About the motion of a heavy flexible string attached to the satellite in the central field of attraction

The motion of a heavy inextensible flexible string attached to the satellite in the central gravitational field is discussed. It is supposed that the mass of the string is infinitesimally small compared to the mass of the satellite and hence it does not affect the latter's motion. Under the assumption that the satellite moves along the Keplerian elliptical orbit (in particular circular orbit), the relative motion of the string is investigated. It has been shown that the motion of the flexible string is unstable which is stable in the case of a solidified string.

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Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Dimensional Analysis of the Flare Distribution Problem

Dimensional analysis is used to derive the distribution of solar flare energies,p() = A-^3/2, in accordance with recent observational and numerical results. Several other scalings, notably _fl ² , where _fl is the flare duration, are obtained as well.     

Структура и эволюция Сверхмассивных вращающихся магнитных политроп

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The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force-lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of general relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radius-mass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.

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English translation will appear in the next issue ofAstrophys. Space Sci.

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Receipt delayed by postal strike in Great Britain     

Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.     

Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem

The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL ₄ andL ₅ form nearly equilateral triangles with the primaries and the pointsL ₁,L ₂,L ₃ remain collinear. It is further observed that for the pointsL ₄ andL ₅, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

F07164+5301: an ESB source with WR features

We report on a new ESB source, as defined by Allenet al. (1991), with Wolf-Rayet (WR) bands in its optical spectrum. The WR bump at 4605-4686 is detected. The bump consists of broad HeII 4686, NV4605-4619, NIII4634-41, and possibly, CIII4647-52 emission. The narrow nebular lines are clearly discernable on our spectrum. The number of WR stars derived from the luminosity of HeII4686 is about 8100. The oxygen abundance is about 9.06×10^–4, greater than the solar value.     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

Free-convection flow of water at 4°C past an infinite vertical porous plate with constant heat flux

An analysis of the two-dimensional flow of water at 4°C past an infinite porous plate is presented, when the plate is subjected to a normal suction velocity and the heat flux at the plate is constant. Approximate solutions are derived for the velocity and temperature fields and the skin-friction. The effects ofG (Grashof number) andE (Eckert number) on the velocity and temperature fields are discussed.Nomenclature u, v velocity components of the fluid inx, y direction - g acceleration due to gravity - coefficient of thermal expansion of water at 4°C - v kinematic viscosity - density - T temperature inside thermal boundary layer - T free-stream temperature - k thermal conductivity - C _p specific heat at constant pressure     

О механззме оптического, рентгеновского и гамма-излучения пульсара в краБе

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Zonal comparison of modern selenodetic reference systems

An account is given of the results of a comparison of existing basic selenodetic systems in the equatorial zone of the Moon together with plan and altitude data, which have been provided by means of a specially worked out method, based on the use of the LAC charts of the Moon (scale 1:1000000), and which does not require the presence of common catalogued reference points. It is shown that systematic differences of the form () for different catalogues are, on the whole, relatively small and do not exceed 2. Systematic differences of the form () have a minimum in the region = ± 20° and significantly increase towards the edges of the visible disk, where they may attain a value of 6 between catalogues. Random errors in latitude have on the whole, a similar behaviour in different catalogues, being practically independent of longitude and not exceeding 3. Random errors in longitude significantly increase towards the limb regions in all the studied catalogues, and may reach values of 6 to 8. Author's estimates of the accuracy of absolute heights in selenodetic catalogues is not always sufficiently precise; in certain cases it was found that the accuracy was underestimated by a factor of one and a half. The data on relative heights in the LAC charts are expressed with a vertical step of 300 m, errors in these values are of the order of 250 m for each step in height. As a result of the comparison a set of better points has been obtained forming a catalogue which may be referred to as LPL. The selection was made on the basis of magnitude and character of both the systematic and random errors.     

Перенос резонансного излучения И случайные ълуждания Фотонов

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Transfer of resonance radiation in infinite medium is considered as a process of random walks of photons. Close relation is shown to exist between the problems of transfer of line radiation and the stable distributions of the probability theory. This relation is used as a basis of a new method for the investigation of the asymptotic properties of the radiation field far from the sources.

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Spectrophotometry of bright Be stars

We present new measurements of the distribution of energy in the continuum for eight Be stars in the optical region (3200-7600 Å). The effective temperatures of these stars have been estimated from their observed fluxes. It is found that, in general, pole-on stars show near-infrared excess emission. It is interesting to note that the Balmer jumps for stars having an infrared excess are systematically smaller than for those lacking the infrared excess.Variability of ultraviolet and infrared excess emissions in these stars has been discussed. The stars 59 Cyg, 66 Cyg, 28 CMa, and 27 CMa show large variations in their continuum at ultraviolet (UV) and infrared (IR) regions.     

Study of the nonradial directional property of the rays of the streamer belt and chains in the solar corona

Based on analyzing corona images taken by the LASCO C1, C2, and C3 instruments, a study is made of the behavior of the streamer belt spanning one half of the 1996–2001 cycle of solar activity, from minimum to maximum activity, in the absence of coronal mass ejections. It is shown that: (1) The position of the streamer belt relative to the solar equator is generally characterized by two angles: _o and _E, where _o is the latitudinal position (near the solar surface) of the middle of the base of the helmet, the top of which gradually transforms to a ray of the streamer belt with a further distance from the Sun, and _E is the latitude of this ray for R>5–6 R from the Sun's center where the ray becomes radial. (2) Only rays lying at some of the selected latitudes _o retain their radial orientation (_oE) throughout their extent. Namely: _o0° (equator), _o±90° (north and south poles), and the angle _o lying in the range ±(65°–75°) in the N- and S-hemispheres. (3) A deviation of rays from their radial orientation in the direction normal to the surface of the streamer belt occurs: for latitudes _o<|65°–75°| toward the equator (>0°) reaching a maximum in the N and S hemispheres, respectively, when _OM40°, and _OM–42° for latitudes _o>|65°–75°| toward the pole (<0°). The regularities obtained here are a numerical test which can be used to assess of the validity of the theory for describing the behavior of the Sun's quasi-stationary corona over a cycle of solar activity.     

Scanner observations of comet P/Crommelin 18181

Spectral scans of the coma of comet P/Crommelin 1818. I have been obtained in the wavelength range 3200–6500 Å. Strong emission features of CN(3883 Å) and C₂ Swan bands (4695, 5165, and 5538 Å) have been identified. Some weak emission features of CH(3890 Å), C₃(4050 Å), CN(4200 »), and C₂ + CH(4358 ») were also detected. Sodium was found to be absent in this comet. An estimate of CN and C₂ abundances has been made and their production rate have been derived.     

Ускорение релятивистских электронов в плазменных реакторах и нелинейные спектры космических радиоисточников

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Evolutionary models of nucleosynthesis in the galaxy

A model of the galaxy is constructed and evolved in which the integrated influence of stellar and supernova nucleosynthesis on the composition of the interstellar gas is traced numerically. Our detailed assumptions concerning the character of the matter released from evolving stars and supernovae are guided by the results of recent stellar evolutionary calculations and hydrodynamic studies of supernova events. Stars of main sequence mass in the range 4M8M are assumed to give rise to supernova events, leaving remnants we identify with neutron stars and pulsars and forming both the carbon-to-iron nuclei and ther-process heavy elements in the explosive ejection of the core material. For more massive stars, we assume the core implosion will result in the formation of a Schwarzschild singularity, that is, a black hole or collapsar. The straightforward assumptions (1) that the gas content of the galaxy decreases exponentially with time to its present level of 5% and (2) that the luminosity function characteristic of young clusters and the solar neighborhood is appropriate throughout galactic history, lead to the prediction that 20% of the unevolved stars of approximately one solar mass (M ) in the galaxy today should have metal compositionsZ0.1Z . As Schmidt has argued from similar reasoning, this is quite inconsistent with current observations; an early generation dominated by more massive stars—which would by now have evolved—is suggested by this difficulty. Many of these massive stars, according to our assumptions, will end their lives as collapsed black hole remnants. It is difficult to visualize an epoch of massive star formation in the collapsing gas cloud which formed our galaxy which would enrich the gas rapidly enough to account for the level of heavy element abundances in halo population stars; we have therefore proposed a stage of star formation which is entirely pregalactic in character. We suggest that the Jeans' length-sized initial condensations in the expanding universe discussed by Peebles and Dicke may provide the appropriate setting for this first generation of stars. Guided by these considerations, and by the need for a substantial quantity of unseen mass to bind our local group of galaxies, we have constructed a model of the galaxy in which this violent early phase of massive star formation produces both (1) approximately 25% of the level of heavy elements observed in the solar system and (2) an enormous unseen mass in the form of black holes. The implications of our model for other features of the galaxy, including supernova nucleosynthesis, the cosmic ray production of the light elements, and cosmochronology, are discussed in detail.     

The Energy Lost by Differential Rotation in the Generation of the Solar Toroidal Magnetic Field

The integrals, I_i(t) = _GL u_i j × B _i dv over the volume GL are calculated in a dynamo model of the Babcock–Leighton type studied earlier. Here, GL is the generating layer for the solar toroidal magnetic field, located at the base of the solar convection zone (SCZ); i=r, , , stands for the radial, latitudinal, and azimuthal coordinates respectively; j = (4)^-1 × B, where B is the magnetic field; u_r,u are the components of the meridional motion, and u is the differential rotation. During a ten-year cycle the energy _cycle I(t)dt needs to be supplied to the azimuthal flow in the GL to compensate for the energy losses due to the Lorentz force. The calculations proceed as follows: for every time step, the maximum value of |B| in the GL is computed. If this value exceeds B_cr (a prescribed field) then there is eruption of a flux tube that rises radially, and reaches the surface at a latitude corresponding to the maximum of |B| (the time of rise is neglected). This flux tube generates a bipolar magnetic region, which is replaced by its equivalent axisymmetric configuration, a magnetic ring doublet. The erupted flux can be multiplied by a factor F_t, i.e., by the number of eruptions per time step. The model is marginally stable and the ensemble of eruptions acts as the source for the poloidal field. The arbitrary parameters B_cr and F_t are determined by matching the flux of a typical solar active region, and of the total erupted flux in a cycle, respectively. If E(B) is the energy, in the GL, of the toroidal magnetic field B = B sin cos , B (constant), then the numerical calculations show that the energy that needs to be supplied to the differential rotation during a ten-year cycle is of the order of E(B_cr), which is considerably smaller than the kinetic energy of differential rotation in the GL. Assuming that these results can be extrapolated to larger values of B_cr, magnetic fields 10⁴ G, could be generated in the upper section of the tachocline that lies below the SCZ (designated by UT). The energy required to generate these 10⁴ G fields during a cycle is of the order of the kinetic energy in the UT.     

On convergence of an asymmetrical body potential expansion in spherical harmonics

The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV _n of the expansion are obtained. It is proved thatV _n decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V _n decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV _n =O (n ^–5/2).

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I I V _n IV _n I . . IV _n I . I. IV _n =O(n ^–5/2 )