets move to their respective
position 1's. At this time, Jupiter has moved 13.000 degree 
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 Sun's rotation rate. 

After a second 1.5993 years, each of the planets move to 
their respective position 2's. Now, Jupiter has moved 26.00 
degrees 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 13.000 degrees 
further ahead of the alternating near and far-side tidal bulges, 
every 1.5993 years. Eventually, Jupiter will get 90 degrees 
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, the Jupiter's movement of 13.000 degrees per 
1.5993 years with respect to closest tidal bulge, means that 
Jupiter will get 90 degrees ahead of the closest tidal bulge in 
11.07 years. This is almost the same amount of time as to 
mean length of the Schwabe Sunspot cycle (11.1 +/- 1.2 years).

In addition, for the next 11.07 years, Jupiter will start to lag 
behind the closest tidal bulge by 13.000 degrees every 
1.5993 years, and so its gravitational force will pull on the 
tidal bulges in such a way as to slow the Sun's rotation rate 

All together there will be four periods of 11.07 years, with 
the gravitational force of Jupiter, increasing the Sun's rotation 
rate over the first and third periods of 11.07 years, and 
decreasing the Sun's rotation rate over the second and fourth 
periods of 11.07 years.

Hence, the basic unit of change in the Sun's rotation rate (i.e. 
and 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)

However, the complete planetary tidal cycle is actually 
(4 x11.07 years =) 44.28 years.   
Now the outer Jovian planets act like a large washing 
machine, stirring the inner terrestrial planets with a 
gravitational force that varies with a frequency that is the 
beat period between two main competing Jovian planetary 

The first is that produced by the the retrograde tri-synodic 
period of Jupiter/Saturn ( = 59.577 yrs) and the second is 
the pro-grade synodic period of Uranus/Neptune (171.41 yrs):

(59.577 x 171.41) / (171.41 + 59.577) = 44.21 yrs

[N.B. This calculation assumes the following sidereal 
orbital period for the Jovian planets: Jupiter = 11.862 yrs; 
Saturn = 29.457 yrs; Uranus = 84.011 yrs; Neptune 
= 164.79 yrs.

In addition, there is a remarkable near-resonance condition 
that exists between the orbital motions of the three largest 
terrestrial planets with:

4 x SVE = 6.3946 years  SVE = synodic period of Venus and Earth
3 x SEM = 6.4059 years SEM = synodic period of Earth and Mars
7 x SVM = 6.3995 years SVM = synodic period of Venus and Mars
28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs 

This means that these three planets return to the same 
relative orbital configuration once every 6.40 years, and 
that exactly 7.0 times this re-alignment period is 44.8 years, 
close to the 44.2 - 44.3 year period cited above for the 
gravitational forcing of the Jovian planets upon the terrestrial 

Further evidence for a link between the re-alignment period 
of the three largest Terrestrial planets and the period of Jupiter 
comes from the fact that: 

69 × SVJ = 44.770 yrs        SVJ = synodic period of Venus & Jupiter
41 × SEJ = 44.774 yrs         SEJ = synodic period of Earth & Jupiter
20 × SMJ = 44.704 yrs            S = synodic period of Mars & Jupiter

This means that Venus, Earth and Jupiter, in particular, form 
alignments at sub-multiples of Jose cycle 178.72 years i.e.

½ × 178.72 yrs = 89.36 yrs 
¼ × 178.72 yrs = 44.68 yrs
1/8 × 178.72 yrs = 22.34 yrs 
1/16 × 178.72 yrs = 11.17 yrs

These alignments only change slowly over hundreds of 
years and they closely match the well known Schwabe 
(~ 11.1 yrs), Hale (~ 22.2 yrs) and Gleissberg (~ 90 years) 
solar cycles.


It would appear that a simple spin-orbit coupling mechanism
proposed in this posting would naturally produce a  link
between systematic changes in the rotation rate of the Sun 
that would be synchronized with the Bary-centric motion of 
the Sun about the centre-of-mass of the Solar System as 
suggested by Wilson et al. (2008). 

APPENDIX - Some additional matches between the
planetary orbital cycles and the long term periodicities
that are observed in the level of Solar activity.


V = 224.70069 days E = 365.356363 days 
=>  VE = 583.920628  VE = 1.59866 years
J = 11.862 years S = 29.457 years; 
JS = 19.9590; 5 x VE = 7.993298 years

Hale cycle (22.1 years)

There is an 8:9 resonance between the Hale and JS cycles

178.73 x 19.859/ (178.73 – 19.859) = 22.341
178.73 = 9 x 19.859
178.73 = 8 x 22.341

Gleissberg Cycle (~ 90 years)

Hale cycle drifts out of phase with the JS cycle by ½ of 
JS cycle

4 x Hale = 4 x 22.341 = 89.364 yrs
4 ½ JS = 4 ½ x 19.859 = 89.366 yrs

DeVries Cycle (208 years)

This period is still a bit of a mystery but it is interesting to 
note that:
26 x PVE =  26 x 7.993 yrs = 207.826 yrs
10 1/2 JS =  208.509 yrs
3 1/2 TJS = 208.509 yrs

PVE = Penta-Synodic periods of Venus and the Earth
JS = Synodic period of Jupiter/Saturn
TJS = Tri-Synodic period of Jupiter/Saturn = 59.574 yrs 

Hallstatt Cycle (~ 2320 years)

A grand alignment of the Jovian planets (Jupiter, Saturn, 
Uranus, Neptune), with all of the planets arranged in a 
line on the same side of the Sun, occurs roughly every 
4628 year. 

This 26 x 178 years (Jose cycle) = 4628 years.

Half this realignment period is 2314 years which is close
to the long term solar cycle called the Hallstatt cycle.


  1. Edit note: "Some additional matches {to between} planetary orbital cycles..."
    {pick one}

    I note that you don't even mention Mars in your gravitational and tidal charts. Is it trivial, or irrelevant?

  2. Brian,

    I have made the correction that you have suggested.

    The tidal influences of Mars upon the Sun are considerably less than those of Venus, Earth and Mercury. This is because the tidal influences vary as the Mass divided by the cube of the distance from the Sun.