Symmetries and Bifurcations in the Sitnikov Problem

We present some qualitative and numerical results of the Sitnikov problem, a special case of the three-body problem, which offers a great variety of motions as the non-integrable systems typically do. We study the symmetries of the problem and we use them as well as the stroboscopic Poincarée map (at the pericenter of the primaries) to calculate the symmetry lines and their dynamics when the parameter changes, obtaining information about the families of periodic orbits and their bifurcations in four revolutions of the primaries. We introduce the semimap to obtain the fundamental lines l ₁. The origin produces new families of periodic orbits, and we show the bifurcation diagrams in a wide interval of the eccentricity (0 0.97). A pattern of bifurcations was found.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Systematic Study of the Stability of Symmetric Periodic Orbits in the Planar, Circular, Restricted Three-Body Problem

We investigate symmetric periodic orbits in the framework of the planar, circular, restricted, three-body problem. Having fixed the mass of the primary equal to that of Jupiter, we determine the linear stability of a number of periodic orbits for different values of the eccentricity. A systematic study of internal resonances, with frequency p/q with 2p 9, 1 q 5 and 4/3 p/q 5, offers an overall picture of the stability character of inner orbits. For each resonance we compute the stability of the two possible periodic orbits. A similar analysis is performed for some external periodic orbits.Furthermore, we let the mass of the primary vary and we study the linear stability of the main resonances as a function of the eccentricity and of the mass of the primary. These results lead to interesting conclusions about the stability of exosolar planetary systems. In particular, we study the stability of Earth-like planets in the planetary systems HD168746, GI86, 47UMa,b and HD10697.     

The flattening of three-dimensional periodic orbits in the restricted problem

A number of partly known families of symmetric three-dimensional periodic orbits of the restricted three-body (=0.4) problem are numerically continued in both ends until they terminate with orbits in the plane of motion of the primaries. The families of plane symmetric periodic orbits from which they bifurcate are identified and many orbit illustrations are given.     

Stability of periodic resonance-orbits in the elliptic restricted 3-body problem

Results of families of periodic orbits in the elliptic restricted problem are shown. They are calculated for the mass ratios =0.5 and =0.1 for the primary bodies and for different values of the eccentricity of the orbit of the primaries which is the second parameter. The case =0.5 is also a good model for planetary orbits in binaries. Finally we show detailed stability diagrams and give results according to the stability classification of Contopoulos.     

First Byurakan Spectral Sky Survey. Blue stellar objects. XI. Region +80 ≤ δ ≤ +90°

The eleventh list of blue stellar objects in the second part of the First Byurakan Spectral Sky Survey (FBS) is presented. The list consists of 64 objects located in the region +80 +90° and 2^h 08^m a 20^h 15^m. The objects haveV magnitudes in the range 12.3–17.4 andB–V color indices in the range -0.55-+0.55. Of the 98 objects, 56 are newly discovered. Tentative classifications are given for 28 objects, of which there is one planetary nebula, 6 possible quasars, 15 possible white dwarfs, and 6 possible cataclysmic variables. Two of the latter are possibly novae having erupted at the epoch of exposure of the FBS plates in this region.Translated fromAstrofizika, Vol. 39, No. 4, pp. 531–540, November, 1996.     

Study of the outer galactic structure for 288°≤l≤310°, −7°≤b≤2°

The structure of the outer part of the Galaxy is studied, based upon 21-cm line observations of Hi in the region 288°l310°, –7°b2°.In this longitude range the galactic plane is strongly bend toward negative latitudes.The principal outer structure is a spiral arm which has a pitch angle of 10° and is formed by several concentrations differing in shape and size. There exists also a secondary concentration which could be a split from the previous structure.Possible hypotheses about the origin of the later feature are discussed.     

Redshift cutoff and evolution of QSOs

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%.     

Integrals of motion in the elliptic three-dimensional restricted three-body problem

Three integrals of motion have been found in the three-dimensional elliptic restricted three-body problem for small eccentricitye of the relative orbit of the primaries and small distancer and eccentricitye of the orbit of the third body around a primary. The integrals are given in the form of formal series in the mass-ratio , the eccentricitiese, e and the coordinates and velocities. These integrals depend periodically on the time.     

A note on the elliptic restricted three-body problem

This work considers periodic solutions, arc-solutions (solutions with consecutive collisions) and double collision orbits of the plane elliptic restricted problem of three bodies for =0 when the eccentricity of the primaries,e _p , varies from 0 to 1. Characteristic curves of these three kinds of solutions are given.     

Cometary motions

The history of the study of cometary motions is described, from the pre-Copernican era until the present time, with emphasis on the determination of orbits, the calculation of special perturbations, and the analysis of nongravitational effects. A brief survey is made of the statistics of cometary orbits and of the implications concerning cometary origin and evolution. 1. Pre-Newtonian Ideas It is said... that the highest region of the air follows the celestial motion. This is demonstrated by those stars that suddenly appear —I mean those stars that the Greeks calledcometae orpogoniae. The highest region is considered their place of generation, and just like other stars they also rise and set. We can say that this part of the air is deprived of the terrestrial motion because of its great distance from the Earth.     

Maximal red shifts of neutron stars

It has been recently established that there exists a maximal red shiftz _max for a homogeneous star of given massM. The relationshipz _max(M) is obtained for neutron stars in the mass range 0.71M/M 12.06.     

Infrared continuum observations of five-minute oscillations

Infrared continuum observations of the Sun at wavelengths between 10 and 30 show a nonisothermal response of the upper photosphere to compression waves associated with the five-minute oscillations. Observations were made with four broad-band filters with effective transmission wavelengths between 10 and 26 and with a 10 aperture. Further observations at submillimeter wavelengths with a 2 aperture did not resolve oscillatory fluctuations of five-minute period.Comparisons with velocity field data of Howard (1976) suggest that the relaxation time of the photosphere exceeds (300/2) seconds at the height of formation of the 26 continuum (_5000Å 10^-2). The photosphere reponds to 3 mHz oscillatory motion with considerably less compression than expected for simple acoustic modes in an adiabatically responsive atmosphere, confirming the evanescent character of the five-minute oscillations.     

The Pomeau-Manneville intermittent transition to chaos in hydrodynamic pulsation models

Hydrodynamic simulations of nonlinear pulsation for less-massive cool supergiants have been performed by several authors. Outburst of large amplitude oscillations at times is one of common features of these models. To find out routes of the transition from the limit cycles to the irregular pulsations. We performed hydrodynamic simulation for a series of models of luminosity log(L/L )=3.505, andT _e =5300 K with the range of the mass 1.4M M1.5M . With decreasing the mass, we confirm a transition from limit cycles to irregular oscillations.The nature of the transition is finally specified by examining the dissipation of pulsational kinetic energies in limit cycle models, when pulsations start with larger amplitudes than their limiting pulsations. We find that the rates of dissipation are so small that they might be marginally stable. Furthermore, the oscillation starting with even larger amplitudes gets the kinetic energies until it reaches a limit where the oscillation induces strong shock waves and dissipates its kinetic energy. Thus, we conclude that the model which has the stable limit cycle near the transition has another unstable fixed point above the limit cycle. The transition, therefore, is induced by disappearance of these two fixed points, as the mass, the control parameter in our case, is varied, and is found exactly in aggreement with the intermittency proposed by Pomeau and Manneville as a route to chaos in dissipative systems.     

Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

Galactic4He and heavy elements enrichment by stellar nucleosynthesis

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.     

Linearized limb-darkening coefficients for use in analysis of eclipsing binary light curves

Linear limb-darkening coefficientsu required in the analysis of eclipsing binary curves, are tabulated for a wide range of effective temperature (50 000° to 4000°), wavelength (0.2 2.2 ), and gravitiesg (2.0logg5.0). The computation is based on the comprehensive range of model atmospheres of Carbon and Gingerich (1969).The results are compared with the theoretical values of Hosokawa (1957), Kopal (1959) and Grygaret al. (1972), and examined in relation to empirically determined values ofu from analyses of eclipsing binary light curves. An improved agreement between theory and observation for the calculated limb-darkening coefficients of the present work is noted.     

The spatial distribution and birth-rate of pulsars

The distribution of pulsars in the wide range of observed luminosities has been obtained. It is shown that the function of luminosity (FL) within 3×10²⁶L2×10³⁰ erg s^–1 conforms to the power law dN/dL–c ₁ L ^–, where =1.76±0.06. ForL3×10²⁶ erg s^–1, FL changes its inclination and may be approximated as , where ₁ = 0.7±0.2. On the basis of statistical selection, including all pulsars withL>3×10²⁸ erg s^–1, the distribution of pulsars has been investigated as a function of the distance to the centreR and galactic planeZ.The obtained laws of the radial andZ-distribution of pulsars and galactic supernova remnants and also the radial distribution of types I and II supernovae in the models Sb and Sc support the hypothesis of their origin from the objects of the flat subsystem of Population I. Since there are some arguments in favour of a possible connection between supernovae I and the objects of the intermediate component of the Galaxy, one cannot exclude the possibility of supernovae explosions at the end of the evolution of stars with masses of 1.5–2M . It is also shown that pulsars and supernovae are evidently objects that are connected genetically, and, within the limits of statistical error, they have a similar birth-rate.The empirical law of the evolution of a pulsar's luminosity as a function of its true age has been obtained, according to whichL=c ₂ t ^–, wherec ₂=(3.69±3.4)×10³⁵, =1.32±0.11.     

Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem

We show that the procedure employed in the circular restricted problem, of tracing families of three-dimensional periodic orbits from vertical self-resonant orbits belonging to plane families, can also be applied in the elliptic problem. A method of determining series of vertical bifurcation orbits in the planar elliptic restricted problem is described, and one such series consisting of vertical-critical orbits (a _v=+1) is given for the entire range (0,1/2) of the mass parameter . The initial segments of the families of three-dimensional orbits which bifurcate from two of the orbits belonging to this series are also given.     

The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid

This paper deals with the stationary solutions of the planar restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The collinear equilibria have conditional retrograde elliptical periodic orbits around them in the linear sense, while the triangular points have long- or short-periodic retrograde elliptical orbits for the mass parameter 0 < _crit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case = _crit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness.     

Viscous Fluid Cosmological Models in a Bianchi Type I Universe

Exact solutions of the gravitational field equations for a Bianchi type I anisotropic space-time, filled with a viscous cosmological fluid obeying an equation of state of the form p = , 0 1, are obtained. We investigate both the viscous Zeldovich ( = 1) and < 1 fluid cases, with constant and time varying (proportional to the mean Hubble factor) shear and bulk viscosity coefficients. It is shown that independently of the matter content, the equation of state and the time dependence of the shear and bulk viscosity coefficients, a viscous Bianchi type I universe experiences a transition to an inflationary era. Due to dissipative processes, the mean anisotropy and the shear of the Bianchi type I universe tend very rapidly to zero.