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 chapters below. 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). "Shaker effects" are probably of influence also on our weather and climate.


Main Conclusions

(a) The planets produce a differential rotation of our sun, which varies with their constellation. This differential rotation generates whirls and turbulence, which we observe as sunspots and solar activities.

(b) The moons of the giant planets are "driving" the rotation of their parent planet up to an extent, that matter may be ejected or expelled at its equator. The ejected matter forms planetary rings or segments of rings.

(c) Mean density and ellipticity of planets depend on the ratio of equatorial velocity to escape velocity. Moons, by "driving" the rotation of their parent planet, are in this way affecting its density and shape. This then applies as well to planets and our sun as to exoplanets and their central stars.

(d) Planets are exchanging angular momentum among themselves in such a way, that mutual disturbances are minimized. This is probably reflected in the Titius-Bode law.

(e) Nebular theories, according to which all bodies of our solar system formed together from one and the same rotating cloud, are becoming less convincing. At least some of the planets or moons came into being separately, are captured and joined our solar system step by step.

Time will show, which ones of these conclusions are correct and which are wrong.

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 more than 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]. This refers, in principle, also to our slower rotating sun and its orbital motion around the center of mass of the solar system.

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 research into shaker effects for more than 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. Some suggestions for testing my ideas 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 data. 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 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. However, 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. But 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." 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 also in research [09].

3.2 Origin of 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 be expelled and 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 motion is 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 and seems 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 being 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.

Moons, by controlling the rotation of their parent planet, are in this way also affecting its mean density and shape. That relationship can be expected to prevail in principle also in case of planets and sun and other stars. This 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 probably cause changes in sun's energy output and 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 and variations in earth's period of rotation and its wobbling of poles. As a result, global circulation systems may be affected  (El Nino, Jet streams etc.) as well as tectonic activities.

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 Refs - [02] , using more recent data, may yield interesting results. This especially, when the Inner Planets (neglected at that time) are included in the studies. The Inner Planets have a negligible influence on sun's orbital motion (Figure-1), but apparently an impact on sun's rotation.

Jacques Bouet wrote [25[: "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". He used the cube of the frequency of revolution of the satellites in his equation, meaning, that satellites close to the primary have a relative stronger impact on its rotation. This must be valid also in case of planets and sun.

Jacques Bouet's "rule-of-thumb" is being supported by an equation developed more recently by Samy Esmael (Cairo) [26]. The Inner Planets, by affecting sun's rotation, thus can be expected to also influence solar activities to a certain extent.

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 look into these data. 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 Analyzing Earth's Motion

Jose's preliminary studies of the earth-moon system indicated, that the same type of forces, which cause solar activities, may affect weather conditions [02]. The mentioned forces produce the described "shaker effects" according to my theory.

Shaker effects occur only in a mass, which is either gaseous, fluid or elastic. Earth's solid core and unevenly distributed masses of different density thus react differently to earth's motion. This causes or contributes to friction and dislocation of masses within earth and on its surface.

Analyzing earth's motion in more detail than Jose could do, taking into account neighboring planets, may be a rewarding project. Irregular shaker motions can possibly explain unusual variations in earth's rotation and in its movement of poles (wobbling). These then may affect not only weather, but also tectonic activities.

6.5 Studies on Solar activities

Following statements need testing and verification:

- "Shaker effects" produced by the motion of the planets are the cause of sun's differential rotation. The differential rotation causes friction and turbulence within solar masses, observed as sunspots and solar activities.
- The intensity of solar activities depends mainly on the eccentricity of sun's path about the center of mass of the solar system.
- The change in polarity of sunspots is caused by sun's alternate motion along larger and smaller loops (Figure-1). This may be verifiable by statistical analysis of sunspot cycles and motion loops over long periods.
- Sun's rotation is speeding up during a sunspot- minimum, as no or little kinetic energy is being diverted to the whirling motion of sunspots during those periods.
- An increased rotational speed causes a blow- up of of sun's diameter, reducing 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.

Several of these correlations are described in many research reports, for instance [15]-[18]. The presented theory needs to be tested against those reports. It might be rewarding, to consider in addition also Galileo's theory of the tides Refs [01], which possibly can explain some short term variations in solar activities.

6.6 Research into Maunder- and Landscheidt- Minimum

During the 17th century there was the prolonged sunspot- "Maunder Minimum". It came along with an anomalous solar rotation, a period of cooler climate in Europe [06][17] and prolonged drought- periods with famine in many parts of the world.

Dr. Landscheidt (1927-2004)[15] predicted already in 1989 a similar prolonged sunspot minimum for the 21st century, with a lowest level of solar activities around the year 2030. It appears, that we are seeing now (2012) the first phase of this "Landscheidt Minimum". Sun's motion curve is very much like that during the Maunder Minimum (Figure-1) since years and solar activities have been unusually low for a long period. NASA experts predict, that the current sunspot cycle 24 will be the weakest in about 100 years. Some experts expect the next cycle 25 to be even weaker, with a very low maximum between 2022 and 2024. There is the obvious possibility, that an additional weak cycle will follow thereafter. That would make the "Landscheidt Minimum" comparable to the "Dalton Minimum", which took place from about 1790 to 1830.

Popular theories about climate change and global warming need a review, if the "Landscheidt Minimum" takes place as predicted. A cooler period, coming along with it, may counterbalance the much discussed man- made greenhouse effect to a certain extent. At same time unusual droughts and extreme weather conditions must be expected according to historical experiences. There may be also unusual earthquakes and volcano eruptions.

Confirmed research reports [20] [21] indicate, that the mechanism causing solar cycles affect also the rotation of earth and Jupiter. To what extent earth's rotation will be affected in the "Landscheidt- Minimum" is open. However, an unusual variation of only milliseconds might trigger off earthquakes or volcano- eruptions. During the "Dalton Minimum" there was the tremendous eruption of the Indonesian volcano "Tambora" (1815). Ejected ash and volcanic matter circled the earth for long periods and temperatures dropped worldwide by several degrees. The following year 1816 became known as the year without summer. It should be of high interest, in view of such eventualities, to follow up earth's motion in coming years, as outlined in paragraph 6.4.

6.7 Studies on Titius-Bode Law

Planets are probably arranging themselves in a way, that mutual disturbances are minimized and an optimum of orbit-stability is being achieved (paragraph 4). This may be reflected in the Titius- Bode Law.

Computer simulations might show, whether this assumption is correct. The Titius- Bode Law presumably identifies areas, in which planets find rather stable orbits. One of these areas, between planets Mars and Jupiter, is not occupied yet by a planet. Instead, numerous smaller celestial bodies are orbiting there in the "asteroid belt". There is the obvious possibility, that some planetoids or other celestial bodies on irregular trajectories end up in this belt, finally finding rather stable orbits there. This should be an ongoing process. Computer simulations may identify such celestial bodies, which are potential candidates for joining the numerous planetoids in the asteroid belt sooner or later.

6.8 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, and
- earth's motion was less stable, with faster and wider wobbling.

These conclusions are in agreement with many geophysical research reports. Attempts might be made, to compare data of such reports with results of calculations done with equations given in [25] and [26].


Comments are most welcome.

F. Heeke, Homepage 3-98 (last updated 6-2012)

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