On the damping of the bending waves in Saturn’s ring

We study numerically the motion of a single particle in the bending wave of finite thickness in Saturn’s ring. We include the forcing due to the planet, a moon, the coriolis force and the self gravity of the ring. In particular, we compute the variation of the velocity arising due to the variation of the amplitude and the phase of the epicyclic motion across the local vertical height of the ring. We suggest that the dissipation of energy due to the collision of ring particles in this shear layer damps out the bending wave of Saturn’s ring at the 5:3 vertical resonance of Mimas within a distance of 150 km from the site of its launching as is observed in Voyager data.     

Giant CP Stars?

This study is part of an investigation of the possibility of using chemically peculiar (CP) stars to map local galactic structure. Correct luminosities of these stars are therefore crucial. CP stars are generally regarded as main-sequence or near-main-sequence objects. However, some CP stars have been classified as giants. A selection of stars, classified in literature as CP giants, are compared to normal stars in the same effective temperature interval and to ordinary ‘non giant’ CP stars. We find no clear confirmation of a higher luminosity for ‘CP giants’, than for CP stars in general. In addition, CP characteristics seem to be individual properties not repeated in a component star or other cluster members.     

Potentials having two orthogonal families of curves as trajectories

We study, using the tool of Joukovsky’s orthogonal coordinates, the determination of the potentials having two families of orthogonal trajectories. We show for compatible cases the existence and the uniqueness, up to a constant factor, of the solution. We note the importance of the ‘isothermal’ nets of curves. We study as an example the net of geometrically similar conic curves and orthogonal trajectories. This revised version was published online in July 2006 with corrections to the Cover Date.     

Results from the Huygens probe on Titan

The Cassini–Huygens mission, comprising the NASA Saturn Orbiter and the ESA Huygens Probe, arrived at Saturn in late June 2004. The Huygens probe descended under parachute in Titan’s atmosphere on 14 January 2005, 3 weeks after separation from the Orbiter. We discuss here the breakthroughs that the Huygens probe, in conjunction with the Cassini spacecraft, brought to Titan science. We review the achievements ESA’s Huygens probe put forward and the context in which it operated. The findings include new localized information on several aspects of Titan science: the atmospheric structure and chemical composition; the aerosols distribution and content; the surface morphology and composition at the probe’s landing site; the winds, the electrical properties, and the implications on the origin and evolution of the satellite.     

Anisotropic Bianchi type-I models with constant deceleration parameter in general relativity

A special law of variation for Hubble’s parameter is presented in a spatially homogeneous and anisotropic Bianchi type-I space-time that yields a constant value of deceleration parameter. Using the law of variation for Hubble’s parameter, exact solutions of Einstein’s field equations are obtained for Bianchi-I space-time filled with perfect fluid in two different cases where the universe exhibits power-law and exponential expansion. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.     

Bianchi type-II space-times with constant deceleration parameter in self creation cosmology

The properties of locally rotationally symmetric Bianchi type-II perfect fluid space-times are analyzed in Barber’s second self-creation theory by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. By assuming the equation of state p=γ ρ, many new solutions are obtained for different era—Zel’dovich, radiation, vacuum and vacuum energy dominated. The solutions with power-law and exponential expansion are discussed. A detailed study of geometrical and physical parameters is carried out. The nature of singularity is also clarified in each case.     

Wisdom system: Dynamics in the adiabatic approximation

A simple approximate model of the asteroid dynamics near the 3:1 mean–motion resonance with Jupiter can be described by a Hamiltonian system with two degrees of freedom. The phase variables of this system evolve at different rates and can be subdivided into the ‘fast’ and ‘slow’ ones. Using the averaging technique, wisdom obtained the evolutionary equations which allow to study the long-term behavior of the slow variables. The dynamic system described by the averaged equations will be called the ‘Wisdom system’ below. The investigation of the, wisdom system properties allows us to present detailed classification of the slow variables’ evolution paths. The validity of the averaged equations is closely connected with the conservation of the approximate integral (adiabatic invariant) possessed by the original system. Qualitative changes in the behavior of the fast variables cause the violations of the adiabatic invariance. As a result the adiabatic chaos phenomenon takes place. Our analysis reveals numerous stable periodic trajectories in the region of the adiabatic chaos.     

Stability of a finite disc under the influence of a spherical halo

We have studied the stability of finite gaseous discs, against large-scale perturbations, under the influence of spherical, massive haloes. A surface-density distribution consistent with the observed spiral-tracer profiles in disc galaxies is considered for the disc. We find that growing eigenmodes with both ‘trailing’ and ‘leading’ spirals exist in ‘cold’ discs for a wide range of values of the halo mass and its radius. The amplification rates of the unstable modes reduce as the ratio of the mass of the halo to the mass of the disc is increased. A uniform halo is not very effective towards stabilizing the disc against these modes. The results from the present study are consideredvis-a-vis previous studies on the global modes of self-gravitating discs.     

Does Si play a role in the formation of extrasolar planet systems?

With the high signal-to-noise ratio spectra, we obtained Si abundances of 22 extrasolar planet host stars, and discussed some constraints on the planet formation. Using our silicon abundance results and other authors’ Si abundance studies about planets-harboring stars, we investigated the correlation between the dynamical properties and the silicon abundance. We propose a hypothesis that higher primordial metallicity in the host stars’ birth cloud with higher abundance of Si will make the cloud more sticky to bypass the time scale restriction in planet formation and easier to form the planets.     

Algorithms for Stellar Perturbation Computations on Oort Cloud Comets

We investigate different approximate methods of computing the perturbations on the orbits of Oort cloud comets caused by passing stars, by checking them against an accurate numerical integration using Everhart’s RA15 code. The scenario under study is the one relevant for long-term simulations of the cloud’s response to a predefined set of stellar passages. Our sample of stellar encounters simulates those experienced by the Solar System currently, but extrapolated over a time of 10¹⁰ years. We measure the errors of perihelion distance perturbations for high-eccentricity orbits introduced by several estimators – including the classical impulse approximation and Dybczyński’s (1994, Celest. Mech. Dynam. Astron. 58, 1330–1338) method – and we study how they depend on the encounter parameters (approach distance and relative velocity). We introduce a sequential variant of Dybczyński’s approach, cutting the encounter into several steps whereby the heliocentric motion of the comet is taken into account. For the scenario at hand this is found to offer an efficient means to obtain accurate results for practically any domain of the parameter space.     

Multiple solutions in preliminary orbit determination from three observations

Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s: they may change according to the value of a parameter that depends on the observations.     

Straight line orbits in Hamiltonian flows

We investigate straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta for arbitrary dimensions and is considered in more detail for two and three dimensions. Next we specialize to homogeneous potentials and their superpositions, including the familiar Hénon–Heiles problem. It is shown that SLO’s can exist for arbitrary finite superpositions of N-forms. The results are applied to a family of potentials having discrete rotational symmetry as well as superpositions of these potentials.     

Gravitational Mesoscopic Constraints in Cosmological Dark Matter Halos

We present an analysis of the behaviour of the ‘coarse-grained’ (‘mesoscopic’) rank partitioning of the mean energy of collections of particles composing virialized dark matter halos in a Λ-CDM cosmological simulation. We find evidence that rank preservation depends on halo mass, in the sense that more massive halos show more rank preservation than less massive ones. We find that the most massive halos obey Arnold’s theorem (on the ordering of the characteristic frequencies of the system) more frequently than less massive halos. This method may be useful to evaluate the coarse-graining level (minimum number of particles per energy cell) necessary to reasonably measure signatures of ‘mesoscopic’ rank orderings in a gravitational system.     

Minima de L'intégrale D'action du Problème Newtoniende 4 Corps de Masses Égales Dans R3: Orbites 'Hip-Hop'

We consider the problem of 4 bodies of equal masses in R ³ for the Newtonian r⁻¹ potential. We address the question of the absolute minima of the action integral among (anti)symmetric loops of class H ¹ whose period is fixed. It is the simplest case for which the results of [4] (corrected in [5]) do not apply: the minima cannot be the relative equilibria whose configuration is an absolute minimum of the potential among the configurations having a given moment of inertia with respect to their center of mass. This is because the regular tetrahedron cannot have a relative equilibrium motion in R ³ (see [2]). We show that the absolute minima of the action are not homographic motions. We also show that if we force the configuration to admit a certain type of symmetry of order 4, the absolute minimum is a collisionless orbit whose configuration ‘hesitates’ between the central configuration of the square and the one of the tetrahedron. We call these orbits ‘hip-hop’. A similar result holds in case of a symmetry of order 3 where the central configuration of the equilateral triangle with a body at the center of mass replaces the square. This revised version was published online in July 2006 with corrections to the Cover Date.     

Plane symmetric string cosmological models in self-creation theory of gravitation

Plane Symmetric string cosmological models are presented in Barber’s second self creation theory of gravitation and obtained Einstein’s plane symmetric string cosmological models as a special case. Some physical and geometrical properties of the models are also discussed.     

Angular velocity glitches of the Vela pulsar in a model with “centrifugal buoyancy” of vortices

The forces acting on the solid crust of a differentially rotating neutron star are examined when a nonuniform excess of chemical potential exists. The resultant of the external forces, a stress force, is expressed in terms of a centrifugal buoyancy force and the deformation of the star’s crust under the action of this force is calculated. It is shown that there is a region within the star where the resulting stresses lead to fracture of the crust when the difference in the angular velocities of the superfluid and normal components reaches a critical value. The “centrifugal buoyancy” mechanism for generating a glitch is used to estimate the parameters of glitches in the Vela pulsar. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 183–197 (May 2007).     

The Inverse Problem of Dynamics for Systems with Non-Stationary Lagrangian

We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric family of evolving orbits. An equation for non-stationary space symmetrical ‘potential’ function of such Lagrangian is given and this stands for the analog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its basis adiabatic invariants of non-stationary two-body problem containing a tangential force are found. This revised version was published online in July 2006 with corrections to the Cover Date.     

Planar Symmetric Periodic Orbits in Four Dipole Problem

We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines” such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn. For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families of three dimensional symmetric periodic orbits.     

Posterior probability of the deceleration parameter q0 from quasars provided with a luminosity indicator

We have worked out a ’statistical algorithm’ for obtaining the posterior probability density of the deceleration parameter q₀ from quasars where there is a luminosity indicator available. We point out that the role of the luminosity indicator is to provide asecond estimate of individual luminosities after a first estimate has been obtained from measured brightness and redshift together with an assumed q₀. Discrimination of q₀ is to be sought in the statistical properties of the set of differences between the two estimates (the residuals). We show that the variance of the residuals and their correlation with redshifts (further refined to luminosity distances) are two independent test-statistics for q₀, whose known distributions then lead to the probability density sought. We have applied the above algorithm to a sample of flat-spectrum radio quasars with measured CIV, MgII and Ly α lines. A combined Baldwin’s relation was used for all 3 lines. Our result is that log q₀ is normally distributed with a mean value of + 0.270± 0.135 (s.d.), or, q₀ = + 1.86 ± 0.135 dex. This result, we believe, is the sharpest result so far published on q₀.     

Meteoroid fragments dynamics: Collimation effect

There is significant evidence that some fraction of meteoric bodies is destroyed in the atmosphere. The evolution of the fragment cloud depends on a large number of factors, amound them: the meteoroid’s altitude and velocity at the moment of greakup, fragment sizes and properties of a body material. The interaction of shock waves forming in front of the fragments may lead to both an increase and decrease of the midsection area of the fragment cloud (Artem’eva & Shuvalov, 1996; Laurence et al., 2007). In this work, we consider the interaction of the fragments in a supersonic flow. The configuration properties of two spherical bodies of different radii are considered. Via numerical simulations, we calculate the pressure distribution in the flow around the two bodies for different relative positions. We construct the functions of the coefficients of transverse and drag forces from the angle between the central line of the two bodies and the flow direction for different distances between the two fragments. We find the conditions for the collimation effect, i.e., fragment involving into the wake of the leading (usually, the largest) fragment. We systematize the simulation results for drag and transverse forces and infer the basic aerodynamic properties of the meteoroid fragments.