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Copyright - Karim A. Khaidarov, March 1, 2005
(Aethereal Theory of Gravitation)

Dedicated to the bright memory of my daughter Anastasia

The concept and outcomes of author's research opening the actual gear of phenomena, dependent on speed of gravitation is stated. It is shown that the existing theories of gravitation, based on absolute vacuum, long-range action, primacy of relativity are artifacts. It is shown that the main problems of the theory of gravitation can decided within the framework of the aethereal approach of Hooke, Gauss, Gerber. The solution of problem of motion of perihelions of planets and stability of a planetary system is discovered. The full table of motion of perihelions of planets and theoretical values of steady eccentricities obtained by the author with the help of the aethereal approach are given.

"I will deliver him; I will protect him, because he knows my name"
[Psalm 91]

Resting on opened by the author during research of properties of space aether the natural phenomena and regularity [1-18], and basing on results obtained by classics of physics: Galileo Galilei [19], Robert Hooke [20], Daniel Bernoulli [21], Leonhard Euler [22], Karl Friedrich Gauss [23], Paul Gerber [24-27], we will consider forces of gravitation dependent on speed and phenomena inevitably following from physics of this process.

However for clearing for readers a motivation of this research, we will consider the background folded since times of Newton in the theory of gravitation and gravitational astronomy as far as the volume of this paper allows.

The myths of mathematical physics

Ye shall make you no idols nor graven image,neither rear you up a standing image, neither shall ye set up any image of stone in your land, to bow down unto it: for I am the Lord your God.

[Leviticus, 26-1]

Unfortunately, since ancient pagan times, inspite of common sense, in a temple of physics not physics itself, but its tool and servant - mathematics which self-reigned itself as empress of all sciences.

Really, being a powerful tools, quantitative methods and models allowed to get magnificent on accuracy outcomes, but no more.

Substantially, mathematics is necessary, but only intermediate between the qualitatively - logical analysis and physical experiment, between theoretical and always abbreviated, idealized logical model of a reality and physical world, which knowledge at its best is partial and abbreviated, and usually it is insecure and scholastically exaggerated.

The monarchic philosophy of quantitative mathematics has resulted in the absurd subordinate position not only physical reality ( if the facts do not confirm the theory, that is worse for the facts ), but also the logic - fundamentals of all sciences.

Last, visible as the advance - mathematization of logic, substantially has resulted in arbitrary pseudo-quantitative manipulation with logical concepts, substitution of concepts of actual logic by illogical pseudo-scientific constructions generating and peaceful coexist with paradoxes - the indicators of violation of logic and thinking.

There was occurrence of the scientific myths as consequence of this unhealthy process. Let's consider those myths which are the brake for development of the theory of gravitation.

The Newtonian mathematical basis of nature [28] - a myth, based on adoption of Robert Hooke's works on aethereal theory of gravitation [20], but excluding aether itself as the fundamentals of the Universe, by declaring a possibility of action in absolute empty Space.

Usage of bare mathematics of motion of celestial bodies in a simple case of motions of trial bodies in a gravitational field of sole heavy body ( the force, inversely proportional to a square of distance) has resulted in dock in the solution of such simple problem as a problem of three bodies.

Substantially has appeared, that the operation of gravitational force is a little differ from a back - quadratic, but if we accept it (Hall's hypothesis), the conservation laws in a mechanics are upset. The calculations of Mercury's perihelion motion produced, ostensibly, within the framework of the Newtonian theory, grounded on rejection from the Newtonian back-quadratic law, and therefore these calculations have no any relation to Newtonian law.

Besides within the framework of the Newtonian theory there is no a solution of the problem of orbits stability, and Newton, when ones asked him about this problem, responded that it is a duty of the Great Watch-maker, who will get orbits on former places.

Perturbation theory - a technology of mathematical approximating in gravitational astronomy of unknown of effects from the third bodies which were generating the myth about super accuracy of the Newtonian law of gravitation. Substantially, using formal proximity of actual forces of gravitation (same narrow class of functions), by adjustment of series of astronomical disturbances to a concrete set of equations, the mathematicians achieved both approximation, and far extrapolation of series. It has enabled to predict behavior of osculating orbits and to calculate unknown planet Neptune by mathematicians Adams and Le Verrier [29, 30].

Substantially, the formulas of a perturbation theory do not correspond to the Newtonian law and laws of conservation of energy, moment and momentum.

Really, if the Newtonian forces are central, it is impossible to change neither mean moment, nor mean energy of a planet by any periodic effect of other planets of the same planetary system.

There are no reasons for such effects. Such basis could be non-central of a field, presence of a direct mechanical connection between planets or presence of the moment of forces applied on a planet. In the Newtonian theory the field is central, so the integral of a disturbance on an infinite interval of time is in essence equal to zero. The planets in the Newtonian theory do not have gravitational sails, that it is impossible to speak about the applying the mechanical moment to a planet.

The perturbation theory has allowed to the touch to use the another's formulas, namely formulas describing forces of a gravitation created by aether.

The tidal theory of interplanetary resonances - a myth constructed on concept of a tidal friction, but completely absurd, disregarding actual absence of an arm on planetary distances and assigning substantially nonexistent friction to elastic micro-strains of planets under operation of a micro-gravitation each other.

Special Relativity Theory (SRT) - a myth, based on illogical concept of irrespective speed of light. Within the framework of this myth the light has a speed in itself, irrespectively to anything.

As is known from classical physics, the concept of speed arises during motion of one object concerning another, and mathematically expresses as a derivative of path on time. Without the second object, concerning which the speed is measured as change of distance in due course, this concept loses any sense.

In the SRT myth speed of light is a constant simultaneously in relation to objects moving with different speeds in different directions. Thus, at acceptance of this myth both time and space lose sense of independent measures.

Objectivity of motion and phenomenon fades. It become dependent from arbitrariness of the observer, place, angle and speed of observation.

Basically, in mathematical model of space - time of Minkowski it would be possible to invert a reality from legs on a head and to fasten this nonsense to quantitative data of physical experiment. But there are some but.

In 1748 M. Lomonosov and after him A. Loviesier in 1789 experimentally have shown, that the substance does not fade and does not occur in chemical reactions. In 1847 Hermann von Helmholtz has extended conservation laws on all kinds of energy and substance [43]. Basically, it also should be expected, if we live in a causal world. In a causal world should not anything fade and come up. That would be violation of causality. If the causality is upset, logic and science are simply senseless, and it is not necessary to be engaged in them.

The principle of causality conducts inevitably to the law of a non-manipulability of time.

The time in a causal world should be homogeneous and unidirectional. At uneven of time measure causality is upset. The conservation laws, which, on definition, make sense only at homogeneity and uniform of time lose their force. It is possible to say same about a mathematical idol - Lagrangian.

Thus, mathematically self-sufficient in themselves, the formalism of curved space - time of SRT do not correspond to a principle of a causality and physical reality.

Though the centenary juggling of facts contradicting to SRT, for example, Sagnac effect, has resulted also in creation of a powerful arsenal of scholastically sharpened examples of its confirmation, more new facts refuting SRT are occurring (invariance of the shape of bodies at subluminal velocity, difference from SRT the data of a global navigational system GPS [37, 38], superluminal velocity in active environments (lasers) [39, 40] and remote coherent states - teleportation) [41].

The General Theory of Relativity - a mythical theory of gravitation, based the formulas of actual aethereal works of Paul Gerber [25-27] and mathematical formalism of David Hilbert [31], binding a relativity of Lorenz - Poincare with the Newtonian theory of gravitation.

This myth not founding of any essential actual confirmation, but having powerful political support, became a banner of mathematical physics of 20-th century and became the brake of new space technologies.

Galileo's Principle, Hooke's Force, Gauss's and Gerber's Potentials in Aether

The true knowledge is knowledge by causes

F. Bacon

As it is shown in [18], each particle of substance, being a pole of a disturbance within aether, creates around of itself a field of deformation, which density drops back to cube of distance. As against Newtonian field this field is additive for several gravitating bodies.

Last allows easily to manipulate by gravitational forces, solving a problem of gravitational interaction of many bodies.

As against existing judgement, that weight and the energy is attribute of substance (material), in a reality, the substance is only aggregate of poles of deformations of aether, and observed property of inertia of substance, and its energy are attributes of a perturbed aether.

Energy E = mc2 is an energy of field of deformations of aether around of mass m, that is energy of gravitational field. As a matter of fact, the inertia of aether subjected to deformation determines a value of mass [10].

The deformation of aether arises together with a pressure differential in aether caused by phase change in aether, the presence of discharges of aether in particles of gravitating material. According to the laws of hydrodynamics discovered in 18-th century by Daniel Bernoulli [21] and Leonhard Euler [22], such difference creates force close to a return square of distance between gravitating bodies. It appears in modern theoretical physics as Newtonian force of a gravitation.

In case of many bodies, close distances and high speed the deviation from Newtonian law of gravitation are essential.

How to calculate these forces? The base it is created centuries ago.

First of all, it is Galilean principle of a velocity addition and Galilean principle of relativity corrected for high speed of movement of deformations in aether. The running speed of a deformation field is known for a long time is a speed of light.

Secondly it is the mathematical theory of the potential, designed by Karl Friedrich Gauss, and in particular, its last modification of 1845 - retarded potentials. Unfortunately ingenious Gauss has left in another world before publishing results on retarded potentials, and his letter with presentation of idea of transmission of potential through environment with final speed of propagation was hide by W. Weber from scientific community, and Gauss's solution is presented in the distorted kind as Weber's own solution [29, 42].

Partly therefore at the end of 19-th century Paul Gerber needed to find the solution of this problem by himself, and he has executed it with honor [24-27], having applied the theory of retarded potentials to a solution of a problem of anomalous motion of Mercury. Unfortunately, soon after publication of his articles Gerber has left in another world, and his transactions utilized for relativistic hoax of Einstein [32-35].

Retarded potential of a gravitational field in aether

The gravity of resting body is nothing else than the retarded motion

M. Lomonosov, 1740

In the concept of the aethereal theory of gravitation celestial bodies do not effect against each other directly, and interact only with a gravitational field in a place of the presence in the given moment.

As it is shown in [18] the energy distribution of a gravitational field is determined by deformation (pressure variation) ether around of a gravitating body of mass m

Hooke = mc2/R3 [Pa],

where c - is speed of light, R - is a distance from a body.

At relative motion of two bodies the gravitational field owing to final velocity of propagation c reaches other body a bit later Δt = R/c, therefore the gravitational field of first body for the second body is visible as

Hooke = m(c-v)2/R3 [Pa],


where v = dR/dt - is velocity of relative motion of bodies (positive at moving away and negative at approach of bodies).

Let's remark, that the velocity addition in this case is purely Gagilean. Namely the value (1) is a potential, which affects the second body. It is additive in relation to potentials created by all other bodies.

The potential (1) can be decomposed on parts dependent and independent of relative velocity

Hooke = mc2(1-2v/c+v2/c2)/R3 [Pa],


The second term of decomposition makes 10-4 parts of first at usual velocity of planets, and third term is 10-8 of first term. As against Newtonian interaction, which is a particular case of the first term in (2) in case of single gravitating (heavy) body, Hooke's potential (1), (2) creates uncompensated effect into orbits of planets by terms dependent from relative velocities of celestial bodies, causing the rotational displacements of perihelions, that is transmitting a moment of momentum from one planet to another.

For illustration of it let's consider figure 1, where the relative motion of planets is shown.

Fig. 1. Interplanetary disturbances in aethereal gravitational field.

( 1 - is relative motion of an external planet, 2 - is relative motion of an internal planet, 3 - is line of quadratures)

In figure 1, where planetary motion is a common counter-clockwise, but the motions of planets are figured concerning a middle planet P, on which an internal planet Pinn and external planet Pout effect Thus, that the orbital velocity of an external planet is less than planet P, the planet Pout goes counter-clockwise relatively P. Contrary, the planet Pinn goes clockwise from the point of view of planet P.

As it is understandable from figure 1 and from formula (2) in the lower quadrants Pout leaves from P, and its effect is less than in upper quadrants. And about Pinn we can say inverse.

In this connection tangential component of circle integrals of gravitational effect will be non-zero. The effect from an external planet will cause to positive motion of a perihelion of planet P, and an effect of internal planet cause to negative motion.

This is a secret of normal motion of planetary perihelion.

In 1898 Paul Gerber has considered the effect of lag of a gravity potential of the Sun on planets having an eccentricities, that is approaching and leaving from the Sun. He wrote about process of a gravitation [24, Ch.J. Bjerknes's translation]:

However, if by the stated process it takes time to move from one place to another place, this means that it ceases to exist at the first position, without simultaneously being in the second place. Therefore, the energy contained in the process would dissipate through time, if it does not pass through the intermediary points between the two places. It equals the stated work when the process applies to the gravitation of two masses found in the positions, since it then likewise depends upon their position and present state of motion, and these cannot signify two different amounts of energy.

Reasoning thus Paul Gerber has received the formula of potential of gravitational field in a view of relative motion of bodies within the second order accuracy relatively c


where γ - is a gravitational constant, M - is a mass of a body creating a gravitational field, R - is a distance up to a planet, c - is velocity of propagation of gravitation.

Really, if we closely consider elliptical orbit, we will see, that in an interval from an aphelion up to a perihelion the planet goes to the Sun, and during motion from a perihelion up to an aphelion it leaves. The operation of a potential (3) (or all the same (2)) results that in halfcycle from an aphelion up to a perihelion the planet meets the greater attraction of the Sun, than in halfcycle from a perihelion up to an aphelion. It results in actual bending of an elliptical trajectory and perihelion advance in the orbital motion direction. There is no any distortion of a space-time in against of mythical GTR. Orbit of a planet gains a kind shown in fig. 2.

Thus Paul Gerber has received precise values of anomalous motion of perihelion which LeVerrier can not find


Variable from velocity of relative motion of bodies the parts of potentials (2) and (3) do not differ in a physical quantity, but only formally - mathematically in the third term of eq. (2), substantially making no more than 10-8 part of a potential (1)

Fig. 2. Motion of a perihelion (the value is exaggerated for visualization).

dω - is a motion of perihelion for one orbital period.

In sum the "normal" and the "anomalous" components of planets effect to each other yield observable motion of perihelion.

The "normal" motions of perihelions according to formula (2) calculated by the author, and components of "anomalous" motions of perihelions according Gerber's formula (3) for planets of Solar system outgoing from abbreviated flat model of Solar system and without considering of resonances of distant planets and influence of Moon, Earth's heavy satellite are listed in table 1.

Table 1. A full composition of components of motions of perihelions of planets

( in arcseconds per century)




































































































In the last line of table the values of perihelions motions observed by NASA are shown.


Stability of Planetary System and Titius-Bode Rule

"Where were you when I laid the Earth's foundation? Tell me, if you understand. Who marked off its dimensions? Tell me, if you know. Who stretched a measuring line across it? On what were its footings set, or who laid its cornerstone - while the morning stars sang together and all the angels shouted for joy?"

[ Job. 38,4:7]

Within the framework of the offered aethereal concept the motion of perihelions is transmission of a moment of momentum from each planet to another. From the table 1 it is visible that as a result of exchange of the moments the part of planets increases the moment (receiving energy), and the part of it reduces moment of momentum (returning energy). What does it connect with? To what it will cause after a long time?

Let's consider closely figure 1. It is visible that at transition through a quadrature the sign of radial component of planetary disturbances varies. Besides if the radii of adjacent planetary orbits have relate equal 2:1:1/2, at absence of disturbances from other external forces, the integral of radial component will be equal to zero.

It is a primitive condition of long-lived equilibrium and stability of planetary orbits appropriate for distant (outer) planets.

However Solar system exists not in itself, but in a gravitational field of Galaxy. This field which can be characterized by Galactic aethereal wind [13], sets parameters of motion of Sun and planets. The relative motion of planets results in reallocation of a moment of momentum between them depending on ratio of radii of orbits.

Considering motion of Sun, it is possible to make a unambiguous conclusion that it has received the moment of momentum during all many billions years life, through a sluggish accretion of interstellar cometary material. This process corresponds in accuracy to Immanuel Kant's concept, 1755 [36].

Being finally refused from Ptolemean geocentric conception, it is necessary to agree that not the Ecliptic, - orbital plane of the Earth, but the plane of Galaxy is a main factor in motion and evolution of Solar system: the plane of rotation of Sun which has arisen from material of Galaxy, orbital plane of a Mercury strictly bounded with Sun are in a plane of Galaxy as far as the orbital motion of Sun around of center of Galaxy allows. The Ecliptic owing to an off-center position of the Earth and influence of Jupiter has 7 deviation from the Galactic plane.

The moment of momentum obtained by Sun corresponds in accuracy to value of velocity of galactic aethereal wind discovered by the author in [13]

vtrans = 47872 [m/s]

Sluggish accumulation (accretion) of material on Sun on galactic orbit appropriate to this value of a galactic aethereal wind yields a solar rotation period


This formula is true for other stars of the Main Sequence.

As shown in [13], the galactic aethereal wind shapes around of a star orbital niches that are zones of minimum interplanetary influence. The proximate to star planet (niche) is leading. Its cycle time around of star and mean radius of orbit are determined by next expressions


Having substituted in (6) the mass of Sun we will receive precise values of cycle time and radius of Mercury's orbit.

The asymptotic values of radii of remaining planets are determined by Titius-Bode Rule, which now has the analytical solution [13]

where i = 1, 2, 3 - is a number of planet.

The rotation of a star creates an off-center gravitational field agrees eq. (2), as left or western hemisphere concerning a direction on a planet goes to the direction of a planet with velocity defined from (5), and east hemisphere, to the contrary, goes from a planet. It creates displacement to west of center of a gravitation as it visible from a planet. The angle between stellar attractive force acting on a planet and inertial Galilean force (centrifugal force) is not equal π. It causes the orbit perturbation until to transition this orbit into a state, at which the integral of disturbance becomes equal to zero. It is reached at a definite eccentricity of orbit. Besides other planets influent to an eccentricity of planetary orbit depending on arrangement of their orbits (see table 1).

In the table 2 the eccentricities of planets of Solar system observed by NASA and calculated by the author for steady state motion are shown.

Table 2. Calculated ecal and observed eobs eccentricities of planets



























In computing model the interplanetary resonances and influence of Moon to an eccentricity of orbit of the Earth are not taken into account. However, that is a problem of techniques.

Interplanetary orbital and axial resonances

Once the Great Watchmaker will come and will place all on the places

Isaac Newton

As it is shown in [18], the deformations arising in aether transfer not only normal effects such as a pressure in an ideal superfluid liquid, but also shearing strain (light) and torsion. Being absolutely elastic medium (up to time, commensurable with Anastasia constant = 1/H, H - is Hubble constant [4]), the aether transmits these deformations from one celestial body to another.

It becomes apparent at imagination of particles of substance as poles of aethereal deformation, when the motion of aether is bound to a particle, when aether feels a motion of pole-particle timelagged on t apart R = ct, and the aether is the carrier of inertia of this particle.

In this notion at once the cubic relation of resonant influences between celestial bodies is understandable. Even these bodies are remote, small and elastic. As it is known for elastic body it is impossible to speak seriously about tidal friction.

Having looked on our Solar system, we see a lot of resonances which are setting in motion each celestial body in a precise commensurability with others, just as the cogwheels in mechanical clocks are connected. Table 3 shows the part of resonances of celestial bodies of our planetary system.

Table 3. Some resonances of celestial bodies






Axial rotation of Sun

29,34 d

Axial rotation of Mercury

58,65 d


Axial rotation of Sun

29,34 d

Orbital period of Mercury

87,97 d


Axial rotation of Sun

29,34 d

Axial rotation of Moon

29,53 d


Axial rotation of Sun

29,34 d

Axial rotation of solar core

9600 s


Axial rotation of solar core

9600,0 s

Daily Earth's rotation

86400 s


Axial rotation of solar core

9600,0 s

Axial Martian rotation

24 h 40 m


Axial rotation of solar core

9600,0 s

Axial rotation of planets and asteroids

10 h 40 m



Galilean law of inertia and concept of aether of great scientists Democritus, Descartes, Hooke, Euler, Gauss and Gerber have allowed to find both physically qualitative, and quantitative solution of a problem of gravitation of many bodies.

As against of modern prejudices of theoretical physics, the Solar system is in quasi-steady and very much stable equilibrium. The radii and eccentricities of orbits, rotation rate of celestial bodies strictly depend from each other and are determined by properties of aether which is a basic matter of the Universe.

The aethereal theory of gravitation allows to understand processes forming planetary systems and allows to increase accuracy of cosmonavigation many orders higher.


The author is grateful to Professor Friedwardt Winterberg, University of Nevada, USA and Nickolay Noskov, National Nuclear Center of Kazakhstan for moral and scientific support of this research.

Author is grateful to Christopher Jon Bjerknes for Gerber's texts in German and English.



  1. Khaidarov K. A. Eternal Universe. - Borovoye, 2003.
  2. Khaidarov K. A. Gravitating Ether. - Borovoye, 2003.
  3. Khaidarov K. A. The New Lights. - Borovoye, 2003.
  4. Khaidarov K. A. Aethereal Breathing. - Borovoye, 2003.
  5. Khaidarov K. A. Aethereal Thermodynamics. - Almaty, 2003.
  6. Khaidarov K. A. Fast Gravitation. - Borovoye, 2003.
  7. Khaidarov K. A. Aethereal Atom. - Borovoye, 2004.
  8. Khaidarov K. A. Aethereal Electron. - Borovoye, 2004.
  9. Khaidarov K. A. Aethereal Theory of Conduction. - Borovoye, 2004.
  10. Khaidarov K. A. The Origin of Masses by Means of Natural Aeter Disturbing. - Almaty, 2004.
  11. Khaidarov K.A. The Nature of electricity as Motion of the Phase Ether. - Almaty , 2004.
  12. Khaidarov K.A. The Nature of Light as Combined Oscillation of Phase and Corpuscular Aethers. - Borovoye, 2004.
  13. Khaidarov K.A. Aethereal Wind. - Almaty, 2004.
  14. Khaidarov K.A. Aethereal Energy. - Almaty, 2004.
  15. Khaidarov K. A. The Structure of Celestial Bodies. - Almaty, 2004.
  16. Khaidarov K. A. The origin of the Sun and Planets. - Almaty, 2004.
  17. Khaidarov K.A. Real Solar Dynamics. - Borovoye, 2004.
  18. Khaidarov K.A. Aethereal Mechanics. - Almaty, 2005.
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Karim Khaidarov

Borovoye, March 1, 2005.

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