Newtonian analogue of force and motion of a free particle in the gravitational field of Kerr-de Sitter space-time

In the first part of the paper the Newtonian analogue of force for the Kerr-de Sitter metric has been investigated. To the first-order of approximation, a component of the force vector corresponds to the Newtonian gravitational force and a cosmic force arising due to the cosmological constant A. Int the higher order of approximation, the relativistic correction terms due to rotation and the presence of A are obtained. In the second part of the paper the motion of a freely-falling body has been investigated. It is found that plane orbits are not possible. Also a radial fall is not possible and there is a rotational drag on the particle which has no Newtonian analogue.     

Gaseous drag on a gravitational perturber in Modified Newtonian Dynamics and the structure of the wake

We calculate the structure of a wake generated by, and the dynamical friction force on, a gravitational perturber travelling through a gaseous medium of uniform density and constant background acceleration   g _ext  , in the context of Modified Newtonian Dynamics (MOND). The wake is described as a linear superposition of two terms. The dominant part displays the same structure as the wake generated in the Newtonian gravity scaled up by a factor  μ⁻¹( g _ext/ a ₀)  , where a ₀ is the constant MOND acceleration and μ the interpolating function. The structure of the second term depends greatly on the angle between   g _ext  and the velocity of the perturber. We evaluate the dynamical drag force numerically and compare our MOND results with the Newtonian case. We mention the relevance of our calculations to orbit evolution of globular clusters and satellites in a gaseous protogalaxy. Potential differences in the X-ray emission of gravitational galactic wakes in MOND and in Newtonian gravity with a dark halo are highlighted.     

VLBI observations of turbulence in the inner solar wind

I discuss the use of Very Long Baseline Interferometer (VLBI) phase scintillations to probe the conditions of plasma turbulence in the solar wind. Specific results from 5.0 and 8.4 GHz observations with the Very Long Baseline Array (VLBA) are shown. There are several advantages of phase scintillation measurements. They are sensitive to fluctuations on scales of hundreds to thousands of kilometers, much larger than those probed by IPS intensity scintillations. In addition, with the frequency versatility of the VLBA one can measure turbulence from the outer corona 5–10R to well past the perihelion approach of the Helios spacecraft. This permits tests of the consistency of radio propagation and direct in-situ measurements of turbulence. Such a comparison is made in the present paper. Special attention is dedicated to measuring the dependence of the normalization coefficient of the density power spectrum,C _N ² on distance from the sun. Our results are consistent with the contention published several years ago by Aaron Roberts, that there is insufficient turbulence close to the sun to account for the heating and acceleration of the solar wind. In addition, an accurate determination of theC _N ² (R) relationship could aid the detection of transients in the solar wind.     

Spacecraft orbit analysis

The true orbit of a spacecraft differs from its reference orbit by small deviations due to erros in planetary and initial data, radiation and impact accelerations, and correction terms to Newton's theory of gravitation. These distortions are usually small enough to haveadditive effects on range, at the 10 m accuracy level, throughout the mission. Closed form expressions are derived (in cylindrical coordinates) for thedeviation inrange due to any given perturbing acceleration.     

An approximate semi-analytical solution for orbit- and attitude maneuvers of spin-stabilized satellites

The mutual interaction of orbit-attitude maneuvers of spin-stablized satellites is investigated by application of theTwo Variable Expansion Procedure to the Euler equations. The resulting semi-analytical solution describes the short periodic nutation, the long-term attitude variation and the mean linear acceleration of the center of mass. Some applications of the solution are shown by means of a few examples.     

On the collapse of neutron stars and stellar cores to pion-condensed stars

The transition from a neutron star to a pion-condensed star is investigated in Newtonian hydrodynamics. It is shown that in a certain range of ultradense equations of state, there occurs a mass ejection with energies comparable with usual supernova outputs. But the ejected mass is only in the order of 0.02M _⊙. Therefore, the observable consequences of this transition are not so dramatic as conjectured recently. In a realistic scenario including a stiff ultradense equation of state and a weak effect of pion condensation the mass ejection disappears. Additionally the collapse of a stellar core to a neutron star with pion-condensed core is considered. In comparison with a standard supernova scenario we find only a slightly reduced explosion energy. Further, the possible consequence of pion condensation during the secular evolution of the bounced core of a collapsing star to the cool final neutron star is discussed.     

The effect of Coriolis force on acceleration covariance in MHD turbulent dusty flow with rotational symmetry

In this paper we have considered MHD turbulent dusty flow of an incompressible, viscous fluid which is nearly isotropic with rotational and spatially homogeneous. The expression for acceleration covariance in the presence of Coriolis force has been derived and solution has been obtained in terms of defining scalars.     

Non-adiabatic interactions in excitedC 2 H molecules and their relationship toC 2 formation in comets

A unified picture of the photodissociation of theC ₂ H radical has been developed using the results from the latest experimental and theoretical work. This picture shows that a variety of electronic states ofC ₂ are formed during the photodissociation of theC ₂ H radical even if photoexcitation accesses only one excited state. This is because the excited states have many avoided corssings and near intersections where two electronic states come very close to one another. At these avoided crossings and near intersections, the excited radical can hop from one electronic state to another and access new final electronic states of theC ₂ radical. The complexity of the excited state surfaces also explains the bimodal rotational distributions that are observed in all of the electronic states studied. The excited states that dissociate through a direct path are limited by dynamics to produceC ₂ fragments with a modest amount of rotational energy, whereas those that dissociate by a more complex path have a greater chance to access all of phase space and produce fragments with higher rotational excitation. Finally, the theoretical transition moments and potential energy curves have been used to provide a better estimate of the photochemical lifetimes in comets of the different excited states of theC ₂ H radical. The photochemically active states are the 2²₊, 2²II, 3²II, and 3²₊, with photodissociation rate constants of 1.0×10^–6, 4.0×10^–6, 0.7×10^–6, and 1.3×10^–6s^–1, respectively. These rate constants lead to a total photochemical lifetime of 1.4×10⁵ s.     

Redshifts and the Hubble diagrams of Quasi-Stellar Objects

In order to investigate the nature of the redshifts of QSOs, Hubble diagrams have been plotted. First, [log (cz),m _v ] pairs have been plotted for a sample of 252 QSOs. This sample has been drawn from the recent catalogue (Burbidgeet al., 1977) of 633 QSOs after excluding those for which either the redshifts are uncertain or theV magnitudes are not known accurately. Before plotting,K-correction has been applied to theV magnitudes. A least-squares linear fit has been obtained for this plot and, as a result, we get a slope of 0.165±0.012 against 0.2 expected theoretically on the basis of the assumption that the QSOs are at cosmological distances implied by their redshifts. The discrepancy in the value of the slope has been attributed partly to the uncertainty in theK-correction and partly to the evolutionary effect. In order to eliminate the uncertainty due to theK-correction, [log (cz), logf(H)] pairs have been plotted for a sample of 52 QSOs and a least-squares linear fit has been obtained which has a slope of –0.497±0.076, in close agreement with the theoretically expected value of –0.5. This lends support to the hypothesis that the redshifts of the QSOs are cosmological in nature. Finally, the evolutionary effect has been examined, and we conclude that the QSOs do evolve in luminosity in course of time.     

The effect of coriolis force on acceleration covariance in turbulent dusty flow with rotational symmetry

In this paper considering the turbulent dusty flow of an incompressible viscous fluid which is nearly isotropic and spatially homogeneous with an extra vector argument (rotation symmetry) the expression for acceleration covariance in the presence of the Coriolis force has been derived and solution has been obtained in terms of defining scalars.     

Perturbation of a satellite orbiter by the oblateness of the primary planet

The perturbation of an orbiter around a large satellite of a giant planet (Jupiter, Saturn, Uranus or Neptune) produced by the oblateness of the planet is investigated. The perturbing force of theJ ₂-term (general case) and theJ ₄-term (special case of small eccentricity and inclination) is expanded in an appropriate form and the main term and the parallactic term are given explicitly. The variations of the orbital elements are derived using the stroboscopic method. An example shows that the perturbation of the orbit cannot be neglected.     

Generation of gravity waves within the ionosphere by transient heating during high-power wave propagation

Generation of short-range gravity waves within the ionosphere due to inhomogenous heating in the presence of space-localized inhomogeneities during high-power radio wave-propagation has been investigated. The magnitude and from of the anticipated atmospheric wave-trains are obtained. The derived experession of electric field within the ionosphere under the stated perturbed condition may be considered to be manifested through Lorentz-force and Joule-dissipation that influence the neutral gas of the atmosphere via collision-mechanism and thereby gravity waves are launched. The expressions for the low-frequency part of the fractional pressure variations have been derived which are applied to theE-region of the ionosphere. The results are presented graphically.     

g Dependent particle concentration due to sedimentation

Sedimentation of particles in a fluid has long been used to characterize particle size distribution. Stokes’ law is used to determine an unknown distribution of spherical particle sizes by measuring the time required for the particles to settle a known distance in a fluid of known viscosity and density. In this paper, we study the effects of gravity on sedimentation by examining the resulting particle concentration distributed in an equilibrium profile of concentration C _m,n above the bottom of a container. This is for an experiment on the surface of the Earth and therefore the acceleration of gravity had been corrected for the oblateness of the Earth and its rotation. Next, at the orbital altitude of the spacecraft in orbit around Earth the acceleration due to the central field is corrected for the oblateness of the Earth. Our results show that for experiments taking place in circular or elliptical orbits of various inclinations around the Earth the concentration ratio C _m,n /C _m,ave , the inclination seems to be the most ineffective in affecting the concentration among all the orbital elements. For orbital experiment that use particles of diameter d _p =0.001 μm the concentration ratios for circular and slightly elliptical orbits in the range e=0–0.1 exhibit a 0.009 % difference. The concentration ratio increases with the increase of eccentricity, which increases more for particles of larger diameters. Finally, for particles of the same diameter concentration ratios between Earth and Mars surface experiments are related in the following way .     

Observations of photometric profiles of two planetary nebulae

It is noted that the Abel integral of a Gaussian function is a Gaussian function. This special property is used in order to develop an analytic method for studying photometric profile in Planetary Nebulae. Monochromatic observations have been made at the Haute-Provence Observatory using the RCA-CCD (320×512 pixels) mounted at theF/6 Newtonian focus of the 1.2 m telescope. Among the observed nebulae, two of them (NGC 6778 and NGC 7354) are regular enough to test the photometric profile method. The nebular emissivity per volume unit is then obtained for H⁺ and O⁺⁺ ions.     

The gravitational field of a static infinite sheet of matter

The solution of the Einstein field equations in the case of an infinite, static, uniform distribution of matter lying parallel to thex–y plane is obtained. This metric is equivalent to the uniformly accelerated metric which causes the particles to move with uniform acceleration parallel to thez-axis.     

The effect of coriolis force on acceleration covariance in turbulent flow with rotational symmetry

In the present paper, we have considered turbulent flow of an incompressible, viscous fluid which is nearly isotropic with an extra vector argument (i.e. rotational symmetry) and spatially homogeneous. The expression for acceleration covariance in presence of Coriolis force has been derived and solution has been obtained in terms of defining scalars.     

The dynamics of driven magnetic reconnection in coronal arcades

The dynamics of interacting coronal loops and arcades have recently been highlighted by observations from theYohkoh satellite and may represent a viable mechanism for heating the solar corona. Here such an interaction is studied using two-dimensional resistive magnetohydrodynamic (MHD) simulations. Initial potential field structures evolve in response to imposed photospheric flows. In addition to the anticipated current sheet about theX-point separating the colliding flux systems, significant current layers are found to lie all the way along the separatrices that intersect at theX-point and divide the coronal magnetic field into topologically distinct regions. Shear flows across the separatrices are also observed. Both of these features are shown to be compatible with recent analytical studies of two-dimensional linear steady-state magnetic reconnection, even though the driven system that has been simulated is not strictly ‘open’ in the sense implied by steady-state calculations. The implications for future steady-state models are also discussed. The presence of the neutral point also brings into question any constant-density approximations that have previously been used for such quasi-steady coronal evolution models. This results from the intimate coupling between the neutral point and its separatrices communicated via the gas pressure. In terms of the detailed energetics during the arcade evolution, preliminary results reveal that on the order of 3% of the energy injected by the footpoint motions is lost purely through ohmic dissipation. We would therefore anticipate a local hot spot between the interacting flux systems, and a brightening distributed along the length of any separatrix field lines. Furthermore, as the resistivityη is reduced, the flux annihilation rate and the ohmic dissipation rate are found to scale independently ofη.     

Mass discrepancies in galaxies: dark matter and alternatives

Neutral hydrogen line observations of the extended rotation curves of spiral galaxies imply that there exist significant discrepancies between the luminous and dynamical mass beyond the bright optical discs. This means either that galaxies contain significant quantities of non-luminous matter (matter with a mass-to-light ratio very much higher than that of ordinary stars), or that the law of gravity on the scale of galaxies is not the usual Newtonian inverse square law. Attempts to account for the observed discrepancy in the context of these two explanations are reviewed here with emphasis given to the second and less conventional alternative. It is argued that the standard picture of spiral galaxy halo and disc formation in the context of cold dark matter cannot account for the observed systematics of the discrepancy — notably rotation curves which are seen to be flat and featureless from the bright inner regions where the visible matter dominates the dynamics (in some cases overwhelmingly) to the outer regions where the dark halo dominates. It is demonstrated that in those galaxies with well-observed rotation curves, the discrepancy apparently appears below a critical acceleration. Any dark matter explanation of the discrepancy must account for this fact. Moreover, this would also eliminate empirically motivated modifications of Newton's law in which the deviation from 1/r occurs beyond a fundamental length scale. The suggestion by Milgrom in which the force law becomes essentially 1/r below a critical acceleration (MOND) can account for most of the observed systematics of galaxy rotation curves and, significantly, leads to the observed luminosity-velocity relationship in spiral galaxies (the Tully-Fisher law). Generally covariant theories of gravity which predict this phenomenology in the weak-field limit are described. Although there is not yet a theory which obviously meets all of the requirements for a physically viable alternative to dark matter, a generalized scalar-tensor theory of the form suggested by Bekenstein (phase coupling gravitation) is the currently leading candidate and has the advantage of being testable locally.     

Numerical integration of dynamical systems with Lie series

The integration of the equations of motion in gravitational dynamical systems—either in our Solar System or for extra-solar planetary systems—being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier and Dvorak, Astron Astrophys 132, 203 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie terms when other major forces are considered. As a matter of fact, previous studies have been done but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework of General Relativity and a simplified force for the Yarkovsky effect. A general iteration procedure is applied to derive the Lie series to any order and precision. We then give an application to the integration of the equation of motions for typical Near-Earth objects and planet Mercury.     

Rotational dynamics of a deformable medium

The aim of the present investigation has been to derive from the fundamental Cauchy's first law of continuum mechanics the explicit form of the Eulerian general equation which governs the three-axial generalized rotation about the centre of mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian) or not, consisting of compressible fluid of arbitrary viscosity, in an external field of force. The generalized rotation is a superposition of the so-called rigid-body (i.e., time dependent only) rotation of the continuum plus a nonrigidbody (i.e., position-time dependent) rotation of its configurations.In Section 2, which follows brief introductory remarks outlining the problem, we develop a mathematical theory which describes the whole phenomenon in terms of two rotation tensors corresponding, respectively, to the rigid-body and nonrigid-body rotation modes. In Section 3, we derive the differmation vectors of velocity and acceleration. The equations we have obtained are a very general version of Navier Stokes' equations, which were not given in previous investigations. In Section 4, we perform integration of the left-hand side of Cauchy's first law, cross-multiplied by the position vector, without any restriction. In Section 6, integration of the right-hand side of the same law, cross-multiplied by the position vector, is carried out, by taking account of actually simplifying assumptions stated in Section 5. All the integral terms occurring in both sides are expressed explicitly by quantities evaluated in terms of components of properly defined moments.Finally, in Section 7, the system of the general Eulerian equations is set up; and some easy modifications are given, which describe nicely physical models of special interest; while the concluding Section 8 contains a general discussion of the results.