astronomical lviv 1771. on representation of magnetized gas structures during mass transfer in beta...
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Astronomical Lviv 1771
On representation of magnetized gas structures
during mass transferin Beta Lyrae system
Skulsky M.Yu.Lviv Polytechnic National University, UkraineE-mail: [email protected]
A little backgroundHalf a century I carry out spectral studies well-known
interacting massive binary system Beta Lyr, the results of which led to some progress in the interpretation of the physical nature of the system. First of all, it concerns the identification lines of accretor and determination of the masses of both components directly from a spectrum of systems, detection and investigation of the magnetic field of the donor, the study of the dynamics and structure of the accretion disk. The most systematic observations carried out on a powerful telescopes of that time, particularly on the 2.6-m telescope of the Crimean and 6-m telescope of the Special astrophysical observatories (SAO).
Schematic model of the interacting binary system Lyrae (view from above of the orbit plane): the bright B8III donor with mass of M1 = 2.9 M and accretor with mass of M⊙ 2 = 13M that is wrapped by thick ⊙disk with pseudoatmosphere of A5III type. For the mass ratio of 0.223 the distance between the centers of the two components is A = 58R . ⊙ With the observer’s eyesight towards the center component are defined scopes of hot regions on disk in phases 0.40P and 0.80P (according to [1]) and other directions observation (0.0P phase corresponds to the center of the main eclipse in the binary system). The mass transfer from the donor up to the accretor (so-called fan structure of gas streams is designated by curved arrows) occurs both in the direction between gravitational centers of the two components along of the orbital phases 0.5-0.0P and in the direction of the magnetic field axis "H" along of the phases 0.35-0.85P. This leads to shock collisions and the appearance of "hot half-arc" on the accretion disk edge (thick line). The orbital phases 0.05P and 0.95P of the optimal projections of the disk edges (so-called satellite-disk) on donor are marked. In these phases in the spectrum of the system is clearly visible so-called satellite-lines with radial velocities of opposite signs (up to 250-270 km/s), reflecting the rotational effect of the disk. The satellite-disk size is marked by two rows of rounded arrows and the small circle within this satellite-disk is showing the center of mass of the binary system.
The recent investigation was caused by the publications of the results of the self-consistent simulations of the light curves of the well-known massive close binary system Beta Lyrae. The one major among them is the statement of the significant contribution of the accretion disk radiation in the light curve of the system. In particular, there were identified two hot regions with temperatures that are 10% and 20% higher than the average on the disk rim. It is assumed that these shock regions might be formed by gas flows in regions of collisions on the disk in the mass transfer between components.
Indeed, the hotter region of the rim disk at the phase 0.40P is explained naturally by the Coriolis force deflection of the main gas flow that is directed from a donor through a Lagrange point to the aссretor's Roche lobe and with a further collision of this flow with the disk. However, this explanation can not be suitable to a wide hot region of the disk rim that is observed at the phase 0.80P.
Our analysis of absolute spectrophotometry, of curves change of magnetic field, of radial velocities and intensities of spectral lines along the orbital phases indicates that the hot region on disk at phases near 0.80P has a special nature. The donor's magnetic field should be taken into account because at these phases its dipole axis is actually aimed to the observer and deflected towards disk of the accretor. This hot region on the disk can be formed by the collision with this disk of magnetized gas which is canalized by the donor magnetic field in a certain way oriented in space. The energy effect of the collision on the disc is significantly strengthened by the counter rotation of the outer edges disc towards the falling gas flows. The structure of the donor's magnetic field is effective at heating and the hotter region on the disk rim at phases near 0.40P. The specific configuration of the magnetic field of the donor explains why at rotation of the donor and the accretor around their common center of masses on line of sight of the observer these two hotter regions dominate on the accretion disk.
At the top - the variability with the orbital phase of the
donor’s effective magnetic field;
in the middle - the variability with orbital phase of absolute
radiation flux in H-alpha emission;
beneath - a 20% increase of the radiation flux in H-alpha emission at collisions with a
disk of gas flows in the phase of 0.40P
Changes of the radial velocities of red (at the
top) and of violet (beneath) emission
peaks in the CIII1175 line with the orbital
phase. Poles of the donor's magnetic field
along the axis of «H» in the phases 0.35P-0.85P are marked as lines with
arrows.
The main result of the comparison of different data methodically following observations: the Beta Lyrae system shows clear correlation the variability with orbital phase of absolute radiation flux in H-alpha emission and the variability with the orbital phase of the donor’s effective magnetic field. The figure shows that both extremes dependencies agree along the orbital phase.
The behavior of the spectral lines outside the Lyman limit varies similarly.
The main conclusion is that the mass transfer, the formation of circumstellar gas structures, their
dynamics and energetics are regulated by magnetic field of the donor.
But there are many questions primarily to specialists such direction Conference. For example, thirty years I have no answers to the 10-second observations in the line H-alpha on the 6-m telescope of SAO. It concerns the unusually large variability of the line H-alpha when observations are conducted in the orbital phase magnetic poles on the donor. What is the nature of this phenomenon? Maybe someone will be surprised and interested? Those who try to meet this challenge, I suggest cooperation.
Now, concerning of our understanding of the new phenomenon according to the second declared theme
On the spatial structure
and wave resonances
in the Solar planetary system
Skulsky M.Yu.Lviv Polytechnic National University, Ukraine
E-mail: [email protected]
Our interest in this research coincided with the discovery of extrasolar planet systems.Several hundreds studied exoplanets and tens their systems promoted a research of scenarios of their dynamical evolution. The main scenarios of formation of planetary systems are researched on the basis of the so-called Nice Model.
The principal conclusion is that there is no universal rule for the ordering of the planets with scientifically proved physical mechanism.Neither the Titius-Bode law and its modifications to the Solar system, or some regularities in the structures of the exoplanet systems are not substantiated certain physical mechanism.
At the same time, for the Solar system were revealed principles the ordering of planets on the basis the program of magnetic field registration of the Sun as a star. Our study of these principles offers a wave algorithm of the ordering of planets in the Solar system.
The results of its wave structurization are publish in: Skulsky M.Yu. // Astron. School's Report. 2011, V. 7, N 1, P. 28-35; and: Skulsky M.Yu. On the wave structure in the spatial organization of the Solar planetary system // Science and Education a New Dimension. Natural and Technical Sciences, III(5), Issue 41, Р. 63-67, 2015. www.seanewdim.com
The planets in Solar System (Kotov V. and Kuchmi S., 1985) is followed to two simple laws:
- for circular orbits of the inner planets,
- for the sections of the orbits of the outer planets
(here - semi-major axis of the orbit, n - the first natural numbers). For the inner planets (Mercury, Venus, Earth and Mars) n = 8, 4, 3, 2, to asteroids - n = 1. For outer (Saturn, Uranus, Neptune) and dwarf planets (Pluto and Eris) this natural numbers is respectively: n = 1, 2, 3, 4, 7. Only by Jupiter n = 1/2, i.e. fractional. The physical nature of these laws was not clear.
nLa /2 nLa 2a
Since the L - scale has the dimension of a wave with a length = c P = 19.24 AU, the both laws L - resonance transformed us into a wave notation. They were similar standing wave equations describing the numerous physical processes. And the planets in the Solar system are located on the algorithm of standing waves with a length
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Standing waves
Thus, the radial arrangement of the outer planets corresponds the definition of the phenomenon of standing waves. It is known that:
a standing wave is formed by the interference between direct and reflected waves at opposite their propagation in the same body; the standing wave is - half wave; linear dimension this body is a multiple of a quarter wave ; along with the multiplicity of the body are the vibration nodes and anti-nodes, respectively, with the double amplitude and amplitude of zero.
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The spatial organization of the Solar planetary system is described by two interrelated kinematic algorithms of the single wave mechanism that is similar to the phenomenon of standing waves with length (here: 19.24 AU, is the speed of light and =160 min is a period of global oscillations of the Sun). The principle of the ordering for outer planets and dwarf planets is represented in the wave form as or (where is a semi-major axis and is a whole number) by arranging these planets at distances from the Sun proportional to a quarter and a half of the wavelength (Jupiter - , Saturn - , Uranium – 2 , Neptune – 3 , Pluto – 4 , Eris – 7 ). The principle of the orbit ordering for inner planets is expressed as with the step and 3, 6, 8, 12 for orbit lengths from Mercury to Mars that is commensurable with the length of standing wave and its harmonics.
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Importantly, it was revealed an explicit resonance of proper oscillations of the Sun and planets. Their global periods are virtually multiples to , where 1, 2, 3. These signs of a quantization of the gravitational interaction of the Sun as a star and planets are related to the length of the standing wave . Wave and gravitational resonances put questions about their origin in the Solar system. Also such interconnected findings should be considered as essential on the background of the current knowledge about the laws of structuring planets in the Solar and exoplanet systems.
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Objective evidence
Table 1 contains the Solar system characteristics: masses, semi-major axes of the planet orbits, semi-major axis ratio to wavelengths and other. The slides are the result of the analysis of this table, figures and other data.
Structural architecture of the outer planets
The regularity of L - resonance for cross sections of the orbits of the outer planets in the wave notation is . It is found that the distances of the outer planets from the Sun are multiple of a quarter or half wave: Jupiter - , Saturn - , Uranus - 2 Neptune - 3 Distances well-known dwarf planets are: Pluto - 4 and more distant Eris - 7 - see Figure 1.
For Jupiter and n = 0.
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Distances of trans-Neptunian comet families
The distribution of periodic comet aphelions with very eccentric orbits and direct motion near the plane of the ecliptic was obtained in the range of 15 - 200 AU (Kozlov V. - Astron. School's Report, 2009, V.6, N2, R.163). Three families of comet at average distances 56, 86 and 106 AU, which corresponds to 2.91, 4.47 and 5.51 or in standing waves to 6, 9 and 11 was located.
Conclusion: The distance trans-Neptunian comet families from the Sun are multiples of the standing wave length as a parameter of their location.
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The principle of outer planet ordering as the phenomenon related to phenomenon of standing waves
Standing waves and outer objects in the Solar system
So, the working formula for the distance of external objects from the Sun: ,where - the length of the standing wave ( = c P = 19.24 AU).The outer planets (except Jupiter) and the majority of trans-Neptunian objects, including a family of comets, described by the relation , when = 1,2,3,…11 (to a distance of 110 AU). The relation described the distance from the Sun by one third of trans-Neptunian objects and Jupiter is: (for Jupiter = 0). The principal conclusion: in this algorithm of standing waves Jupiter is located at the shortest distance from the Sun, and this algorithm can not describe the radial ordering of the inner planets.
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The wave structure of inner planets
The inner planets can not obey the wave algorithm inherent in the outer planets, as they are located from the Sun within
And really for them there are the another principle of L – resonance:
Transforming this principle to the form we obtaine an equation of standing waves for circles orbits of the inner planets.
Here: - “daughter" standing wave;
numbers 3, 6, 8, 12 commensurate to the length of the standing wave and its harmonics quantized the length of orbits of the inner planets, respectively, from Mercury to Mars.
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The inner planets: structural architectureThe relation for lengths of planet orbits (see Table 1) from Mercury to Mars is represented in the form:
or
The length of the orbit of Mars is directly equal to the length of the standing wave , in the lengths of the orbits of Venus and Mercury are embedded on one of its first and third harmonic, and in the length of the orbit of the Earth - its two second harmonics.
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Fragments of schematic orbits of the inner planets are presented in the fractions of the wavelength .
Distances to the planets are normalized to the semi-major axis of Earth's orbit
Therefore, the spatial organization of the Solar planetary system could be formed in one physical process but in two interrelated kinematic algorithms of the one wave mechanism.
The length of the standing wave seen as the structural factor in the Solar planetary system. These results are unusual but they are interconnected on the basis of the simple physical equations for standing waves that are identical to those in many physical processes
What is the nature of the phenomenon?
Phenomenon of standing waves and resonance of the proper oscillations of the Sun and the planets
It is known that the academician B. A. Severnydrew attention to the surprising proximity of the detected 160-minute oscillations of the Sun and a "global" proper oscillations of the Sun, equal to 167 minutes.
In connection with the phenomenon of standing waves we are interested in this and discovered the resonance of such proper oscillations of the Sun and planets...
Periods of proper oscillations of the Sun and the planets
The formula used to estimate the "global" periods of proper oscillations of the Sun and the planets of mass M and radius R, is known: It is valid for spherical gravitating objects with mass M, assuming a homogeneous gravitational field of a spherically symmetric distribution of mass. It is true and for a period in which a particle of mass m execute harmonic oscillations at a distance X from the center of the sphere (and at its surface, where X = R):
Here: and G - the gravitational constant.
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)/(2)/(2)/(2)/(2 3 GMRgRgXkmT 2/ RGMg
The resonance of proper oscillations of the Sun and the planets
Proper period of the Sun oscillation is 167.3 minutes and close to the period of global pulsations (P = 160 minutes). Calculated T-periods are, respectively for the inner planets from Mercury to Mars 85, 90, 84 and 100 minutes, and for the outer planets from Jupiter to Neptune - 172, 236, 177 and 158 minutes. Proper oscillations of the inner planets (with a average deviation of about 5%) are in resonance with the global oscillations of the Sun at a ratio of 0.5: 1, and outer planets - as a 1: 1 (for Saturn - 1: 1.5), that are its first harmonics, reflecting in 0.5 P comprehensive resonance of proper oscillations of the Sun and the planets -Table1
The resonance of proper oscillations of the Sun and the planets
This can be described by the simple equation . It obeys the rules of integers k = 1, 2, 3 and here P/2 as the first harmonic of P-pulsations of the Sun is the least common multiple for these T-periods (with an average relative error in 5%). It is recognized that there is a common resonance of global oscillations of planets and Sun. It is the first unusual result: the whole “planetary orchestra” is tuned to the frequency of global pulsations of the Sun. Table 1 shows also for all of these objects that there is the second simple equation , where k = 1, 2, 3. Consequently, global oscillations of planets are determined of this standing wave. There is the second unusual result: periods of global oscillations of planets and the Sun are directly associated with the standing wave as with the structural factor in the Solar system.
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The resonance of proper oscillations of the Sun and the planets
•So, the relative positions of both types of planets, their sizes and weight as related phenomena are immediately related to the length of the standing wave as a structural factor •In general, these simple calculations gave unexpected results about the unusual aspects of gravitational interactions between the Sun and the planets. These data can be be seen as proof the the existence of global “enigmatic” P-pulsations of the Sun.
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As to a criticism of standing waves phenomenon and the Solar system structure -1
The problem consists in that the wave algorithm in the structure of the Solar system confirms existence of P-pulsations of the Sun, while theoretical studies of internal structure of the Sun do not confirm the existence of these pulsations (Appourchaux and Palle 2013). They note the fast damping of low-frequency g-modes at their transfer to surface of the Sun. However, it should be noted that one of possible variants in searches of an answer can consist in consideration of the interaction of gravitational and magnetodynamic processes. First, we consider here the own pulsation of the Sun as a whole (it is the global period). Indeed, the surface P-pulsations of the Sun (Severny et al. 1976, Kotov and Khanejchuk 2011) were revealed by the method of registration the magnetic field of the Sun as a star.
As to a criticism of standing waves phenomenon and the Solar system structure -1 (continuation)
Second, it is known that tachocline region which is responsible for the enhancement of the magnetic field of the Sun and plays a key role in nature solar cycle lies on the bottom of the convection zone. The global g-modes should reach this zone without significant damping. It allows to suppose the modulation of general magnetic field by g-modes and their transfer together with this field to surface of the Sun. Then the impact on the structure of planets will be carried out the magnetic field of the Sun which is modulated by the low-frequency oscillations of global g-modes. In this aspect, such observation method is a promising in the study of the internal structure of the Sun and solar-planetary interactions. In particular, one can expect to detect the variability of the P-pulsations of the Sun within the 22-year cycle.
As to a criticism of standing waves phenomenon and the Solar system structure - 2
This is a question about the origin and nature of this phenomenon. Empiric data offer a suggestion that global P-pulsations of the Sun, regardless of reason and time of their origin, were able to synchronize and save the wave structure of the Solar system in the process of its evolution up to the present tense, although now these pulsations can be observed in relict form. In the terms of the current knowledge, it is not difficult to represent the scenario of forming of the Solar system by the mechanism of interference of coherent waves within a protoplanetary disk but without considering the physical nature of these waves (Skulsky 2011, 2015). These waves have the velocity of light, but it is difficult to study them with the help of hypotheses of the electromagnetic or gravitational nature.
As to a criticism of standing waves phenomenon and the Solar system structure – 2 (continuation)
The energy of electromagnetic waves with 19.24 AU is very small. Nevertheless, it would be interesting to model the formation of planets in the protoplanetary disk taking into account the influence of the Schumann-like resonances (Schuman 1952) in the cavity between the surface of the young Sun and ionized gravitational shafts. A possibility of origin and interference of coherent waves from spherical objects interacting gravitationally is problematic because this is forbidden in the general theory of relativity. However, there are other possible interpretations of gravitation. For example, the gravitational field can have not only the tensor component (as in the general relativity) but also the scalar one. The scalar component may be emitted in spherically symmetric oscillations of any source of gravitation, including the Sun. The phenomenon of wave structurization of the Solar system can be represented as a relativistic delay of scalar part of the gravitational field or a disturbance on the newtonian potential. In any case, the hypothesis of the possible existence of gravitational waves (including those with length in 19.24 A.U.) and their interaction can have the right to existence although it is not easy to interpret in terms of the accepted modern concepts.
• The task outlined by the Crimea AO in 1960s for registration the magnetic field of the Sun as a star advanced afterwards systematic measurements of global photospheric oscillations. They based on measurements of the Doppler effect in iron line on 512.37 nm with zero Lande factor. This program led to discovery of “enigmatic” pulsations of the Sun with a period 160 min (Severny et al. 1976) and the ordering of planets in the Solar system (Kotov and Kuchmi 1985, Kotov and Khanejchuk 2011).
Severny A., Kotov V., Tsap. T. Nature 1976, V. 259, P. 87; Scherrer P.H, Wilcox J.M. Solar Phys. 1983, V.82, P.37
Kotov V., Kuchmi S. Izv. Crim. Astr. Obs.1985, V. 72, P. 199;
Kotov V., Khanejchuk V. Izv. Crim. Astr. Obs. 2011, V.107, P. 99.
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Kotov V. and Kuchmi S. (Izv. Crim. Astr. Obs.1985, V. 72, P. 199) discovered resonance proportionality orbital sizes of
the planets of the Solar system with "scale” L = c P = 19.24 AU, where c - speed of light and P = 160 min - the pulsation period of the Sun.
Their "resonance spectrum" (similar to the power spectrum) showed a single strong peak corresponding to L - scale. The statistical significance of the peak (16 objects for the system) is now estimated (Kotov V., Khanejchuk V. Izv. Crim. Astr. Obs. 2011, V.107, P. 99) at around 4 sigma pointing to a common “L - resonance" of the planets in Solar System (SS).
What is the nature of the phenomenon?
Indeed, according to estimates made by Molchanov (Molchanov А.М., Icarus, 11, 95, 1969) the probability of casual formation of the planetary system with properties of the Solar system is about from 10-10 to 10-11.
The length of the standing wave seen as the structural factor in the Solar planetary system. These results are unusual but they are interconnected on the basis of the simple physical equations.
Therefore, let us consider the prehistory of this phenomenon at a well-known critical attitude to the pulsations of the Sun with a period of 160 min
The principle of outer planet ordering as the phenomenon related to phenomenon of standing waves
Standing waves and transneptunians objects
•Outside the orbit of Neptune (Edgeworth-Kuiper area) near 20 objects with the apparent size from 600 to 2600 km and determined kinematic parameters of their orbits are known•1) semi-major axes of the majority of these TNOs are commensurated to even number •Pluto, Orcus and Ixion - 4.1 - 4-th node •2002AW - 4.9 - 5-th node •GK147, SM331, VK305, XR190, YW134 - 6 - 6-th node
•Eris and 2007OR - 7 - 7- th node
•2) semi-major axes of these TNOs are multiple to odd numbers• Haumea, Quaoar and Varuna - 4.5 or 9
•2007UK126 и CP105 - 7.5 and 8.5
•Conclusion: The distances between the Sun and the largest TNOs are multiple to
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The inner planets: the structure and resonances
A new form of equation of standing waves for circles orbits of the inner planets follows from simple resonant relations of length orbits for the planets Mercury - Venus, Venus - Earth, Earth - Mars. They are close to 1: 2, 3: 4, 2: 3.
Number 12 as the common denominator of these resonances is denoted a discrete set of "daughter" of standing waves or embedded into - the basic standing wave. In consideration of this, from the equation in a natural way (the number 24 is evenly divisible by the number m = 3, 6, 8, 12) we determine the relation for orbit lengths of four inner planet at wavelengths.
2/12 1 swsw 24/12/1 swsw
12 swma sw
Fragments of schematic orbits of the inner planets are presented in the fractions of the wavelength . Distances to the planets are normalized
to the semi-major axis of Earth's orbit
Limitedness of the inner planets in the Solar system
•It is logical to expect as follows from relations where m = 3, 6, 8, 12, that a wave train of the inner planet orbits have terminated the planet with the length of the orbit is equal (by m = 24). The absence of the inner planet from behind Mars (in place of the asteroid belt) can be explained not only conventional "pumping out" planetesimals Jupiter, but also the negative role of a powerful resonance 1: 1, what arises through equality the wavelength of the length and the orbit of a hypothetical planet. •The absence of the planets Mercury front with a minimum length of the orbits (m = 1, 2) can probably be explained by the role of the resonance wavelength of such orbits with the length of a "daughter " standing wave (for m = 1 the distance a planet from the Sun is 0.127 AU - in the exoplanet systems at such distances and up to 0.02 AU from the central star locate, as a rule, several planets - the Solar system is unique).
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Standing waves and the structure of the Solar system: Conclusions
The results of the wave represent in the two variants structuring of the Solar system are consistent in a united physical mechanism similar to the phenomenon of standing waves. The ordering of all the planets obeys the laws of integers or quantized, corresponding to a clear resonance relations. Deviations of the planetary system objects from the calculated position are within 2-5% what could be explained long evolution of the Solar system. Factor of standing waves become a new aspect of the wave planetary physics.
The mechanism of standing waves is simply to explain the basic questions of planetary cosmogony: why the planets' orbits are nearly circular and coplanar, why the distances of the planets from the Sun are arranged in a certain way, why the space of the Solar system is divided into two parts, and there are two groups of planets, the inner group of which consists of four planets.
Lovis et al. AAMan N HD10180,2010
As for the structure of the known planetary systems, first of all find out what the interaction between the planets moving, usually in orbits with large eccentricity, may lead to their migration. We also note that the first planet Mercury is a much greater distance than in the first planets in other systems (they have the same distance from the star filled several planets). And among the exoplanet systems that have planets with a mass of Jupiter, our Jupiter is at the greatest distance from the Sun as a star. In this respect, the structure of the Solar system is unique.
Objective evidence
Table 1 contains the Solar system characteristics: masses, semi-major axes of the planet orbits, semi-major axis ratio to wavelengths, calculated T –periods, specifically in parts of P-pulsations of the Sun. The slides are the result of the analysis of table, figures and other data.
Conclusions: phenomenon of standing waves and the Solar system structure - 1
The results of the wave investigation of the Solar system structure could be explained by existence of a physical mechanism similar to the phenomenon of standing waves presented in two variants but with the same length of the standing wave. The ordering of all planets obeys the rules of integers according to distinct resonance relations. These results can be considered as empirical and are quite accurate. Their average deviations from the calculated positions are within 3-5% which could be explained as a result of long-term evolution of the Solar system. It is reasonable to suppose that the formation of both groups of planets in the Solar system could be realized by means of a specific wave process. And their movements in a circle on the orbits corresponded to these wave processes.
Conclusions: phenomenon of standing waves and the Solar system structure - 2
Secondly, the analysis of the standing waves phenomenon evinced the common resonance of global oscillations of the Sun and planets. This resonance irrespective of the inner structure of these objects showed the definite connection between gravitational and waves processes. We should take into account that the gravitational interactions between the planets and the Sun as a star can be characterized without considering their detailed internal structure (the formula for the global period reflects the averaged densities for all objects). Their interactions are described by certain quantized parameters. It should be considered as an accomplished fact the good coincidence of effective radii of all objects according to the equation and their observed radii.
)/(2 3 GMRT
2/kPT
Conclusions: phenomenon of standing waves and the Solar system structure - 3
It is obvious that the Sun as a star and the planets are showing signs a quantization of their gravitational interaction and this is associated with the length of the standing wave as the structural factor in the Solar planetary system. These results are unusual but they are interconnected on the basis of the simple physical equations. In general, the discovered findings of this research are related to the basic foundations of our worldview and represent problem in their interpretation. Such studies should be continued because they raise questions about the formation of Solar and exoplanet systems. Thus, it is worth paying attention to the need for a more complete analysis of this physical problem.
Стоячие волны в Солнечной системе
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