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1.
In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies 1 and 2. In terms of thecritical masses mj(2), or the associatedcritical energies j 2 (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |2– j 2 |<j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 021, lying in: and (2) despite the clustering of j 2 (m) atj=, the family () includes, for 2=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL 3.In a similar manner, the family () can be extended to the horseshoe branch 1<2 2 2 .  相似文献   

2.
A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( i+1/ i [r i /r i+1] is approximately equal to the exponentN in a continuous density law (=aR –N) provided (r i /r i+1)3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c 2 R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s–1 Mpc–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c 2 R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R N ,N2); (j) for the Galaxy, theory predictsp G7×10–12 dyn cm–2, observation givesp G5×10–12 dyn cm–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 1012 g s–1, compared to 1011 g s–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×109 years for the Sun and 1010 years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN B of baryons; (o)N B1057N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L max1059 erg s–1); (r) larger bodies have longer time-scales of energy radiation atL max (10–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR –N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.  相似文献   

3.
The optical depth at the head of the Lyman continuum, H, is determined at a number of positions in three hedgerow prominences using spectroheliograms (5 × 5 resolution) of C III 977, LC 896, and O IV 554 observed with the Harvard experiment on Skylab. At heights greater than 10 above the limb the maximum value of H is 30 to 50, which occurs at the central part of the prominences. For one of the prominences the determination of H is found to be consistent with data from spectroheliograms of Mg X 625. The degree of ionization of hydrogen is estimated from the intensity of LC 896 at H 1. In the central part of a model prominence N P/N HI1.9 for a reasonable range of the electron densities, where N P and N HI are the proton density and the neutral hydrogen density, respectively.  相似文献   

4.
The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR eff one obtains the amounts of actionA c(M), the effective densities eff(M)=(M)3(M), the densities of action and of energy (or mean presures in the stellar interior)a c(M),e c(M), and the potential energiesE p(M).The amounts of action areA cM k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M –1.81, (M)M0.6.The cases for the M stars (e c(M)M –1) and for the A and earlier stars (betweena c(M)=constant and eff(M)M –1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA c(M), Ep(M), eff M –p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE p(M)M –p according to the stellar models used here and the observed frequency function (MM –q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.  相似文献   

5.
In this paper I present a new evolution model of QSOs luminosity. The model is based on edges distribution of apparent magnitude-redshift of QSOs. After the quasars were formed, the luminosities were increasing until they attained their maximum value atz=2+a, where –0.1a0.6, then the luminosities were decreasing. If the QSOs originate from superconducting cosmic string of same initial massM i 1012 M , the formation epochs are different, most of the quasars start atz cutoff5.6. The most luminous QSOs start at later epochz cutoff5.15. The present sky survey echniques may give us the possibility to see the formation of QSOs at apparent magnitudem V 22.5 by chance of 0.3%.  相似文献   

6.
An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z and if (z) and p(z) are not too rapidly varying, then (t) m (z , t)+N p(z , t) where m and N depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

7.
In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE n which is denoted as n (). The main result of this analysis enables us to establish a two-term recurrence formula for n (0) and a three-term recurrence formula for n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.  相似文献   

8.
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  相似文献   

9.
The contribution to the galactic abundance of He and heavy elements by stellar nucleosynthesis is calculated as a function of time, keeping account of present knowledge about stellar and galactic evolution. A model is used which distinguishes the phase of the contracting halo from the subsequent history of the disc. Various uncertainties involved both in stellar and in galactic evolutionary theory are discussed. The amount of4He produced by stars of different masses and ejected in interstellar medium is fairly well known from stellar theory, while we have assumed its primordial abundance as a free parameter, ranging from 0 up to 0.4. We find that stellar activity provides a significant contribution to the cosmic4He, though not sufficient to explain the observed abundance. The best agreement with observational data (Y 0.26 andY now0.28) is obtained starting with a primordial abundanceY =(0.20–0.23), which is consisten with the Big-Bang theory predictions and with recent observational estimates. The contribution to the abundance of heavy elements depends on the last stellar stages and on the final explosion mechanism, which are only now beginning to be understood. Nevertheless, in the framework of present theories, we individuate a stellar evolutionary scheme reproducing the observedZ abundances for Populationi and Populationii stars, with the correctly estimated Y/Z value. In this scheme, only stars belonging to two narrow mass ranges (10m/m 15 andm/m 80) are allowed to eject metal-enriched matter, possibly with the solar (C+O)/(Si+Fe) ratio.  相似文献   

10.
Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) 1/2–1/2 - M magnetic field parameter - N u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - 1 suction velocity att0 - 2 suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function  相似文献   

11.
The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines Hei D3 andH quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of H is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely Hei D3, which is optically thin, and H, which is optically thick ( = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line.It is then possible to determine without ambiguity the polarity of the prominence magnetic field with respect to that of the photospheric field: 12 prominences are found to be Inverse polarity prominences, whereas 2 prominences are found to be Normal polarity prominences. It must be noticed that in 12 of the 14 cases, the line-of-sight component of the magnetic field vector has a Normal polarity (to the extent that the notion of polarity of a vector component is meaningful; no polarity can be derived in the 2 remaining cases); this may explain the controversy between the results obtained with methods based on the Hanle effect with results obtained through the Zeeman effect. A dip of the magnetic field lines across the prominence has been assumed, to which the optically thick H line is sensitive, and the optically thin Hei D3 line is insensitive.For the Inverse prominences, the average field strength is 7.5±1.2 G, the average angle,, between the field vector and the prominence long axis is 36° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 29° ± 20°, and the average electron density is 2.1 × 1010 ± 0.7 × 1010 cm–3. For the Normal prominences, the average field strength is 13.2±2.0 G, the average angle,, between the field vector and the prominence long axis is 53° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 0° ± 20° (horizontal field), and the average electron density is 8.7 × 109 ± 3.0 × 109 cm–3.  相似文献   

12.
General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities 0, where 0 = 2.8×1014 g cm–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of –-hyperons at > c , where c 40. The electric resistivities along and acrossB, and , and the Hall resistivity H are calculated and fitted by simple analytical formulae at c and > c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If c , one has = [1 + (B/B 0)2] for the normal neutrons, and for the superfluid neutrons, while H = B/B e for both cases. HereB e 109 T 8 2 G,B 01011 T 8 2 G, andT 8 is temperature in units of 108 K. Accordingly for the normal neutrons atBB 0, the transverse resistivity suffers an enhancement, 1/4 1. When 50 andB varies from 0 toBB p 1013 T 8 2 G, increases by a factor of about 103–104 and H changes sign. WhenBB p , remains constant for the superfluid neutrons, and H B 2 for the normal neutrons, while H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.  相似文献   

13.
The present work is a review of papers related to the theory of prominence radiation. Special attention is paid to stationary equations and the theory of radiation diffusion in the lines and continua of hydrogen, helium and metals.We conclude that prominences are low-temperature formations T e 7000 K, of low density 1012 particles per cm3, n e 1011 cm–3, effective thickness 109 cm, and that the chemical composition of prominences and that of the Sun's atmosphere are the same. The prominence radiation in the lines of hydrogen, helium and metals is due mainly to quasiresonance scattering of the photospheric radiation.  相似文献   

14.
D3 and H pictures of prominences were obtained with a 21-in. Lyot coronograph and a Fabry-Perot etalon used as a narrow band filter. The monochromatic images of quiescent, quasiquiescent and loop-prominences were studied. The comparison of the isophotes of quiescent and quasi-quiescent prominences in D3 with those in H shows the similarity of the prominence structure at both wavelength, although there is a strong tendency for an increase in the intensity ratio D3/H in the upper region of prominences. It seems that it is due to lower temperature in the upper regions of prominences. Probably, the relaxation processes establishing ionization equilibrium play some role. Measurements of the knot intensities of the loop-prominence show strong variations of the intensity ratio D3/H (more than one order of magnitude).  相似文献   

15.
Unsteady laminar free convection flow of a viscous incompressible and electrically conducting fluid past an accelerated vertical infinite porous plate subjected to a suction velocity proportional to (time)–1/2 is studied in presence of a uniform horizontal magnetic field. Results are discussed with the effects of the Grashof number Gr, and the magnetic field parameterM for Pr (the Prandtl number)=0.71 and 7.0 representing air and water respectively at 20 °C.Nomenclature a suction/injection parameter - C p specific heat at constant pressure - B 0 magnetic induction - g acceleration due to gravity - Gr Grashof number (vg(T'w-T')/U 0 3 ) - K thermal conductivity - M magnetic field parameter (B 0 2 e 2 /U 0 2 ) - Pr Prandtl number (C p/K) - T' temperature of the fluid near the plate - T' w temperature of the plate - T' temperature of the fluid at infinity - t' time variable - t dimensionless time (t' U 0 2 /v) - u non-dimensional velocity (u'/U 0) - U' velocity of the plate - U dimensionless velocity of the plate (U'/U o) - U 0 reference velocity - v' 0 suction velocity - v 0 nondimensional suction velocity (v' 0/U 0)=at–1/2 - v' normal velocity component - v dimensionless normal velocity - Ec Eckert number ((vU 0)2/3/C p(T' w -T' )) - T dimensionless temperature of the fluid near the plate ((T'-T' )/T' w –T' )) - x',y' coordinates along and normal to the plate - y dimensionless ordinate (=y' U o/v) - v kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - similarity variable (y/2t) - w density of the fluid at the plate - density of the fluid at infinity - ' skin-friction - dimensionless skin-friction - coefficient of viscosity - e magnetic permeability  相似文献   

16.
A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) T and T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.  相似文献   

17.
Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant - 1.69. This serves to provide a physical understanding of the Titius-Bode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R p= Rap, where R pare the radii of the solar nebula at various halts during the collapse, R the radius of the present Sun and a = 1.442. a is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T p = T 0(a3/2)p, where T p are the orbital periods at the radii R p, T 0 - 0.1216d - 3 h, and a the Roche constant. We are inclined to interpret T 0' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T pcorresponding to the radii R psubmit themselves to the Laplace's resonance relation.  相似文献   

18.
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values i = i + i ,v i = i + v i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v 2 = 10–8) grow many times in marginally-stable state.  相似文献   

19.
The intensity ratios E(H)/E(D3) and E(H)/E(D3) in prominences depend on the total optical thickness in H of the layer. The emission of the He D3 line appears relatively enhanced in thin layers and in outer parts of the prominences.  相似文献   

20.
An expansion of the force function ofn-body dynamical systems, where the equations of motion are expressed in the Jacobian coordinate system, is shown to give rise naturally to a set of (n–1) (n–2) dimensionless parameters ki li {i = 2,...,n;k = 2,...,i – 1 (i 3);l =i + 1,...,n (i n – 1)}, representative of the size of the disturbances on the Keplerian orbits of the various bodies. The expansion is particularized to the casen=3 which involves the consideration of only two parameters 23 and 32. Further, the work of Szebehely and Zare (1977) is reviewed briefly with reference to a sufficient condition for the stability of corotational coplanar three-body systems, in which two of the bodies form a binary system. This condition is sufficient in the sense that it precludes any possibility of an exchange of bodies, i.e. Hill type stability, however, it is not a necessary condition. These two approaches are then combined to yield regions of stability or instability in terms of the parameters 23 and 32 for any system of given masses and orbital characteristics (neglecting eccentricities and inclinations) with the following result: that there is a readily applicable rule to assess the likelihood of stability or instability of any given triple system in terms of 23 and 32.Treating a system ofn bodies as a set of disturbed three-body systems we use existing data from the solar system, known triple systems and numerical experiments in the many-body problem to plot a large number of triple systems in the 23, 32 plane and show the results agree well with the 23, 32 analysis above (eccentricities and inclinations as appropriate to most real systems being negligible). We further deal briefly with the extension of the criteria to many-body systems wheren>4, and discuss several interesting cases of dynamical systems.  相似文献   

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