The reader should be familiar with the contents of the

following paper before continuing with this post:

Wilson I.R.G.,

*The Venus–Earth–Jupiter spin–orbit *
*coupling model, *Pattern Recogn. Phys., 1, 147–158,

2013

which can be freely downloaded at:

http://www.pattern-recogn-phys.net/1/147/2013/prp-1-147-2013.html
In this paper, Wilson (2013) constructs a Venus–Earth

–Jupiter spin–orbit coupling model from a combination

of the Venus–Earth–Jupiter tidal-torquing model and

the gear effect. The new model produces net tangential

torques that act upon the outer convective layers of the

Sun with periodicities that match many of the long-term

cycles that are found in the 10Be and 14C proxy records

of solar activity.

**Wilson (2013) showed that there are at least two **
**ways ****that the Jovian and Terrestrial planets can **
**influence bulk ****motions in the convective layers **
**of the Sun. **
**The first is via the VEJ tidal-torquing process:**
– Tidal bulges are formed at the base of the convective

layers of the Sun by the periodical alignments of Venus

and the Earth.

– Jupiter applies a tangential gravitational torque to these

tidal bulges that either speed-up or slow-down parts of

the convective layer of the Sun.

– Jupiter’s net tangential torque increases the rotation rate

of the convective layers of the Sun for 11.07 yr (seven

Venus–Earth alignments lasting 11.19 yr) and then

decreases the rotation rate over the next 11.07 yr.

– The model produces periodic changes in rotation rate

of the convective layers of the Sun that result a 22.14 yr

(Hale-like) modulation of the solar activity cycle ( 14

Venus–Earth alignments lasting 22.38 yr).

– There is a long-term modulation of the net torque that

is equal to the mean time required for the 11.8622 yr

periodic change in Jupiter’s distance from the Sun to

realign with the 11.0683 yr tidal-torquing cycle of the

VEJ model.

**The second way is via modulation of the VEJ **
**tidal-torquing ****process via the gear effect:**
The gear effect modulates the changes in rotation rate of

the outer convective layers of the Sun that are being

driven by the VEJ tidal-torquing effect.

– This modulation is greatest whenever Saturn is in

quadrature with Jupiter. These periodic changes in the

modulation of the rotation rate vary over a 19.859 yr

period.

– The gear effect is most effective at the times when Venus

and the Earth are aligned on the same side of the Sun.

– There is a long-term modulation of the net torque that

has a period of 192.98 yr.

Note: The sidereal orbital periods used in this post are

those provided by:

http://nssdc.gsfc.nasa.gov/planetary/planetfact.html
= sidereal orbital period of Venus = 0.615187(1) yrs

= sidereal orbital period of the Earth = 1.000000 yrs

= sidereal orbital period of Jupiter = 11.8617755(6) yrs

= sidereal orbital period of Saturn = 29.45663 yrs

= synodic period of Venus/Earth = 1.59866(5) yrs

= synodic period Jupiter/Saturn = 19.8585(3) yrs

**The Physical Meaning for each of the ****Periodicities**
**The 22.136 Year Period of the VEJ Tidal-Torquing Model **

This is the time over which the angle between the nearest

VE tidal bulge (formed in the convective layers of the Sun)

and Jupiter moves from 0 to 180 degrees

Jupiter's net tangential torque increases the rotation rate of

the Sun's convective layers for the first 11.068 years and

then decreases the rotation rate for the remaining 11.068

years.

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 × 11.068 yr = 22.137 yr. This is essentially equal

to the mean length of the Hale magnetic sunspot cycle of

the Sun, which is 22.1 ± 2.0 yr (Wilson, 2011).

The 22.136 year period is simply half the realignment

time between Venus, the Earth and Jupiter (= 44.272

years) and it can be represented by the equation:

(Paul Vaughan - private communications).

**The 165.42 year Modulation Period of the**
**Net Tangential Torque of Jupiter **

The 11.068 year period in the net tangential torque of

Jupiter acting upon the base of the Sun's convective

layer is modulated by the 11.862 year variation in the

mean distance of Jupiter from the Sun. This produces

a 165.42 year modulation in Jupiter's peak net tangential

torque given by:

**The 193.02 year Modulation Period of the Gear Effect**
The is the time required for the 22.137 yr periodicity of the

net tangential torque of Jupiter associated with the VEJ

Tidal-Torquing model to re-align with the 19.859 yr period

associated with the gear effect:

which can also be written as;

linking this modulation cycle to a multiple of the

period of time required for the planets Venus, the Earth,

Jupiter and Saturn to re-synchronize their orbits.

**The 88 Year Gleissberg Cycle**

The 88 year Gleissberg Cycle is a well identified

long-term periodicity that is seen in the level of solar

activity. The following equation shows that is merely

the synodic beat period between half the synodic

period of Jupiter/Saturn (= 9.9293 yrs) and seven

time the synodic period of Venus/Earth = 11.191 yrs.

Half the synodic period of Jupiter/Saturn is the time

between successive quadratures of Jupiter and Saturn

which is the main periodicity of the gear effect, while

seven times the synodic period of Venus/Earth

is the periodicity of the link between the VEJ

tidal-torquing model and the gear effect.

Of course, multiples of the Gleissberg period

correspond to long-term periodicities that were found

by McCracken et al. [2012]:

1 x 88.09 = 88.09 yrs --> 87.3 ± 0.4 yrs

4 x 88.09 = 352.36 yrs --> 350 ± 0.7 yrs

6 x 88.09 = 528.54 yrs --> 510 ± 15 yrs

8 x 88.09 = 704.72 yrs --> 708 ± 28 yrs

**7 x 165.42 yrs = 6 x 193.02 yrs ≈ 1158 yrs**
The following formula are direct consequence of

the above commensurablity:

The last equation links the orbital periods Venus and

the Earth to those of Jupiter and Saturn.