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. . ,e, , . . e, . , .
Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.
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Stability of the libration points of a rotating triaxial ellipsoid   总被引:1,自引:0,他引:1  
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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qp qz : (1) -, qi , (2) - (R=0.01–0.1R ) (3) - . qs. (1) - 0.1 10–4 cm –2, . - . (2) 108 . . 1042–43 , (25 ). 10% - (0.1 ). , , , , , . . (3) , , - . . (2×1041 ) (1021 ). - 1038–1039 , 0.25 . , , qq . - , , .
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 1042–43 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 1038–39 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.
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6.
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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7.
, . () . , , , . ( ), , , . . (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) .  相似文献   

8.
The explicit expressions for the orientation distribution function of interstellar and interplanetary dust grains in the anisotropic corpuscular or radiation fluxes, with consideration for the magnetic field influence, are obtained. An orientation is shown to be possible in a medium having an anisotropic temperature, which is usually the case for a non-equilibrium plasma in a magnetic field. It is noted that the small inhomogeneous dust grains should possess a specific rotation of polarization. The orientation of these dust grains is considered. The time required for the orientation is estimated. A possibility of explaining the interstellar polarization and polarization of the cometary radiation is discussed.
. , . , . . .
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The shifts of Fraunhofer lines of different chemical elements in a homogeneous medium with a plane monochromatic progressive adiabatic sound waves are derived. The calculations indicate that lines of neutral elements (6 0 14) with lower excitation potentials 0 i= 0–2 eV are red shifted, those with excitation potential 0 i= 4–12 eV are blue shifted, and with 0 i= 3 eV are both blue and red shifted. The lines of ions are shifted toward the blue. The shifts of Fraunhofer lines are found to decrease from the centre of the solar disk to the limb. These results agree qualitatively and quantitatively with observations.  相似文献   

12.
The ion composition instrument (ICI) on ISEE-3 has observed the isotopes of helium of mass 3 and 4 in the solar wind almost continuously between August 1978 and July 1982. This period included the increase towards the maximum of solar activity cycle 21, the maximum period, and the beginning of the descent towards solar minimum. Observations were made when the solar wind speed was between 300 and 620 km s–1. For part of the period evidence for regular interplanetary magnetic sector structure was clear and a number of3He flares occurred during this time.The long-term average4He++/3He++ flux ratio R, was 2050 ± 200, a agreement with a previously reported result obtained using part of this data set, and in very good agreement with the previous measurements made over much shorter periods of time with the foil technique. The R values for 6-month intervals show statistically significant differences. The highest of these values is 2300 and coincides with the solar maximum of cycle 21 indicating that at solar maximum there may be changes in the character and rate of occurrence of short-term variations in R. We also find that R drops under conditions of low proton flux in the solar wind, and that it is high when solar wind speeds are lowest.At solar wind speeds above 400 km s–1 R is nearby constant at about 2000; at lower speeds it is larger and more variable, in agreement with the idea that the sources of high and low speed wind are different. At times of sector boundary current sheet crossings, identified with coronal streamers, there is a characteristic rise in the value of R indicating an encounter with a plasma with reduced3He++ abundance. Autocorrelations have been computed for4He++ and3He++ and indicate correlation times of about 14 and 20 hr, respectively. Periods of duration of about one day whenR is less than 1000 tend to coincide with the observation of compound streams.The possibility of detectable increases in3He++ flux in plasma which left the Sun at the time of3He flares has been investigated, but no significant increase was seen.  相似文献   

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It is shown theoretically that the emission efficiency of amorphous grains with radii smaller than 100 Å has a -1-dependence in the wavelength region longer than 100 , whereas those of crystalline, metallic, and larger amorphous grains are proportional to -2 in far infrared. Astrophysical implications of the amorphous grains are discussed.  相似文献   

15.
The implications of the intrinsic luminosity evolution with cosmological epoch on the value of the density parameter () and evolution of radio sizes of extragalactic radio sources have been considered. It is shown that a power law evolution model of the sortP (1 +z) can be used to contrain the value of . In the presence of a strong luminosity evolution, the model yields an upper limit of 0.5.It is also shown that the angular diameter redshift ( – z) relation for quasars can be interpreted in terms of the assumed luminosity evolution combined with a luminosity-linear size correlation with little or no linear size evolution required. On the other hand, strong linear size evolution is needed to explain the – z data for radio galaxies independent of luminosity.  相似文献   

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, . . . (10R ) ( 10 000R ). NGC 5457, NGC 6946 NGC 5236. , , II I . . . , . . 1050÷1052 , .  相似文献   

17.
(Kilyachkoet al., 1978) , . l ( I II). (Kilyachkoet al., 1978) : (1) 800 Å , , UV Cet. EV Lac; (2) UV Cet EV Lac 8000 Å , ; (3) 8000 Å . — MO-KS; (4) 1–3 m.  相似文献   

18.
Based on a general planetary theory, the secular perturbations in the motion of the eight major planets (excluding Pluto) have been derived in polynomial form. The results are presented in the tables. The linear terms of second order with respect to the planetary masses and the nonlinear terms of first order up to the fifth (and partly seventh) degree with respect to eccentricities and inclinations were taken into account in the right-hand members of the secular system. Calculations were carried out by computer with the use of a system that performed analytic operations on power series with complex coefficients.
qA ( ). . ( ) . .
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Some attempts of polarimetric sounding of Comet Halley will be undertaken from the flyby probes. In order to facilitate the final planning and the future interpretation of these experiments we have done a thorough analysis of practically all available polarimetric observations. An emphasis is made on interpretation attempts and their discussion. The results of the phase dependence of polarization investigations are presented covering a wide range of phase angles . The chief peculiarities of this dependence are: maximum polarization at = 90, diminishing through zero at 20, negative values up to several per cent and a final growth to zero at zero . A division into gaseous and dusty comets on polarimetric basis is revealed. The wavelength dependence of polarization is discussed. The numerous results of detailed polarimetry are compared to the negative results of attempts to detect the elliptical polarization. New observational problems arising from the evidence given by the negative polarization at small phase angles and by the opposition effect recently discovered are discussed.  相似文献   

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