sun spots occur in a regular pattern of minima and maxima. They travel from left to right as seen from Earth, or Eastwards. The sun is spinning on its axis.

Here is one representation of 400 years of records, courtesy of WP. http://en.wikipedia.org/wiki/File:Sunspot_Numbers.png

Jupiter exerts the largest force on the sun.

The gravity force is given by Newton's equation G.M.m/R2

R here is the orbit radius.

G is 6.67 x 10 -11 m3/kg/s2

the mass of the sun is about 2 x 10 30 kg.

planets with m/R2 calculated. units kg/km2 x 10 7

M/R2 orbit days

Mercury 9.8 88

Venus 40 225

Earth 27 365

Mars 1.2 687

Jupiter 310 4333

Saturn 28 10759

Uranus 1 36685

Neptune <1 60189

The Jupiter force is about 4.2 x 10 23 Newtons

Force = acceleration x mass

So the Sun accelerates toward Jupiter all the time at a rate of 2.1 x 10-7 m/s2.

We also know that the centripetal force = wR'2

R' is the instantaneous orbit radius.

and the Sun's rate of rotation must be close to Jupiter's rate, which is 17x 10-9 rads/s

'

solving for R', the instantaneous centre of rotation due to Jupiter is 7.3 x 108 m from the sun centre.

Except that actually it is varying all the time.

Jupiter's orbit is eccentric ranging or changing by +- 75 million kilometres, about ten per cent!

The maximum and minimum values of the M/R2 term due to Jupiter's eccentricity is thus about +- 20%. Greatest at the perihelion, the closest approach to the sun.

Therefore due to Jupiter alone the orbit centre of the sun varies from just inside to just outside the sun radius R.

The jupiter perihelion occurred in the years (to one decimal point):

1703.2, 1714.9, 1726.7, 1738.6, 1750.5, 1762.3, 1774.2, 1786.0, 1797.9, 1809.8, 1821.6, 1833.5, 1845.3, 1857.2, 1869.1, 1880.9, 1892.8, 1904.6, 1916.5, 1928.4, 1940.2, 1952.1, 1963.9, 1975.8, 1987.6, 1999,5, 2011.4.

Sun spot minima occurred in the years:

1714, 1725, 1734, 1748, 1757, 1777, 1786, 1798, 1824, 1835, 1845, 1857, 1868, 1878 to 1881, 1901, 1914, 1925, 1936, 1945, 1955, 1966, 1972, 1988, 1998, 2008.

Counting from 1714 to 1999 there are 25 minima and 25 perihelions of Jupiter.

There are deviations from an exact match. There is a lesser effect from Saturn, Venus and the Earth. Saturn takes a long time coming into alignment with Jupiter every 19.8 years. Earth and Venus will line up within about a year each time.

The Saturn conjunction years are:

1707.6, 1727.4, 1767.1, 1787.0, 1806.9, 1826.7, 1846.6, 1866.4, 1886.3, 1906.1, 1926.0, 1945.9, 1965.7, 1985.6, 2005.4.

I venture to suggest that when Satrun is lined up there is a suppression of sunspot numbers and it periods where it is opposed, as in most of the 20th C, the sunspot numbers are higher.

The causal relationship: we now believe that the sun has a central core of very hot and dense plasma. Sometimes two protons combine to make a helium nucleus. Energy radiates outwards getting cooler until there is a change where the outer layer becomes opaque and convection starts at a transition called the tachocline.

The sun bathes the Earth in about 1.2 Kw/m2. So its total output is about 3.4 x 10 23 kW

or at its visible surface, (about 6 x 10 18 m2) about 55 MW/m2.

The core, a ball spinning on its axis once every 24 days approximately,

at about a radiancy of 3x10 -6 rads/s.

The sun's radius R is 7 x 10 8 metres. At the tachocline the radius is about 5 x 10 8 m.

Equatorial tangential speed there (radius times angular rate) is 1500 m/s.

If we view the sun from above its north pole in a fixed frame it is in orbit around a point close to its outer surface,which varies from about 0.5 R to about 1.5R.

When the orbit radius is 0.5 R, a point at the tachocline (0.7R) nearest the point of orbital rotation is moving anticlockwise at about 2 m/s.

When the orbit radius is 1.5R the same point has about 16m/s.

These are added to the 1500m/s due to the spin. A change of about 1%.

For a ball of hot dense plasma setting off to reach the surface, 1% is significant.

When the SOHO satellite VIRGO instrument found a 0.015% reduction in total sun output during a solar minimum it was a dramatic event because sun modellers had assumed the output was unwavering. The Solar Maximum mission has shown it can change by 0.1% over a few days or weeks.

At the tachocline, bubbles of plasma are heated by the radiant heat from the core and behave rather like thermals in our atmosphere. They become less dense and float radially away from the tachocline.

The density there is thought to be about 2 gm/cc ( twice water) and reducing to very little at the outside.

So the sun inside the tachocline is a third of the volume but nearly all the mass of the sun.

The pressure there is due to the column of fluid above, just like our atmosphere.

The distance is 2.1x 10 8 m so crudely there is a column mass of 2 x 10 11 kg

assuming a linear drop of density with altitude.

Using the same gravity equation the weight of this column per square metre is 56 x 10 14 Newtons.

The pressure is 56 x 10 14 Pascals or about 5.6 x 10 9 earth atmospheres.

It is thought these bubbles of heated plasma travel at a few km per second (from 1 to 6 km/s)

The average is thought to be 2 km/s.

Consider a “trial” bubble of radius 1 km, it would be about 8 Gigakg and like thermals we can imagine that cooler fluid rushes in to cut it off as a bubble as it rises from the tachocline.. This bubble then has a start velocity of 2000m/s radially. (according to sun experts).

If it is a polar bubble it has a fifth of a million km to go, so it will take perhaps 10 5 seconds; just more than one day.

However if it is an equatorial bubble it starts with a tangential velocity also of about 1500m/s so it starts off at an angle with a velocity of about 2.5 km/s. The angle is arctan (1.5/2) to the radial, about 37 degrees.

It is travelling in a spiral out through downward spiralling cooler fluid.

To explain Coriolis acceleration, as the bubble travels radially, it has to be accelerated to the higher speed, eastwards.

Using Coriolis to calculate this the acceleration is 2 x dr/dt x w.

dr/dt is 2000 m/s w is 3 x 10 -6 rad/s thus acceleration is 12 10-3 m/s2,

using the 10 5 second time the distance travelled tangentially is:

1500 x 10 5 + ½ x 12 x 10 -3 x 10 10 = (15 + 6) x 10 7 m

In this result the first term is due to initial velocity and the second due to coriolis effect. Note the start velocity is important.

Clearly it will expand many times in its journey because of the drop in pressure, this will cause cooling but it will stay hotter than the falling fluid surrounding it. If the start pressure is so enormous the size near the surface will be gigantic. If the “trial” bubble near the surface has expanded say a thousand million times, its diameter is now 2000 km and if it spreads out to a layer 100 km thick, it becomes a patch 10 thousand km across. These figures are just to help visualise the process. There is room, the equatorial circumference is 4,300,000 km.

For interest, at 55MW/m2 our trial bubble now delivers something like 5 x 10 15 Watts for its short life before cooling and sinking. The turnover of granules on the sun (the bubble is now a granule ) is said to be around 1000 seconds. If that applies to our trial bubble the heat content is 5 x 10 18 Joules.

That is 6 x 10 8 Joules per kg.

The general view is that the cooled outside layers flow from equator to pole. If they do there must be increased rotation there as the angular momentum of the reducing radius flow will speed it up as it then sinks near the poles. I think there must be substantial inward, spinning flow at all lattitudes due to gravity.

The picture then is of rising bubbles of hot plasma through an eastward rushing cooler down-draft.

The equatorial radial flows take a longer path and see greater flows, so have more chance to lose heat. This suggests that the stable bubble size is larger at the equator, small bubbles being broken up in the cooler downdraft.

If for any reason the heat flow is more efficient, even a little more, the surface radiation would increase and the temperature of the tachocline would decrease. And vice versa.

One way to influence the convection efficiency is to change the tangential start velocity of the bubbles, as happens to a small degree due to orbit shift.

Vortices: Cooler flows at all mid lattitudes will spin up as they fall to maintain their angular momentum and becoming denser under increasing pressure will tend to spin at smaller radius, faster. This encourages another meta stable form, the vortex. A vortex is a central zone of high angular rate low pressure fluid supporting by its centrifugal force a higher pressure exterior. Vortex flow is well known on Earth in whirlpools and tornados. If the vortex reaches a hotter zone it will tend to suck hot material in at the base and a different flow model can emerge with hot high angular rate fluid rising and cooler denser slower moving fluid falling around it. (Like a thunder cloud)

In a free vortex the local velocity is related to the local pressure by Bernoulli's equation.

P + ½ ro .v2 + ro.g.h = K,

ro is the density

At the assumed tachocline density of 56 10 14 Pascals, density 2000 kg/m3,

a free surface implies a tangential velocity of about 2.5 10 6 m/s. The radius depends on the average circulation around that point, that is the angular momentum of the vortex.

This “atmosphere” of relatively low energy protons and electrons is nearly a perfect gas so there is no viscosity and such vorticity is possible and could continue indefinitely.

The electromagnetic and inertial effects tie such vorticity into knots.

Such a vortex would separate like a centrifuge, separating the heavier protons from the lighter electrons and this would introduce huge currents of electrons spinning up through the centre of the vortex, pushed upwards by the hot high pressures fluids entering at the base.

The upward moving spinning electron current would generate a solenoidal magnetic field with a pole at the surface. Every such vortex would produce a similar pole with a diffused annular opposite pole around it in the proton flow.

If the protons spread out at the surface while they cool this would create a huge annular anode or positively charges protons through which the electrons would be accelerated, to form a corona discharge.

Each vortex would also repel its similar neighbours creating a chaotic nest of snakes.

Transition from bubble flow to vortex flow could be the point at which inertial forces play a part.

If there is a strong vortex flow from inner to outer there is the gyroscopic force. A spinning mass moving radially and tangentially is being forced to precess by the rotation of the sun's spin and by its rotation around the orbit centre. This effect is strongest at the equator.

Any spinning mass will move at right angles to the applied forced precession couple. This effect is also altered by the orbit radius to the order of one per cent.

While the transport of heat uses a short cycle time the heat of the core will not change quickly. A period of high heat flow will start to cool the tachocline and possibly to move its radius but the cooling will have a high inertia so (presumably) it takes years to cool to the point where the heat flow regime starts to collapse to a less efficient one. This is an inherent cycle within the sun.

However if the the flow is encouraged or discouraged by external forces, then a long period of high output, (sunspot active) would cause a deeper than usual cooling of the tachocline and a period of lower output would follow. This is exactly the pattern of a small forcing frequency on a cyclic system.

Hypothesis:

There is a natural cycle of heat output within the sun where periods of slightly higher output cause a cooling of the tachocline over a period of years, (about five to six years) which leads to a reduction of output and this causes a rise in temperature of the tachocline during a further five years. The actual heat transfer is most effective by vortices, and least effective by convective bubbles. There is a small forcing frequency caused by the variation of the orbital radius of the sun, due to Jupiter, which affects the momentum of convective flow and the forced precession of vortex flow.

When the Saturn Jupiter conjunctions coincide with the perihelion, there is a decrease in sunspot activity and a reduced output of the sun leading to cool periods on Earth.

The mechanism is that increased orbital radius disrupts the heat transfer flows by coriolis, gyroscopic and angular momentum effects on the radial mass transfer cycle. These cyclic effects are of the order of one percent of the same effects due to the sun's own spin.