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 

http://www.wbabin.net/Science-Journals/Essays/View/3812

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?

http://www.publish.csiro.au/?act=view_file&file_id=AS06018.pdf

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 

down.

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 

alignments.

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.

http://nssdc.gsfc.nasa.gov/planetary/]

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 

planets.

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.

CONCLUDING REMARKS

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.

DATA VALUES USED  

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.

cycle