The stability parameters of three-body periodic orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination.     

Some fundamental elements of universe mechanics

An essential part in the mechanics under study is taking into consideration the effect of motions of the Universe objects upon that of an individual one surrounded by them including those infinitely far from it. Only macro-objects of the Universe are meant here.

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Zusammenfassung Ein wesentlicher Bestandteil der Mechanik unter unserer Betrachtung ist die Berechnung des Einflusses auf die Bewegung eines individuellen Objektes von Bewegungen der Universum Objekte die es umringen einschließlich jene Objekte, die unendlich entfernt sind. Nur Makroobjekte des Weltalles sind in der Absicht dabei.

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Спектр и поляризация источника синхротронного излучения при релятивистском разлете его компонент

, , , . () , . , .     

Индуцированное комптоновское рассеяние изотропного излучения релятивистскими электронами

, kT _b mc ² . . , , . E ^–5, - E ², mc ²(kT /mc ²)^1/7. , (>2.10⁵ cm ^–3) . , -, , .     

Сопоставление модели карлсона с моделью сплошной среды

, (1962, 1963) . , (1) (2) .     

εлектроны космических лучей радиогало галактики

,      

Three-Dimensional p–q Resonant Orbits Close to Second Species Solutions

The purpose of this paper is to study, for small values of , the three-dimensional p–q resonant orbits that are close to periodic second species solutions (SSS) of the restricted three-body problem. The work is based on an analytic study of the in- and out-maps. These maps are associated to follow, under the flow of the problem, initial conditions on a sphere of radius around the small primary, and consider the images of those initial points on the same sphere. The out-map is associated to follow the flow forward in time and the in-map backwards. For both mappings we give analytical expressions in powers of the mass parameter. Once these expressions are obtained, we proceed to the study of the matching equations between both, obtaining initial conditions of orbits that will be 'periodic' with an error of the order ^1–, for some (1/3,1/2). Since, as 0, the inner solution and the outer solution will collide with the small primary, these orbits will be close to SSS.     

О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

-- () ., , , , , . , , . , .     

Critical inclinations in planetary problems

The general conception of the critical inclinations and eccentricities for theN-planet problem is introduced. The connection of this conception with the existence and stability of particular solutions is established. In the restricted circular problem of three bodies the existence of the critical inclinations is proved for any values of the ratio of semiaxes . The asymptotic behaviour of the critical inclinations as 1 is investigated.

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. . . 1.

     

О природе всплесков γ-излучения

- . , - . -.     

Оь излучении звезд типа Т Тельца в далеком ельтрафиоле те

, oqn ANS (1500–3300 Å) , I , 3–15 . , <2000 Å nepexo , 1.5 MB . ₀ , . .     

ОJ 287: Поляризационное и фотометрическое поведение В 1971–1976 гг

J 287 1972–1976. , . . J ( ), () . (₀=80°) . J 287 ¶ . p=42.8%, ₀=101°. (50%).     

Взаимооействие Излучения Рентгеновскооо Истооника с АтмосФерой Нормальной Звезды в Тесных Двойных Системах

, . : , . , . . ( ) . . . HZ Her=Her X1, . . , . , ., hv 15–30 . , . Sco X1 .     

The development and production of new,non-standard methods of observations with the radio telescope RATAN-600

The recent modernization of the RATAN-600 radio telescope at the Special Astrophysical Observatory has provided an opportunity to develop new procedures, called relay and zoned relay, for utilizing the new cone-surface secondary reflector. The geometric area, the horizontal beamwidth spatial resolution, and the permissible radiometer bandwidth are discussed. We are also able to estimate the changes in the sensitivities of the radio telescope-radiometer systems. The new procedures, called relay and zoned relay, allow us to obtain two-dimensional images of radio objects and to track the development of rapidly varying sources in any azimuth.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.     

Возможный механизм радиоизлучения пульсаров

, , , , , . , , . - . — , , .     

A role of cosmic rays in generation of radio and optical radiation by plasma mechanisms

The radiation of ultrarelativistic particles is examined in a quasi-uniform magnetic field superimposed by a wide spectrum of magnetic, electric, and electron density inhomogeneities created in a turbulent plasma. The radiation spectrum from a particle of a given energy is shown to acquire a high-frequency power-law tail with the same spectral index as the index of small-scale turbulence. For a power-law spectrum of ultrarelativistic electrons, dN()/d ~ ^–, with a cut-off at some energy _max, the radiation spectrum consists of a few power-law ranges; the radiation intensity may suffer jumps at frequencies which separate these ranges.In the high-frequency range the spectral index is determined by small-scale magnetic and electric fields. At intermediate frequencies the main contribution comes from the synchrotron radiation in a large-scale field; the radiation spectrum has an index =(–1)/2. The same index may be produced by large-scale Langmuir waves. At lower frequencies the radiation spectrum increases owing to the transition radiation caused by electron density fluctuations; in this case the spectral index is equal to +1–.The possibility of diagnostics of high-frequency cosmic plasma turbulence from radiation of high-energy particles is discussed. It is shown that the proposed theory may explain some features in the spectra of several cosmic objects.     

Three-dimensional,periodic, ‘halo’ orbits

A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L₁, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing .     

Имп␣льсное γ-излучение нейтронных, коллапсирующих qiх qi qsверхновых qzвезд

qp qz : (1) -, qi , (2) - (R=0.01–0.1R ) (3) - . qs. (1) - 0.1 10^–4 cm ^–2, . - . (2) 10⁸ . . 10^42–43 , (25 ). 10% - (0.1 ). , , , , , . . (3) , , - . . (2×10⁴¹ ) (10²¹ ). - 10³⁸–10³⁹ , 0.25 . , , qq . - , , .

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The following three mechanisms of generation of gamma-ray bursts at advanced phases of stellar evolution are considered; (1) gamma-ray bursts as a result of absorption of neutrino propagating through the envelope of a collapsing star, (2) gamma-ray burst due to thermal radiation of external layers of a compact star (R=0.01–0.1R ) heated by powerful shock wave, and (3) gamma-ray burst as a consequence of possible ejection of matter from neutron star at some active phases of its evolution. In the case (1) the gamma-ray flux at the top of the Earth's atmosphere is about 10^–4 (0.1 MeV photons) cm^–2, if a collapsing star is at Galactic distance (10 kpc). It is considerably less than observed one. The observations of such gamma-bursts however would be an important supplement to the direct detection of neutrino radiation from collapsing stars. In the case (2) external layers of a star are heated up to 10⁸ K. As a result we have a short pulse of thermal radiation with total energy of the order of 10^42–43 erg. The main fraction of the radiation is in the X-ray ( 25 keV), about 10% of total energy being radiated in gamma-ray ( 0.1 MeV). The energy of such a burst is sufficient for explaining observed gamma-bursts provided the supernova outburst probably takes place in our Galaxy and as a result we have some trouble with explanation of observed frequency and spectra of gammabursts. In the case (3) ejection from neutron star of chemically nonequilibrium matter results in the intensive gamma-radiation in consequence of superheavy nuclei fission followed by beta-decays and radiative captures of free neutrons. The ejection of matter from neutron stars may be connected with observed jumps of pulsar's periods. The total ejected mass ( 10²¹ g) can be evaluated from increase of kinetic energy ( 2×10⁴¹ erg.) of Crab nebula filaments. The resulting theoretical energy of gammabursts is of the order of 10^38–39 erg. It is in accordance with observations provided the mean distance of gamma-ray sources is about 0.25 kpc. Contrary to the supernova-outburst mechanism in this case we have probably no troubles with frequency and spectra of gamma-bursts. Among the three mechanisms considered above ejection of matter from neutron stars seems to be a more suitable one for explanation of observations.

     

Радиоизлучение Быстрых космических ионов

, . () . , , , . ( ), , , . . (2.7). ( ₁ k ₁ ,V — , — .) (k ₁) (k) §2 ( (2.14)). , (3.6) (3.4), (3.8) . (3.9)–(3.13) ( (3.9), (3.10) (3.11) , (3.12)–(3.13) ). (3.14), (3.16)–(3.19). - . (3.15). ( (4.14)–(4.15)). (4.23)–(4.25). (4.26)–(4.28). §5. , . ((5.5)–(5.6)). , . (5.10) .     

Le développement du potentiel dans le cas d'une densité analytique

The potential of a body of revolution is expanded in a series of spherical functions. It is proved that, for a body with analytical density limited by an analytical surface the coefficients of expansion decrease in geometrical progression.

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. , , , .