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 most certain 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 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 also to planets and our sun and 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 from one and the same rotating cloud, are not convincing anymore. 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 . They are produced by “lifting” masses against centrifugal forces. Masses at different radii thereby react differently to a particular pattern of shaking because of greater or smaller centrifugal forces. A fluid or gaseous body thus will show a differential rotation.

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 orbital motion around sun, leads to an acceleration and deceleration of earth's surface every 12 hours - Refs [01]. This occurs, in principle, also in sun's surface in combination with its rotation and its orbital motion around the center of mass of the solar system. Galileo's theory of the tides got rejected later on, 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 40 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 then will show a differential rotation.

My theory requires mathematical modeling and testing. Some suggestions for testing the ideas are given 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 used, probably because of limited computer capacities at his time, data of the five outer planets only. He compared his research results with the then available sunspot data and found, nevertheless, a correlation between sun's motion and sunspot cycles. 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. Friction between the differentially rotating masses then produces the turbulence and whirls, which we observe as sunspots and solar activities. The intensity of solar activities varies with 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. Masses, which are pushing ahead when sun is being shaken along a small loop, are falling back, when sun is traveling along a large 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]. These are supporting my theory. Worthy of mention here is also a more recent publication of A.G. Tlatow - Refs [29].

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 has been produced in this way. Some of it probably derived from the formation process (conservation of angular momentum). But the satellites, planets and moons, carrying the bulk of their system's total angular momentum, 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. 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.

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 in research paper [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 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 ( Figure-2 ) indicate, 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 controlling 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 (with it the solar constant), 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 (Kant-Laplace nebular hypothesis). Sun, planets and moons are supposed to have formed from the same nebular material. 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 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 most probably 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:

- Our sun is at times rotating faster or slower [04]-[06]. This, in my opinion, because of shaker effects as described. A faster or slower rotation then goes along with variations in solar radius [16]-[18], meaning changes in sun's density. These will cause changes in sun's energy output and in 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 suggested [02].

Shaker effects produced by the moon may cause a diversion of global wind and surface currents (Jet streams, El Niño, Gulf Stream). They may be responsible also for hitherto unexplained sudden movements of poles, which in turn may cause tectonic activities like earthquakes and severe volcanic eruptions. In 1815 the volcano Tambora in Indonesia erupted, ejecting more than 100 cubic kilometers of tetra and ash up to 20 kilometers into the atmosphere. Ash and sulphur dioxide circled the earth for many months and the global temperature dropped by several degrees. The following year 1816 became known as the year without summer in the Northern Hemisphere. This happened during the prolonged sunspot “Dalton Minimum”.

6. Areas of Research

There are 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 assumption is correct with regards to the emergence of a differential rotation and the position of the axis of rotation - upright to the plane of shaking.

6.2 Updating of Jose - Study

Updating of Jose's study ( Refs [02] ) should yield interesting results, when data of the Inner Planets are included in the studies. Shaker- effects of Inner Planets are overlapping the large shaker motion of our sun ( Figure-1 ), are thus of influence on solar rotation and solar activities. The "rule-of-thumb" of Jacques Bouet [25[ and the mathematical equation of Samy Esmael [26] and the more recent publication of A.G. Tlatow [29] should be taken into consideration in updating work.

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 density and spectrum of stars if the indicated correlation is proven to be true.

6.4 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 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.
- 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).

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.

6.5 Research into Maunder- and “Landscheidt”- Minimum

The prolonged sunspot- "Maunder Minimum” (17th century) came along with an anomalous solar rotation, a period of cooler climate [06][17] and prolonged drought- periods with famine in many parts of the world. This, according to my theory, must be explainable by a difference in shaker- effects.

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 (2017) already the first phase of this "Landscheidt Minimum". Sun's motion curve is very much like that during the Maunder Minimum (Figure-1) and solar activities have been low for a longer period now. The current sunspot cycle 24 is the weakest since more than 100 years. Experts expect the next cycle 25 to be even weaker, with a very low maximum around 2025. 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 for some time to come. At same time unusual droughts and extreme weather conditions must be expected according to historical experiences. These extremes most certainly will be caused to a wide extent by unusual “shaker- effects”, leading to a deviation in ocean- and atmospheric circulation systems. This could mean changes in El Niño, the gulf stream and southern ocean circulations and in jet streams and trade winds in the atmosphere.

Confirmed research reports [20] [21] indicate, that solar cycles also affect the rotation of earth and Jupiter. To what extent earth's rotation will be affected during the "Landscheidt- Minimum" is open. However, an unusual variation of only milliseconds in earth's rotation rate could trigger off unloading of existing tensions in earth's crust, causing severe earthquakes or volcano- eruptions. This may remind us of the tremendous eruption of the volcano "Tambora" during the “Dalton Minimum” in 1815 (chapter 5) with world temperatures dropping by several degrees. Or, of the less powerful eruption of volcano Pinatubo in the Philippines in 1991, which nevertheless caused a drop in global temperatures by 0.5 degrees C. World market prices for wheat went up rather sharply in the following years.

6.7 Studies on Titius-Bode Law

Planets are probably arranging themselves in a way, that an optimum of orbit-stability is being achieved (chapter 4). Computer simulations will show, whether this assumption is correct.

The Titius- Bode Law thus 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 planetoids or other celestial bodies on irregular trajectories end up in this belt, finally finding rather stable orbits there. This then should be an ongoing, possibly observable process. Computer simulations may identify celestial bodies, which are potential candidates for joining the planetoids in the asteroid belt some day.

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].


F. Heeke, Homepage 3-98 (last updated 02-2017)

Back to (index)