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1.
Determination of the potential field in a fixed (inertial) system may be accomplished by the solution of a homogeneous linear partial differential equation when a family of orbits of a body moving in the field is given. This partial differential equation was presented and thoroughly analyzed earlier. The present paper discusses the same problem in a rotating system where the centrifugal and Coriolis effects render the pertinent partial differential equation in general non-homogeneous and non-linear. A linear, though non-homogeneous, partial differential equation for the determination of the synodic potential is obtained only in the special case of iso-energetic families of orbits.  相似文献   

2.
In this paper a method is concerned which makes it possible to describe numerically and analytically the most famous structures in the non-equilibrium ionosphere, such as stratified and yacht sail like structures, flute jets, wakes and clouds. These problems are of practical interest in space sciences, astrophysics and in turbulence theory, and also of fundamental interest since they enable one to concentrate on the effects of the ambient electric and magnetic fields. Disturbances of charged particle flows due to the ambient flow interactions with bodies are simulated with taking into account the ambient magnetic field effect. The effects of interactions between solid surfaces and the flows was simulated by making use of an original image method. The flow disturbances were described by the Boltzmann equation. In the case of the ambient homogeneous magnetic field the Boltzmann equation is solved analytically. The case of diffuse reflection of particles by surface is considered in detail. The disturbances of charged particle concentration are calculated in 3D space. The contours of constant particle concentration obtained from numerical simulations illustrate the dynamics of developing stratifications and flute structures in charged particle jets and feffect. The wakes under the ambient magnetic field effect. The basic goal of this paper is to present the method and to demonstate its possibility for simulations of turbulence, plasma jets, wakes and clouds inthe ionosphere and Space when effects of electric and magnetic fields are taken into account. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

3.
Newton's apsidal precession theorem in Proposition 45 of Book I of the 'Principia' has great mathematical, physical, astronomical and historical interest. The lunar theory and the precession of the perihelion of the planet Mercury are but two examples of the applications of this theorem. We have examined the precession of orbits under varying force laws as measured by the apsidal angle θ( N , e ), where N is the index for the centripetal force law, for varying eccentricity e . The paper derives a general function for the apsidal angle, dependent only on e and N as the potential is spherically symmetric. Further, we explore approximate ways of the solution of this equation, in the neighbourhood of   N = 2  which happens to be the case of greatest historical interest. Exact solutions are derived where they are possible. The first derivatives  ∂θ/∂ N   and  ∂θ/∂ h   [where h ( N , e ) is the angular momentum] are analytically expressed in the neighbourhood of   N = 2  (case of the inverse square law). The value of  ∂θ/∂ N   is computed numerically as well for  1 ≤ N < 3  . The resulting integrals are interesting improper integrals with singularities at both limits. Some of the integrals, especially for   N = 2  , can be given in closed form in terms of generalized hypergeometric functions which are reducible in terms of algebraic and logarithmic functions. No evidence was found for isolated cases of zero precession as e was increased. The   N = 1  case of the logarithmic potential is also briefly discussed in view of its interest for the dynamics of eccentric orbits and its relevance to realistic galaxy models. The possibility of apsidal precession was also examined for a few cases of high-eccentricity asteroids and extrasolar planets. We find that these systems may provide interesting new laboratories for studies of gravity.  相似文献   

4.
The Lagrange expansion, which may be used to derive the Fokker-Planck equation, is here used to derive the corresponding expression for the flux of particles subject to a stochastic scattering process. The coefficients which occur in this expression are, in general, not the same as the coefficients which occur in the Fokker-Planck equation itself. In the special case that the particle distribution involves only one independent variable, the particle flux is determined by the familiar Fokker-Planck coefficients. Evaluation of particle flux is of special interest in the study of stochastic acceleration.  相似文献   

5.
Pseudopotential analysis has been employed to derive a modified Sagdeev potential-like wave equation for studying the sheath formation in astroplasma problems. Complexity in process urges to derive the new findings numerically by using fourth-order Runge-Kutta method. Main emphasis has been given to investigate the role of Coriolis force on the formation and changes on coherent structures of sheath suitably thought for the configuration of astroplasma. Study determines the sheath thickness and potential variation with the interaction of Coriolis force and thereby finds dynamical behavior of levitated dust grains into the evaluated sheath region. This leads to find the dust size, and corresponding forces generated on dust grain with a view to relate theoretical observations to real astrophysical phenomena and could be of interest to explain formation of dust clouds in spaces. To support the observations, we some thoughtful numeric plasma parameters for the case of Earth’s Moon, have taken for graphical presentations. Overall observations expect the study could be of interest as an advanced knowledge in rotating astroplasmas, and expecting many salient features which are yet to be known.  相似文献   

6.
Szebehely's equation for the potential generating a prescribed family of orbits in two dimensions is generalized for three-dimensional orbits. A simultaneous system of first-order linear partial differential equations is derived for the determination of the potential in the three-dimensional case. Solutions of this system are found in several cases including Kepler's problem too.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.This paper is dedicated to Professor Victor Szebehely on the occasion of his 60th birthday.  相似文献   

7.
The orbits of a family of three-dimensional periodic orbits in the restricted problem of three bodies form a surface. In this paper we determine the equation of this surface in the case of the orbits of double symmetry of the family which emanates from the equilibrium pointL 1. This equation is obtained numerically by a least squares approximation method.  相似文献   

8.
A class of equilibrium solutions of the Vlasov equation for self-gravitating systems is discussed. The density and the potential are derived in form of Jacobi polynomials, which in a special case give rise to a model with uniform density.  相似文献   

9.
Szebehely’s equation is a first order partial differential equation relating a given family of orbits f (x, y) = q traced by a unit mass material point, the total energy E=E(f), and the unknown potential V=V (x, y) which produces the family. Although linear in V, this equation cannot generally be solved. In this paper we develop the reasoning for finding several cases for which Szebehely’s equation can be solved by quadratures. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

10.
In this paper, we present in detail the whole process by which the Eulerian general equation is obtained, holding in case of a differentially rotating gaseous polytrope. The explicit form of this equation is derived on the basis of a model developed in a previous investigation.  相似文献   

11.
Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.  相似文献   

12.
The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrödinger equation coupled to a Poisson equation determining the gravitational potential. This approach has a number of interesting features, many of which were pointed out in a seminal paper by Widrow & Kaiser. In particular we show that this approach yields an elegant reformulation of an idea of Jones concerning the origin of lognormal intermittency in the galaxy distribution.  相似文献   

13.
We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w 0 =  p x0/ρx0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.  相似文献   

14.
Abstract— Asteroids and comets are of great scientific interest: their interior structure and composition, which are poorly known, provide information about conditions and processes that occurred during the early stages of solar system development. They are also of interest for social and economic reasons. Their proximity to Earth and abundance in the solar system make them potential sources of raw materials as well as a threat, as evidenced by past catastrophic impacts. Information on their composition and structure is therefore important to assess both the potential benefit of these objects and mitigate the potential risk they pose. This paper describes the use of radio reflection tomography for studying the interiors of asteroids and comets. We discuss technical issues regarding benefits and challenges of implementing a radio reflection tomography instrument and present potential solutions. This paper addresses a range of topics including (1) data collection scenarios, (2) data processing and inversion, and (3) instrument implementation. A “strawman” instrument capable of imaging the full interior of an asteroid or a comet with dimensions of a few kilometers is presented. Such an instrument can play a significant role in studying the near‐Earth objects, both for scientific and socio‐economic purposes.  相似文献   

15.
Following the formalism on the polarization transfer equation presented recently by the same authors, solutions to this transfer equation under several special cases of interest are discussed in this paper. Analytic solutions for the Stokes parameters for several special cases of interest are given, and numerical solutions to these parameters for arbitrary propagation direction and two types of inhomogeneity of the medium are presented.  相似文献   

16.
An isothermal hydrodynamic model of the motions of a multi-ion plasma in a gravitational field is developed and the properties of the flow are discussed for the case of major astrophysical interest in which the gas undergoes a subsonic-supersonic transition. It is shown that the existence of critical points thorough which the plasma has to pass will determine a large number of the plasma parameters, especially the temperature of the minor ions. The equation of motion of a two ion gas (hydrogen-helium) are solved numerically and yield the interesting result that the bulk velocity of the plasma constituents are not equal at 1 AU.Operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation.  相似文献   

17.
Szebehely's renowned equation given in 1974, allowing for potential determination from a given orbit or family of orbits, is proved to be equivalent with an equation deduced in 1963 by Drǎmbǎ. This basic equation in the inverse problem of dynamics, for which the denomination of Drǎmbǎ –Szebehely equation is proposed, is generalized for the motion in the n-dimensional Euclidean space. A method for the determination of the potential function from motion equations is extended to this space.  相似文献   

18.
The inertial effect on the structure of the magnetosphere of a rotating star is investigated, in the corotation approximation for a surrounding quasi-neutral plasma. The equation of motion reduces to a usual static balance equation between the electromagnetic and the centrifugal forces, in the rotating frame. However the MHD condition, which can be regarded as a special form of the generalized Ohm's law, is modified by the inclusion of inertial effect, with a violation of the frozen-in condition in case of a general (i.e., not restricted to corotation) plasma motion. The inertial effect on the electromagnetic field is summarized in a partial scalar potential named the non-Backus potential, which is proportional to the centrifugal potential in the corotation approximation.An approximate solution of this corotation problem is given, in which another characteristic radiusr M appears besides the light radiusr L . This radius defines a distance beyond which the inertial effect becomes dominant over the electromagnetic one, and is useful in estimating the magnitude of the terminal velocity of a centrifugal wind. A few examples of the modification of dipole magnetic field due to the inertial effect are visualized. In an oblique-rotation case, it can be seen that such a warp of the neutral sheet (the surface ofB r =0) is reproduced as observed in the Jovian magnetosphere.  相似文献   

19.
In a simple approximation, the evolution of a stellar system can be described in terms of the solutions to a diffusion equation for motion in a harmonic potential. This paper presents a discussion and characterization of the normal modes for this equation. These solutions are of particular interest in that they provide a simple example of the interplay between dynamical and relaxation phenomena. For the case of a large system, in which the relaxation timet r is much greater than the dynamical timet d,there exists a well-defined sense in which the effects of relaxation may be viewed as a perturbation of motion in the fixed field: the dynamical effects give rise to a purely oscillatory behavior, whereas collisions among stars provide a dissipative mechanism that drives the system towards the unique isothermal equilibrium. Alternatively, the presence of the fixed potential serves to alter the e-folding time for the various modes. In the limit thatt r t d , all characteristic relaxation times are essentially doubled. This suggests a danger in the use of velocity space equations to model the effects of evaporation.  相似文献   

20.
We study the propagation of solitary waves of vortices within a spherical shell which constitutes the uppermost layer of a solid planet. This solid-liquid configuration rotates with constant angular velocity about an axis which is fixed with respect to the solid surface. The fluid within the shell is inviscid, incompressible, and of constant density. The motion imparted by the planetary rotation upon this fluid mass is governed by the Laplace tidal equation from which the potential of the extraplanetary forces has been deleted. Consistent with this ocean model, we establish that the stream function of a solitary wave of vortices must satisfy a third-order partial differential equation. We obtain solutions to this wave equation by imposing the condition that the vertical component of vorticity be functionally related to the stream function. We find that this dependence must necessarily be of the exponential type and that the solution to the wave equation then reduces to a quadrature depending on some arbitrary parameters. We prove that we can always choose the values of these parameters in order to approximate the integral in question by means of an analytic function: we reach a representation of the stream function of a solitary wave of vortices in terms of hyperbolic functions of time and position.This paper is dedicated to the memory of Professor Zdenek Kopal.  相似文献   

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