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Stability of a solar system

Nikolay Noskov
Translated from Russian by Jury Sarychev

As soon as it has become clear, that the motion of planets is subjected to the laws of a mechanics of a rigid body, and their interaction to law of universal gravitation, then at the came time arose a problem on the future of a solar System. Whether is it possible to imagine its geometry and qualitative features through many millions years?

Yes, theoretically it is possible under following conditions:

From these conditions it is visible, that the problem looks practically insoluble. However physicists and the mathematicians have learned to make model, simplified problems. They select only essential characteristics and effects. The approximate methods of problem solution of a perturbation theory then multiply are checked up in practice.

The science is obliged to Poincare [1] (1854...1912) and Ljapunov [2] (1857...1918) to creation of a mathematically stringent and consistent theory of stability of motion. But for the first time problem of motion stability of planets was put forward by two outstanding mechanics and mathematicians Laplace [3] and Lagrange [4] (1773). The problem is to compound differential equations of motion of planets taking into account all disturbances and interference as well as to fix whether the inequalities is cyclic or century thus to determine whether the system is unstable or not. The Laplace and Lagrange by joint efforts have decided a problem of stability of a solar System only as a first approximation, which has appeared obviously insufficiently. It is necessary to note that all these activities on definition of stability of a solar System would be impossible without a laborious long work of the astronomers and mathematicians on definition of evolution of planetary orbits during several hundreds thousand years.

Arnold [5] (Russia), after the Poincare and Ljapunov, has prolonged to solve the problem of stability. He, it is considered, practically has decided a problem of stability of a solar System. But, despite of such apparently, outstanding outcome of the complicated mathematical researches, feelings of final victory above a problem do not arise. And that is why.

All of physicists and the mathematicians participated in activities on stability, were assured of finalities of a classic mechanics (the most of physicists is assured of it and now). However there are facts and theoretical premises, which one convince that the classic mechanics is not finished, and there are certain laws of the nature, which one are not open yet. The incompleteness of a classic mechanics also has brought physics in crisis in the beginning of XX century, to occurrence of a relativity theory and to waiving classic invariants.

Already more than two centuries the formula of Titsius- Bode [6] (1772) for planetary distances are in a center of attention of the researchers, however its secret while remains not open. In spite of the fact that the values of distances differ a little from calculated with formula, due to it the asteroid belt between Mars and Jupiter was retrieved, and Adams and Lever'e used it by search of Neptune. The sense of this formula became clear after the rise of quantum mechanics (1915). Distances of planets up to the Sun are expressed in this formula through an ordinal number of a planet that means only one – quantization! So, the solar System is quantized?!

After appearance in hand of the scientists of the powerful tool of a quantum mechanics for the description of a radiation spectrum and absorption of atom, the riddle of quantization has risen before the researchers in all beauty and inaccessibility. And it became clear, that the mechanism of radiation and absorption is connected to quantization of electronic shells. But, not having solved this secret in atom, the priests of science have imposed the secret veto on existence of the same secret in gravitation. So, in "to Nuclear physics" of Born [7] is readable: "...Stability of atoms is completely not clear from the classic point of view. For comparison let us imagine a system of planets revolved around of the Sun, each of which goes, if there is no disturbing effect, on definite constant orbit. Let's assume, however, that the solar System would appear suddenly in immediate proximity, for example, to the Sirius. Then this neighborhood already in itself would distort a trajectory of planets. If then the solar System was again deleted from the Sirius, the planets would become revolved around of the Sun already on new orbits with new angular rate and cycle times..."

Further Born makes a magnificent zigzag in logic, not noting that he contradicts himself. However, let's read up: "...If the electrons in atom were subject to the same mechanical laws, as planet of a solar System, a foregone corollary of any interaction between two atoms would be full change of base frequencies of electrons. So that after interaction each atom would radiate light of completely other lengths of waves. However, this is in the radical contradicts... with the experimental fact" (is selected by me – N.N.). Born has not noted here, that "the experimental fact" can contradict and with a solar System, as "stability of atoms is completely not clear from the classic point of view".

Let's return now again to a problem of stability of a solar System. We now see, that this problem can be resolved completely in other way, thus for in stance Chetaev [8] attempted to decide it. He has stated thought that "...the stability is principle general phenomenon. It should, apparently to appear in fundamental laws of the nature". The search of such laws has led him to quantum mechanics and to Schrödinger equations. However long-term activity in this direction, except for the expression of a hypothesis about quantization of a solar System, has led to nothing. And it is natural so far as quantum mechanics itself "is made" only "by guessing of equations and it has no reasonable basis". Besides Chetaev has not decided to refuse from Planck's constants, having indicated that this constant is suitable only for an electromagnetic interaction, while in a gravitation other constants should be used. You see nobody will use gravitation constant from a law of universal gravitation in a Coulomb's law!

After failure of Chetaev, Molchanov [9] has put forward idea that "evolutionally mature vibratory systems inexitably are resonance, and their constitution is formed (similarly to quantum systems) by set of integers". However idea about resonance is departure back in relation to quantization of Chetaev. You see in quantum mechanics and one electron in atom of hydrogen is subordinate to the laws of quantization. Therefore, the laws of quantization depend on more fundamental reasons inside the mechanics of motion. And such reasons lie on a surface: a resonance of oscillations imposed on one body. It is a widespread phenomenon in a mechanics. Thus, the resonance should be a solution of quantum mechanics.

After appearance of the formula of Titsius – Bode of hundred researchers attempted to improve this law, or to find another of causal character, but even most known of them of Smith [10] and Fisenkov [11] can not be considered as the formulas of quantization, as number of a planet enters in them only indirectly. It is necessary especially to mark importance of the formula of Fisenkov, as it includes mass of planets. For us it is very important for a following reason: the mass of planets can appear in the formula of quantization only in case if at it there is a ratio for lengths of de Broglie's waves. As at usage only of second Newton's law for calculation of the characteristics of orbits the planetary mass is not taken into account.

However it is necessary now to inform to the reader, that the new laws of a mechanics were already disclosed. Those are laws of delay of a potential (graviodynamics). In what is their essence? It appears, at grasping of the meaning of the laws of interaction and of transference of an interaction potential on distance, the researchers inevitably ought to come to concept of velocity of interaction. If the velocity of interaction is finite, and it is real so, the potential of interacting bodies starts to lag behind a moving body and laws of dynamics of the Galilei – Newton start to be distorted. The laws of delay of a potential of Gauss [12], of Weber [13] and Clausius [14] for an electromagnetic interaction and law of Gerber [15] for a gravitation display these distortions. Now it is very difficult to understand, why the scientific world of a planet till now has not understood importance of these discoveries, but I think, that it is connected to rise of a relativity theory and scrambling around of it.

About what reasons the relativity theory has appeared for, why it somewhat could substitute for the theory of a delayed potential and why it can not be considered valid, I wrote in the article "The General principle of relativity does not exist".

Investigating delay of a potential to moving bodies, I have found out, that the lag happens nonuniformly, therefore the body is subject to longitudinal vibrations (see article "Brilliance and poverty" of quantum mechanics"). Thus, the delay of a potential results in two fundamental consequences: 1) to reduction of force of interaction from velocity and 2) to longitudinal vibrations of moving bodies having the formula of a de Broglie's view for lengths of waves. That means a way out to quantum mechanics for any interaction, including for gravitation.

Hence, stable motion on orbit is on principal general phenomenon for any interaction. Therefore, quantization is necessary term. However at an obtaining of the formula for length of longitudinal vibrations (view of de Broglie) was found out, that the constant of quantization by a complicated way (through the law of interaction) depends on mass of a body. As in an electromagnetic interaction mass of electrons on orbit is constant, Planck's constant remains constant too.

The check of the retrieved relation for quantization of a solar System has shown following: as a first approximation without effect of mass of planets a theoretical curve of quantization (parabola) is close to observed. However detection of effect of mass on change of proportionality factor has appeared rather complicated and is in stage of search.

The finding of the law of quantization of planetary distances will have an effect on cosmogony. The mechanism of formation and evolution of planetary systems will be explained. That, in its turn, gives us the answer to a question: are we lonely in Universe?


The literature:

  1. A. Poincare. Selected transactionses in 3 volumes, v. 1, Gravitational astronomy. Science, M., 1971. In Russian.
  2. A.M. Lapunov. Selected transactionses. AS USSR, 1959. In Russian.
  3. P.S. Laplace. The report in Parisian AS, 1773. In: V.G. Djomin. "Destiny of a solar system". Science, M., 1969. In Russian.
  4. J.L. Lagrange. The article 1784. In: V.G. Djomin. "Destiny of a solar system". Science, M., 1969. In Russian.
  5. V.I. Arnold. The solution of a problem on motion stability in arbitrary Hamiltonian systems if there is permanent disturbances. In: V.G. Djomin. "Destiny of a solar system". Science, M., 1969. In Russian, page 209...240.
  6. I.E. Bode. The law of planetary distances established I.D. Titsius. 1772. In: R. Kurt "A dimensional Analysis in an astrophysics. World, M., 1975, page 196. In Russian.
  7. M. Born. Nuclear physics. Science, M., 1981. In Russian.
  8. N.G. Chetaev. Motion stability. Activities on an analytical mechanics. A S USSR, M., 1967. In Russian.
  9. A.M. Molchanov. Resonance of frame of a solar System. In: V.G. Djomin. "Destiny of a solar system". Science, M., 1969. In Russian.
  10. O.Ju. Shmidt. Four lectures about the theory of a geogenesis. AS USSR, M., 1954.
  11. V.G. Fisenkov. Transactionses of the First conference on cosmogony April 16...19, 1951. AS USSR, M., 1951.
  12. C.F. Gauss. Transactionses, V. 5, Royal science foundation, Goettingen, 1867. In: N.T. Roseveare. Mercury's perihelion from Le Verrier to Einstein. World, M., 1985, page 145. In Russian.
  13. W. Weber. Werke, Vol. 4, 247...299, Springer, Berlin, 1894. In: N.T. Roseveare. Mercury's perihelion from Le Verrier to Einstein. World, M., 1985, page 140...144. In Russian
  14. R. Clausius. Ableitung eines neuen electrodynamischen Grundgesetzes. J. Reine angew. Math., 82, 85...130, 1877. In: N.T. Roseveare. Mercury's perihelion from Le Verrier to Einstein. World, M., 1985, page 146. In Russian
  15. P. Gerber. Spatial and temporary propagation of a gravitation. Z. Math. Phys., 43, p. 93...104, 1898.

Is published earlier:

"Science of Kazakhstan", 15, 1999.

Date of the publication:

June 24, 2000

Electronic version:

© NiT. Current publications, 1997

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