A tilted Bianchi type-V perfect fluid solution for stiff matter

We present a solution to the Einstein field equations for a massless scalar field in a Bianchi type-V spacetime, which can be interpreted as a solution for a perfect fluid with the equation of state of stiff matter. This solution complements a solution previously given by us for an anisotropic fluid.     

A discussion of the solution for the motion of Pluto

In a previous paper, a semi-analytical solution for the long-term motion of Pluto was presented. The present paper contains: (1) a comparison of the present solution with the solution by Williams and Benson; (2) a discussion of the effect of the near resonance between Pluto and Uranus; and, (3) a calculation of the librational period of the eccentricity, inclination and perihelion.The semi-analytical solution is shown to agree very closely with the long-term solution for Pluto obtained by Williams and Benson using numerical integration of the averaged equations of motion. A small difference between the two solutions is attributed to neglecting the eccentricity and inclination of Neptune in the semi-analytical solution.     

Note on the asymmetry of bipolar sunspot groups

It is shown that the analytical solution of the equilibrium plasma equation which is a superposition of the axial-symmetric solution and the solution with helical symmetry can describe asymmetry of elements for a bipolar sunspot group.     

Self-consistent solution for gaseous shock and stellar density wave

In this paper, the self-consistent density wave theory containing both a gaseous shock and a linear stellar density wave is studied, and a quasi-stable, tightly-wound, two-arm solution is obtained. The solution is convergent if the incomplete, linearized hydrodynamic equations are used, and the solution then gives the same dispersion relation as the local, asympotic solution, but the density and field profiles will be non-sinusoidal. The stellar wave will be unstable if the complete, linearized hydrodynamic equations are used.     

Comment on the Brans-Dicke-Bianchi type-III vacuum solution

We wish to point out that the Brans-Dicke-Bianchi type-III vacuum solution recently given by Tiwari and Singh (1984) is not new. Moreover, the solution given has no correct Einstein limit, contrary to what is claimed by these authors. The Ellis-MacCallum vacuum solution in the Einstein case can be obtained from the Brans-Dicke solution first given by Lorenz-Petzold (1984a).     

Comment on the vacuum Bianchi type I solution in the Brans-Dicke theory

We wish to point out that the axialsymmetric Bianchi type I vacuum solution recently given by Ram, is wrong. Moreover, the correct solution is only a special case of the general triaxial Bianchi type I solution given by Ruban and Finkelstein.     

A new plasmon solution with centrifugal pressure

The 'plasmon' solution of De Young & Axford describes the interaction between a high-velocity clump and the surrounding medium. Even though this solution is probably too simplistic, it has proven to be most useful in the study of diverse astrophysical flows. In the present paper, we discuss a more detailed solution of the plasmon problem, which includes the centrifugal effects of the environmental material flowing around the plasmon. We derive both numerical and approximate analytic solutions of this problem, and compare them with the analytic solution of De Young & Axford.     

On the free rotation of a rigid body

It is well known that the equations governing the motion of a freely-rotating rigid body possess an exact analytical solution, involving Jacobi's elliptic functions. Andoyer (1923) and Deprit (1967) have shown that the problem may be very usefully reduced to a one-degree-of-freedom Hamiltonian system. When two of the body's principal moments of inertia are very nearly equal, the Hamiltonian system has the same form as the Ideal Resonance Problem. In earlier publications (Jupp, 1969, 1972, 1973), the author has constructed formal power-series solutions of the latter problem.In this article, the general solution of the Ideal Resonance Problem is employed to formulate a second-order formal series solution of the problem of a freely-rotating rigid body which has two of its principal moments of inertia differing by a small quantity. This solution is firstly expressed in terms of the mean elements, and then in terms of the initial conditions. The latter solution is global in nature being applicable over the whole phase plane. It is demonstrated that the exact solution and the second-order formal series solution, written in terms of the initial conditions, differ by terms of at most third order in the small parameter, over the whole domain of possible motions. This serves as an important check on the general results published in the earlier articles.     

Reduction the secular solution to periodic solution in the generalized restricted three-body problem

The aim of the present work is to find the secular solution around the triangular equilibrium points and reduce it to the periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some numerical and graphical investigations for the effects of the perturbed forces are introduced. This model can be used to examine the existence of a dust particle near the triangular points of an oblate and radiating binary stars system surrounded by a belt.     

Runaway of Line-driven Winds toward Critical and Overloaded Solutions

Line-driven winds from hot stars and accretion disks are thought to follow a unique, critical solution that corresponds to a maximum mass-loss rate and a particular velocity law. We show that in the presence of negative velocity gradients, radiative-acoustic (Abbott) waves can drive shallow wind solutions toward larger velocities and mass-loss rates. Perturbations that are introduced downstream from the critical point of the wind lead to a convergence toward the critical solution. By contrast, low-lying perturbations cause evolution toward a mass-overloaded solution, developing a broad deceleration region in the wind. Such a wind differs fundamentally from the critical solution. For sufficiently deep-seated perturbations, overloaded solutions become time-dependent and develop shocks and shells.     

Monoenergetic-source solutions of the steady-state cosmic-ray equation of transport

A non spherically-symmetric monoenergetic-point-source solution of the steady-state equation of transport for cosmic-rays in the interplanetary region, in which monoenergetic particles are released isotropically and continuously from a fixed heliocentric position is derived by a Laplace transform method. The solution is for a spherically-symmetric model of the propagating region incorporating anisotropic diffusion, with a diffusion tensor symmetric about the radial direction, and the solar wind velocity is radial and of constant speedV. The spherically-symmetric monoenergeticsource solution of Webb and Gleeson (1973) and of Toptygin (1973) is regained from the spherically-symmetric component of the point-source solution.     

The eccentric case of a fast-rotating,gravity-gradient-perturbed satellite attitude solution

A closed-form first-order perturbation solution for the attitude evolution of a triaxial space object in an elliptical orbit is presented. The solution, derived using the Lie–Deprit method, takes into account gravity-gradient torque and is facilitated by an assumption of fast rotation of the object. The formulation builds on the earlier implementation of Lara and Ferrer, which assumes a circular orbit. The previously presented work—which assumes spin about an object’s axis of maximum inertia—is further extended by the explicit presentation of the transformations required to apply the solution to an object spinning about its axis of minimum inertia. Additionally, several numerical analyses are presented to more completely assess the utility of the solution. These studies (1) validate the elliptical solution, (2) assess the impact of varying the small parameter of the perturbation procedure, (3) analyze the assumption of fast rotation, and (4) apply the solution to the common and important scenario of a tumbling rocket body.     

Exponential instability of collision orbit in the anisotropic Kepler problem

The straight-line collision solution in the anisotropic Kepler problem is extended to a periodic solution by means of Sundman's analytic continuation. It is shown that this collision periodic solution is always exponentially unstable.     

Diffuse reflection and transmission of solar radiation by a finite atmosphere bounded by a reflecting surface

The problem of diffuse reflection and transmission of solar radiation through a planetary atmosphere bounded from below by a reflecting surface is solved. The solution method based on rewriting the solution of the proposed problem in terms of the well known standard problem solution, where the planetary surface does not reflect. The solution of the standard problem can be found elsewhere or as we did by using the maximum entropy method. Numerical results for the angular radiation intensity and for the reflection and transmission coefficients are presented and compared with those obtained by Chandrasekhar's method.     

Lambert problem solution in the hill model of motion

The goal of this paper is obtaining a solution of the Lambert problem in the restricted three-body problem described by the Hill equations. This solution is based on the use of pre determinate reference orbits of different types giving the first guess and defining the sought-for transfer type. A mathematical procedure giving the Lambert problem solution is described. This procedure provides step-by-step transformation of the reference orbit to the sought-for transfer orbit. Numerical examples of the procedure application to the transfers in the Sun–Earth system are considered. These examples include transfer between two specified positions in a given time, a periodic orbit design, a halo orbit design, halo-to-halo transfers, LEO-to-halo transfer, analysis of a family of the halo-to-halo transfer orbits. The proposed method of the Lambert problem solution can be used for the two-point boundary value problem solution in any model of motion if a set of typical reference orbits can be found.     

Refined model for the evolution of distant satellite orbits

We consider a model that describes the evolution of distant satellite orbits and that refines the solution of the doubly averaged Hill problem. Generally speaking, such a refinement was performed previously by J. Kovalevsky and A.A. Orlov in terms of Zeipel’s method by constructing a solution of the third order with respect to the small parameter m, the ratio of the mean motions of the planet and the satellite. The analytical solution suggested here differs from the solutions obtained by these authors and is closest in form to the general solution of the doubly averaged problem (∼m ²). We have performed a qualitative analysis of the evolutionary equations and conditions for the intersection of satellite orbits with the surface of a spherical planet with a finite radius. Using the suggested solution, we have obtained improved analytical time dependences of the elements of evolving orbits for a number of distant satellites of giant planets compared to the solution of the doubly averaged Hill problem and, thus, achieved their better agreement with the results of our numerical integration of the rigorous equations of perturbed motion for satellites.     

A complex exponential solution to the unified two-body problem

A complex exponential solution has been derived which unifies the elliptic and hyperbolic trajectories into a single set of equations and provides an exact, analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this complex exponential solution formulation, a variation of parameters formulation for the perturbed two-body problem has been derived. In this paper, we present the analytical formulation of the complex exponential solution, numerical simulations, a comparison with classical solution methods, and highlight the benefits of this approach compared with the classical developments. Previously presented as AAS 07-136 at the 17th AAS/AIAA Spaceflight Mechanics Meeting Sedona, Arizona, AAS 08-206 and AAS 08-230 at the 18th AAS/AIAA Spaceflight Mechanics Meeting Galveston, Texas.     

The ideal resonance problem a comparison of two formal solutions I

Garfinkel's solution of the Ideal Resonance problem derived from a Bohlin-von Zeipel procedure, and Jupp's solution, using Poincaré's action and angle variables and an application of Lie series expansions, are compared. Two specific Hamiltonians are chosen for the comparison and both solutions are compared with the numerical solutions obtained from direct integrations of the equations of motion. It is found that in deep resonance the second-mentioned solution is generally more accurate, while in the classical limit the first solution gives excellent agreement with the numerical integrations.This article represents a summary of a much more extensive programme of research, the complete results of which will be published in a future article.     

广义相对论中静态荷电球体的内解

本文在假设荷电球体内部物质密度为ρ_m=μγ~α,电荷密度为ρ_e=ρ_0γ~(b_e-λ/2)的情况下,严格求解Einstein-Maxwell场方程,求得了静态荷电球体的一个较为普遍的内部解。这个解可以看作是Wyman得到的内部解推广到荷电情况下的结果,并且将Wilson,李鉴增,Santos,Pant和Sah等人给出的许多结果作为自己的特例包括在内。     

Rigidly rotationg perfect fluids

A class of stationary rigidly rotating perfect fluids in General Relativity is investigated. This class which is characterized by zero Simon tensor contains only the Wahlquist solution and its limits. It is shown how a recently given solution follows from the Wahlquist solution by a limiting procedure.