A fluid in a glass rotates, when eccentrically shaken. My hypothesis: Such "shaker effects" play an important role in celestial mechanics, driving and controlling the rotation of sun and planets.  The assumed mechanism of  interaction is described in following chapters. "Shaker effects" are probably of influence also on our weather and climate.

The phenomenon of a rotating fluid in a shaken glass is well-known.  The fluid derives its spin angular momentum from the eccentric motion, the axis of rotation stands upright to the plane of shaking. There is, to my knowledge, no technical term for this phenomenon, so the term "shaker effects" is being used here. A spinning plate on an artists rod follows the same law of physics, likewise a weight, which is being swung around on a string. Shaker effects are in principle equivalent to the effects observed in a swing Figure 3/5 . 

The angular momentum transfer in "shaker effects" depends on the pattern of shaking and the eccentricity  of the shaken mass. Masses at different radii react differently to a particular pattern of shaking and swinging. That is easily noticed, when swinging around masses on strings of different length. It is also easily noticed, that "shaker effects" occur only in case of eccentric shaking. There are no "shaker effects" in case of a circular motion.

General ideas about shaker motions in celestial mechanics are not new.  Galilei Galileo studied water movements in a shaken vase about 400 years ago.  He tried, to explain the phenomenon of the tides with his experiments. Galileo pointed out, that the rotation of earth, in combination with its motion around sun, leads to an acceleration and deceleration of earth's surface every 12 hours, Refs - (01). Galileos theory of the tides was rejected later, but nevertheless may be partly correct, if earth's swinging motion about the barycentre of the Earth-Moon system is being taken into account.

As a mechanical engineer and amateur astronomer I have done some research into shaker effects for more than 25 years, stimulated by a paper of  Paul D. Jose (1965):  "Sun's motion and sunspots" - Refs  - (02).  As is known, most central celestial bodies are being shaken around eccentrically by their satellite(s). This produces, according to my theory,  spin angular momentum in these central bodies, if they are gaseous, liquid, or to a certain extent elastic.  The axis of rotation then tends to stand upright to the plane of shaking, which is the mean orbital plane of the satellite(s).  Gaseous central bodies will show a differential rotation, since their masses at different radii react differently to a particular shaking and swinging motion.

I cannot prove my theory as yet. It requires mathematical modelling and testing.  The outlined ideas may be wrong in details, but I am confident, that the underlying basic assumptions are correct. Some suggestions for testing my theory are outlined in chapter 6.
 

Paul D Jose calculated and analysed sun's motion about the center of mass of the solar system for the years from 1843 to 2013.  He  compared his research results  with the then available sunspot curves. Finding a correlation between sun's motion and solar activity, he concluded:  "The relationships set forth here imply, that certain dynamic forces exerted on the sun by the motion of the planets, are the cause of the sunspot activity", .. and furthermore:  "Similar preliminary studies for the earth and moon indicate, that weather conditions may be dependent on such forces".

Sun's motions, as calculated by Jose, are partly shown in - Figure-1 . It occurred to me, that the mentioned "certain dynamic forces" are producing the described "shaker effects". This leads, in my opinion, to following basic explanation of solar activities:

2.2 Sunspots

Shaker effects are driving and controlling the rotation of our sun, thereby producing a differential rotation, since  masses at different radii are reacting differently to sun's eccentric motion. Frictions between differentially rotating masses then produce the turbulences and whirls, which we observe as sunspots and solar activities. The intensity of solar activities varies according to changes in sun's motion, and sunspot polarities reverse, whenever the pattern of shaking changes.

Our sun is moving about the center of mass of the solar system alternately along larger and smaller eccentric loops, as shown in  Figure-1. Sun's motion along each one of those loops corresponds in principle with the duration of one solar cycle, as marked.  Whenever sun travels from one loop towards or into the next one, there is a basic change in sun's velocity and in the curvature of its motion. The pattern of shaking thus changes, and with it the differential rotation. Masses, which are pushing ahead, when sun is being shaken along a large loop, are falling back, when sun is travelling along a small loop, and vice versa. This causes a reversal in energy- transfer,  which we observe as a reversal in sunspot polarities.

Variations in the general and  differential rotation of our sun, in relation to solar cycles, are described in several research papers - Refs - (03)-(06).  This appears to support my explanation. Variations in sun's general rotation  are also quite plausible in this connection: The mechanical energy, which goes into the whirls of sunspots, is being diverted from sun's rotational energy. Sun's rotation thus is slowing down with the appearance of sunspots. Our sun rotates  faster, whenever there are no or only few sunspots. A comparison with earth's rotation lies at hand: The length of a day on earth (LOD) varies from day to day by milliseconds. This is being explained by turbulences in our atmosphere,  Ref. - (10).
 

Shaker effects are driving and controlling the rotation of sun and planets, but this does not mean, that all their spin angular momentum must have been produced in this way. Some of it may have been derived from the formation process. However, the satellites, planets and moons, carry the bulk of their system's total angular momentum, and with this they have a controlling influence on the rotational period of their central mass. They also control the position of its axis of rotation, which tends to stand upright to the mean orbital plane of the satellites.

Publications  Refs   (25) and (26)  are describing in mathematical terms a correlation between the rotational period of a central mass, and the masses and orbital periods of its satellites. This indicates, that an exchange of angular momentum takes place between satellites and their central mass. However, transfer of angular momentum in celestial systems is not one- sided, towards the central mass only. Some transfer and balancing may occur also from a central mass towards its satellite(s), and between the satellites themselves within a system. As is known, the orbit of Mars- moon Phobos is contracting, meaning a transfer of angular momentum towards the spin of Mars. On the other hand, our moon's orbit is slowly expanding, meaning a transfer of angular momentum from earth to moon. Earth's rotation is slowing down.  Textbooks say, these phenomena are because of "tidal drag" and "tidal friction", Refs - (14). My view is, that "shaker effects" are also involved in this.

The controlling influence of satellites on the axis of rotation of their central mass is being confirmed in several research reports,  for instance -  Refs ( 07) : "...Because of the gravitational pull exerted by their masses, planets make their star wobble....."  However, here again "shaker effects" are probably more involved than gravitational forces. The controlling influence of our moon on earth's axis of rotation is being described in - Ref (09).

3.2 Planetary Rings

My assumption is, that the spinning of a planet can be accelerated by "shaker-effects" up to the point of disintegration. Planetary matter then may escape at the planet's equator, forming planetary rings. This possibly under combined influence of centrifugal-, eruptive- and other forces. The escaped matter, once in orbit, then may mix up with matter captured from outside (meteoritic material etc).

Figure-2  shows, roughly calculated, the eccentric motion of planets Jupiter and Saturn about the center of mass of their planetary system. Their motions are naturally much narrower and faster than those of the sun. Both planets are being shaken along one complete loop in less than 20 days. As a result, a rapid rotation of Jupiter and Saturn can be expected.

Planetary rings exist, as far as we know, only around the rapidly spinning planets Saturn, Jupiter, Uranus and Neptune, here mentioned in order of size of their ring system. These planets show, in the same order, a rather favourable ratio of equatorial velocity to escape- or orbital velocity ( Figure-2  / Table 2).  This appears to be a strong argument in support of my thesis.

As may be seen, there is a remarkable difference in the shaking- pattern of Jupiter and Saturn (Figure 2). The eccentric motion of Saturn is rather smooth, that of Jupiter more turbulent. This should show up in the surface structure of these planets. It seems indeed to be reflected in Jupiter's more turbulent surface (Red Spot, differential rotation etc).

3.3 Mean Density of Planets and Sun

Celestial bodies have a natural tendency to contract under influence of self-gravity. This process is opposed by centrifugal forces in case of a rotating body. The rapidly spinning giant planets, as a consequence, can be expected to have a rather low mean density. Data in  Table 2  suggest, that for planets a distinct relationship exists between equatorial velocity, escape- or orbital velocity (mass), mean density, and ellipticity. The faster a planet rotates, the lower is its mean density.

The assumed relationship can be expected to prevail in principle also in case of sun and other stars. This then means, that sun's diameter and mean density are changing, whenever sun's rotation is speeding up or slowing down in the course of solar cycles.
 

Our solar system, according to most prevailing theories, was formed out of a rotating nebular disk. Sun, planets and moons are supposed to have been formed from the same nebular material, coming into being at about the same time. However, these theories have problems with explaining the distribution of angular momentum. Our sun holds more than 99 % of the total mass, but less than 1 % of solar system's total angular momentum (Ref 14). This implies under prevailing theories,  that sun must have lost most of its initial angular momentum to the outer members of  the system. How this could have happened, is difficult to explain.

The distribution of solar system's angular momentum explains itself, should my theory be proven true. Likewise the position of sun's axis of rotation and equator level, which are being forced into their present  position by the planets.

With this it becomes conceivable and more likely, that at least some of the bodies in our solar system formed separately and independently from our sun. Some planets, moons and other bodies may have been captured, coming from distant regions of the universe, assembling around sun gradually over time.

We know, that man made satellites can leave our solar system, ending up perhaps in another star system. In a similar way also larger natural celestial bodies might travel from one star system to another. Mass loss of a star, for instance, may reduce its gravitational attraction to an extent, that outer planets or moons can leave the system, wandering around in universe till joining another system.

If there is an exchange of angular momentum within the solar system as described, one may expect a distinct tendency in it. The planets possibly are arranging themselves in a way, that perturbations are minimized, and an optimum of orbit-stability is being achieved. This then might be reflected in the Titius-Bode law.
 

There are following main mechanism, by which shaker effects may influence our weather and climate:

- Variations in rotation of sun: Our sun is, at times,  apparently rotating faster or slower,  Refs - (04)-(06). This is, in my opinion, because of shaker effects, as described.  Faster or slower rotations then are going along with variations in solar radius,  Refs - (16)-(18), which means changes in sun's density. These probably cause variations in sun's energy output (solar constant - Ref - (15).

- Movements of sun's poles: Planets make their star wobble, Refs - (17). This is also because of shaker effects, according to my theory (axis of rotation tends to stand upright to plane of shaking). Wobbling of our sun then may cause variations in the direction of sun's radiation (solar wind etc)..

- Shaking and wobbling of earth: The same type of dynamic forces, which are the cause of solar activities, are to be expected also in the earth-moon system, as Jose, Refs (02) already suggested,  This means, "shaker effects",  produced by the moon, may cause turbulences in earth's atmosphere, variations in its period of rotation, and in its wobbling of poles. As a result, global circulation systems in the atmosphere and oceans (El Nino etc) will be affected.
 
 

There are certainly many ways of testing the outlined ideas. I expect, that especially research in following areas will show, whether my theory is tenable or not:

6.1  Laboratory Tests

"Shaker effects" apparently can be studied in practical laboratory tests. The experiments should show, that my assumptions are correct with regards to the emergence of a differential rotation, and the positioning of the axis of rotation - upright to plane of shaking.

6.2 Computer - Simulations

"Shaker effects" probably can be studied also in computer simulations.  Preliminary work of the well-known mathematician Riemann may be useful in developing the mathematical models required for such simulations.  Refs (23).

6.3 Updating of Jose - Study

Updating and adjusting of Jose's study, using now available more accurate data, may yield interesting results. His paper, Refs  (02), does not mention, to what extent data of the Inner Planets went into his calculations. The Inner Planets contribute little to sun's overall motion, as shown in  Figure 1. However, they probably have an important impact on sun's rotational motion.

Jacques Bouet published a paper in 1984, saying  "A rule-of-thumb relation has been observed between mass and frequency of revolution of satellites, on the one hand, and, on the other hand, the mass and frequency of rotation of the planet around which they gravitate." (Ref. 25).  Bouet used the cube of the frequency of revolution of the satellites in his equations. That means, that satellites close to the primary  have a much stronger impact on the rotation of the primary than those on distant orbits. A comparison of planets Mars and Earth may serve as an example: Mars, with two mini-moons very close to their primary, shows about the same period of rotation as Earth, with its massive moon on a distant orbit.

Jacques Bouet's "rule-of-thumb" is being supported by an equation, which was  developed more recently by  Samy Esmael (Cairo) - Refs - (26). Both equations might be taken into consideration in updating of Jose's study.

6.4 Planetary - Research

Data of Table 2 ( Figure-2 ) suggest, that a correlation exists between the ratio of equatorial velocity to escape velocity (mass) on one hand, and density and ellipticity of planets on the other hand. Planetary researchers may have to look into these data one day. New aspects will come up regarding several astronomical problems, if the indicated correlation exists on a general base.

6.5 Solar activities

There is, in my view,  following chain of causes and reactions in connection with solar activities:

- The curvature of sun's motion (  Figure-1  ) is at times rather circular, not eccentric. There are nor "shaker effects" in such periods. This reduces sun's differential rotation, leading to a sunspot minimum - with some time lag because of the moment of inertia.
- Sun's speed of rotation increases during a sunspot minimum, since no mechanical energy is being diverted from sun's rotational motion to the whirling motion of spots during this time.
- Sun's diameter blows up to some extent, when its rotation is faster. This reduces sun's mean density, which then causes a variation in the solar constant.
- Variations in the solar constant are of influence on our weather and climate on earth.

Future research results may support this point of view. Some of the outlined correlations are described already in research reports, for instance - Refs (15) (16) (17) (18) .
 

6.6 Maunder Minimum

From about 1645 to 1715 there was a prolonged sunspot minimum (Maunder minimum). It seemingly came along with an anomalous solar rotation, and a period of cooler climate in Europe,  - Ref. (06)(17).

The suspected causes for and consequences of sunspot minima are outlined in aforegoing chapter. Sun's motion (Figure-1) must have been rather circular during the Maunder minimum. This should show up, when Jose's study is being updated and extended to the period in question. There would be no transfer of angular momentum, no differential rotation of our sun, and no sunspots at all, if sun was swinging about the centre of mass in a perfect circle. An example of a swinging motion with little eccentricity is offered by planet Saturn   Figure-2 . Saturn shows, as is known, a rather smooth surface.

A favourable position of sun's axis of rotation (minimum of wobbling) may have contributed to the prolonged sunspot minimum in the 17th century. Updating of Jose's study might show, whether this is true, and an extension of it into the future might give some warning, when to expect the next "Maunder Minimum" .

6.7 The Titius-Bode Law

As has been suggested, planets are possibly arranging themselves in a way, that an optimum of orbit-stability is being achieved (chapter 4). This might be reflected in the Titius-Bode Law.  Computer simulations may show, whether this assumption is correct or not.

It may be expected, that re-arrangements of orbits are taking place also in Planet-Moon systems. Especially the Jupiter - moon system may offer opportunities for relevant research, because of Jupiter's erratic motion (Figure 2).

6.8 Climate Research

There are numerous scientific reports available on suspected or proven correlations between solar activities and climate variations on earth. Many of these reports might gain in plausibility, if investigated under viewpoint of the described chain of causes and reactions (chapter 6.5). Of special interest will be the challenge, to predict the timing of the next  "Maunder Minimum", as Dr. Theodor Landscheidt tried to do Refs (15).  A prolonged sunspot minimum, coming along with a cooler period, might offset to some extent the much discussed greenhouse effect.   

6.9 Geophysical Research

Earth's rotation apparently was faster than at present during earlier periods of our solar system,  Ref. - (24), and its equator then was in a different position. This means, if the assumptions in aforegoing chapters are correct, that

- earth's diameter was larger, its shape more elliptical, and its mean density lower than at present, and
- moon's revolution period was shorter, moon's orbit at a different angle.

Some research reports support this statement to a certain extent. More investigations might be of interest. The periodical growth in coral fossils, for instance, permits conclusions with regards to the number of days per month and per year many million years ago, Ref - (24). One might attempt, to calculate, whether data  of such research are in agreement with the equations given in Ref (25) and (26).

F. Heeke, Homepage 3-98  (last updated 4-2007)

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