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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Irregular behaviour and eccentricity increase in the trajectories of a dynamical system modelling asteroidal motions

Many trajectories of the third body are integrated numerically in a modified elliptical restricted three body problem (ERTBP), in which the eccentricity, e, of the orbit of the second primary varies sinusoidally with time. It is found that, in the case of the 2:1 resonance, the introduction of the time variability of e modifies significantly the behaviour of the trajectories of the third body. In particular their osculating eccentricity e, present the following two notable features: (a) In all cases it shows a definite chaotic variation, which appears at significantly shorter time-scales than the one found by Wisdom in the e = constant case. (b) In many cases it shows a significant increase, up and beyond the (critical) value e _crit = 0.52. As a result the third body approaches the first primary at distances smaller than 0.29 (where by we denote the semi-major axis of the trajectory of the second primary around the first), which in the actual Sun-Jupiter-asteroid problem corresponds to the semi-major axis of Mars. Our result might be of interest in the context of explaining the Kirkwood gaps at the resonances where the osculating eccentricity of asteroid trajectories calculated in the classical (e = constant) ERTBP does not reach Mars crosser values.     

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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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.     

Libration effects for retrograde satellites in the restricted three-body problem

Numerical explorations of the restricted problem have shown that for stable large nonperiodic retrograde satellite orbits, the motion can be decomposed into a fast reference motion and a slow libration aroundB ₂ We study here this libration in the circular plane Hill's case, for which the reference motion is elliptic. We establish the equations of motion for the coordinates of the centre of this ellipse. We find two integrals of motion: the first is the semi-major axis of the ellipse; the second is essentially Jacobi's integral, translated into the new coordinates. We give a formula for the period of the libration and we find its limiting value for small libration amplitudes. A numerical verification gives very good agreement for all these results.     

Bifurcations in systems of three degrees of freedom

We study the bifurcations of families of double and quadruple period orbits in a simple Hamiltonian system of three degrees of freedom. The bifurcations are either simple or double, depending on whether a stability curve crosses or is tangent to the axis b=–2. We have also generation of a new family whenever a given family has a maximum or minimum or .The double period families bifurcate from simple families of periodic orbits. We construct existence diagrams to show where any given family exists in the control space (, ) and where it is stable (S), simply unstable (U), doubly unstable (DU), or complex unstable (), We construct also stability diagrams that give the stability parameters b₁ and b₂ as functions of (for constant ), or of (for constant ).The quadruple period orbits are generated either from double period orbits, or directly from simple period orbits (at double bifurcations). We derive several rules about the various types of bifurcations. The most important phenomenon is the collision of bifurcations. At any such collision of bifurcations the interconnections between the various families change and the general character of the dynamical system changes.     

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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Simulation of evolutionary mechanism of planetary rings

We devised a numerical model of planetary ring in which the inelastic collision and the gravitation between ring particles are considered. We adopt Hill's equations and the differential algorithm of circular mesh for computation of the particle orbits. The evolutional processes are presented for different coefficient of restitution and dynamical optical depth . The results show that the semi-major axis and eccentricity of the ring particles are changed with and . We compute the average energies transferred and loss in inelastic collisions for various values of the parameters. The dynamical equilibrium properties are discussed in the different cases.     

εлектроны космических лучей радиогало галактики

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О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

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Сопоставление модели карлсона с моделью сплошной среды

, (1962, 1963) . , (1) (2) .     

О природе всплесков γ-излучения

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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 , . .     

Возможный механизм радиоизлучения пульсаров

, , , , , . , , . - . — , , .     

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

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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.

     

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%).     

Спектр и поляризация источника синхротронного излучения при релятивистском разлете его компонент

, , , . () , . , .     

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) .     

Stability of the libration points of a rotating triaxial ellipsoid

The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.

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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) . , -, , .