Shaker Effects in Celestial Mechanics

Franz Heeke, Muenster (Germany)

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.

1. Shaker Effects - Definition and Explanation

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 on 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. A differential rotation will show up. 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]. Galileo's theory of the tides was rejected later, but nevertheless may be partly correct, if earth's swinging motion about the barycenter of the Earth- Moon system is being taken into account.

As an engineer and amateur astronomer I have done some research into shaker effects for about 30 years now, stimulated by a paper of Paul D. Jose (1965): "Sun's motion and sunspots" - Refs - [02]. All central celestial bodies are being shaken around eccentrically to a minor or greater extent, depending on mass, orbit and orbit eccentricity of their satellite(s). This produces, according to my theory, spin angular momentum in central bodies, if these are gaseous or "elastic" to some degree. The axis of rotation 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 modeling and testing. The outlined ideas may be wrong in detail, but I am confident, that the underlying basic assumptions are correct. Some suggestions for testing my theory are outlined in chapter 6.

2. Sun's Motion and Sunspots

2.1 Sun's Motion

Paul D. Jose calculated and analyzed sun's motion around the center of mass of the solar system for the period 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 motion, as calculated by Jose, is 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 sunspots and 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 react differently to sun's eccentric motion. Friction between differentially rotating masses then produces the turbulence 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 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 traveling 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 [03]-[06]. This appears to support my explanation. Variations in sun's general rotation are also quite plausible in this connection: The kinetic 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 turbulence in our atmosphere, Refs - [10].

3. Rotation of Sun and Planets

3.1 Rotation of Central Celestial Bodies

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 celestial body 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" [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 [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 [09].

3.2 Origin 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 favorable 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. 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 during the course of solar cycles.

4. Origin and Structure of the Solar System

New ideas about the origin and structure of our solar system will come up, once it can be proven, that the planets are indeed driving and controlling the rotation of our sun:

Our solar system, according to prevailing theories, was formed out of a rotating nebular disk (nebular hypothesis). 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 about 99,9 % of the total mass, but in its rotation less than 1 % of solar system's total angular momentum, Refs - [14]. This implies under prevailing theories, that sun must have lost most of its initial angular momentum to the planets and moons. 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 of 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 mutual disturbances are minimized and an optimum of orbit- stability is being achieved. This then might be reflected in the Titius- Bode law.

5. Shaker Effects and Climate Variations

There are following main mechanism, by which shaker effects may influence our weather and climate, whether to a minor or more significant extent, may be left open at this stage:

- Variations in rotation of sun: Our sun is, at times, apparently rotating faster or slower, [04]-[06]. This, in my opinion, because of shaker effects as described. Faster or slower rotations then are going along with variations in solar radius [16]-[18], meaning changes in sun's density. These then probably cause changes in sun's energy output (solar constant, Refs - [15].
- Movement of sun's poles: Planets make their star wobble [17]. This 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 already suggested [02]. This means, "shaker effects", produced by the moon, may cause turbulence in earth's oceans and atmosphere, variations in its period of rotation and in its wobbling of poles. As a result, global circulation systems may be affected (El Nino, Jet streams etc.).

6. Areas of Research

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

6.1 Conducting Technical Experiments

"Shaker effects" obviously can be studied in practical experiments. That will show, whether my assumptions are correct with regards to the emergence of a differential rotation and the position of the axis of rotation: upright to the plane of shaking. Carrying out such tests appears to deserve some priority attention. Understanding the differential rotation of sun and planets is a key issue and there is, to my knowledge, no generally accepted theory as yet to explain this phenomenon.

6.2 Updating of Jose - Study

Updating of Jose's study, using now available more accurate data, may yield interesting results. Jose's paper of 1965 Refs - [02] indicates, that data of the Inner Planets were neglected at that time. These data have indeed only a very minor influence on sun's orbital motion (Figure-1), but the Inner Planets have a significant impact on sun's rotation, if my theory is correct.

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." [25[. Bouet used the cube of the frequency of revolution of the satellites in his equation. That means, satellites close to the primary have a 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) [26]. The Inner Planets thus most probably have some effect also on solar activities by influencing sun's rotation.

6.3 Research into Planetary Systems

The equations [25] and [26], if correct, must be valid also in case of exoplanets and other planetary systems. Trying to calculate in this way the rotation periods of other central stars might be an interesting challenge.

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 with regards to several astronomical problems, if the indicated correlation exists on a general base (density, spectrum of stars etc.).

6.4 Studies on Solar activities

According to the presented theory there are following chains of cause and reaction regarding sun's motion and solar activities:

- "Shaker effects" produce a differential rotation of sun, depending on the eccentricity of sun's path about the center of mass of the solar system (Figure-1). This leads to friction and turbulence within the gaseous solar masses.
- The eccentricity of sun's motion curve changes over time and sun's motion is rather circular during certain periods. There are no "shaker effects" during such periods and sun rotates less differentially. This leads to a minimum of solar activities.
- A minimum in solar activities means, that no or little kinetic energy is being diverted from sun's rotational motion to the whirling motion of sunspots. As a result sun's general speed of rotation increases during the period of a sunspot minimum.
- An increased rotational speed causes a blow-up of of sun's diameter. This reduces sun's mean density, which in turn causes a change in radiation (solar constant).
- Variations in the solar constant are reflecting on our weather and climate to some extent.

Some of these correlations are described in a number of earlier research reports, for instance [15]-[18]. Additional research in this field is of special economic interest. Solar activities (flares etc.) are at times causing a severe disruption in worldwide telecommunication systems. Losses incurred can be minimized, once reliable forecasts are available.

6.5 Research into Maunder- and Landscheidt- Minimum

From about 1645 to 1715 there was the prolonged sunspot minimum known as "Maunder Minimum". It seemingly came along with an anomalous solar rotation, a period of cooler climate in Europe, [06][17] and prolonged drought- periods with famine conditions in parts of Asia and Africa.

Sun's motion Figure-1 must have been less eccentric and rather circular during the Maunder minimum, if the described theory is correct. 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 center 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.

Dr. Theodor Landscheidt, Refs - [15] , predicted the next prolonged sunspot minimum (Landscheidt Minimum) for the coming decades, with a lowest level of solar activities around the year 2030. This prolonged sunspot minimum may have commenced already. Figure-1 shows part of sun's motion curve, as calculated by Jose. The curve is rather circular for the last few years, and solar activities have been very low for more than two years now (4/2009). It is expected, that the current Sunspot Cycle 24 will remain weak up to its end. The possibility, that two or more weak cycles might follow, like those during the Dalton Minimum from 1790 to 1830, cannot be denied. This obviously is of considerable interest in view of discussions about global warming and climate change. A prolonged sunspot minimum, coming along with a cooler period, may counterbalance the much discussed man-made greenhouse effect to a certain extent, at same time triggering off extreme weather conditions and severe droughts in some parts of the world.

6.6 Studies on Titius-Bode Law

Planets are possibly arranging themselves in a way, that mutual disturbances are minimized and an optimum of orbit-stability is being achieved (Chapter 4). This may be reflected in the Titius- Bode Law. Computer simulations will show, whether this assumption is correct or not.

The Titius- Bode Law presumably identifies areas, in which planets can find stable orbits. One of those identified areas, between planets Mars and Jupiter, is not occupied by a planet. Instead numerous smaller celestial bodies are orbiting there in the so-called "asteroid belt". The idea lies at hand, that minor planets or other bodies on irregular trajectories may end up in the asteroid belt, where they finally find stable orbits. This could be an ongoing process, which possibly can be verified by observation.

6.7 Geophysical Research

Earth's rotation apparently was faster than at present during earlier periods of our solar system [24], and its equator then was in a different position. This means, if the assumptions in foregoing 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 and moon's orbit at a different angle.

Some research reports support this statement. 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 [24]. One might attempt, to calculate, whether data of such research are in agreement with the equations given in [25] and [26].

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Comments to the outlined ideas are most welcome.

F. Heeke, Homepage 3-98 (last updated 4-2009)

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