Dynamical evolution of two associated galactic bars

We study the dynamical interactions of mass systems in equilibrium under their own gravity that mutually exert and ex‐perience gravitational forces. The method we employ is to model the dynamical evolution of two isolated bars, hosted within the same galactic system, under their mutual gravitational interaction. In this study, we present an analytical treatment of the secular evolution of two bars that oscillate with respect to one another. Two cases of interaction, with and without geometrical deformation, are discussed. In the latter case, the bars are described as modified Jacobi ellipsoids. These triaxial systems are formed by a rotating fluid mass in gravitational equilibrium with its own rotational velocity and the gravitational field of the other bar. The governing equation for the variation of their relative angular separation is then numerically integrated, which also provides the time evolution of the geometrical parameters of the bodies. The case of rigid, non‐deformable, bars produces in some cases an oscillatory motion in the bodies similar to that of a harmonic oscillator. For the other case, a deformable rotating body that can be represented by a modified Jacobi ellipsoid under the influence of an exterior massive body will change its rotational velocity to escape from the attracting body, just as if the gravitational torque exerted by the exterior body were of opposite sign. Instead, the exchange of angular momentum will cause the Jacobian body to modify its geometry by enlarging its long axis, located in the plane of rotation, thus decreasing its axial ratios. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mutual gravitational potential,force, and torque of a homogeneous polyhedron and an extended body: an application to binary asteroids

Binary systems are quite common within the populations of near-Earth asteroids, main-belt asteroids, and Kuiper belt asteroids. The dynamics of binary systems, which can be modeled as the full two-body problem, is a fundamental problem for their evolution and the design of relevant space missions. This paper proposes a new shape-based model for the mutual gravitational potential of binary asteroids, differing from prior approaches such as inertia integrals, spherical harmonics, or symmetric trace-free tensors. One asteroid is modeled as a homogeneous polyhedron, while the other is modeled as an extended rigid body with arbitrary mass distribution. Since the potential of the polyhedron is precisely described in a closed form, the mutual gravitational potential can be formulated as a volume integral over the extended body. By using Taylor expansion, the mutual potential is then derived in terms of inertia integrals of the extended body, derivatives of the polyhedron’s potential, and the relative location and orientation between the two bodies. The gravitational forces and torques acting on the two bodies described in the body-fixed frame of the polyhedron are derived in the form of a second-order expansion. The gravitational model is then used to simulate the evolution of the binary asteroid (66391) 1999 KW4, and compared with previous results in the literature.     

Is the description of the gravitational force as a manifestation of deviation of a body from the geodesic the correct interpretation of the general relativity theory?

A deeper analysis connected to general relativity is presented, considering dynamics of a solid body in a gravitational field. Two basic situations are described: namely, the case of weightlessness in free fall, and that when a solid body at rest relative to the source of the gravitational field has weight. Finally, the principle of equivalence is reformulated.     

双星系统中大质量比致密天体质量四极矩对轨道频率的影响分析

极端质量比旋进系统是空间引力波探测器最重要的波源之一。对引力波的探测需要高精度波形模版。当前主流的极端质量比旋进系统引力波计算模型中,人们一般将小质量天体当作试验粒子进行计算,而忽略了其结构及自身引力对背景引力场的影响。利用Mathisson-Papapetrou-Dixon方程研究延展体在弯曲时空中的运动,以及小天体自旋和质量多极矩对引力波信号识别产生的影响。结果表明,质量比在10?6-10?4范围的旋进系统,其自旋达到很大时,自旋对延展体的轨道运动有不可忽略的影响;在质量比10?4-10?2区间内,需要考虑中心黑洞潮汐作用导致的白矮星形变;在质量比大于10?4,且白矮星自旋很大时,其自旋产生的形变会对小天体轨道运动产生不可忽略的影响。大质量黑洞潮汐作用导致的恒星级黑洞或中子星产生的形变可以忽略,中子星和黑洞的自旋会对轨道运动产生不可忽略的影响,而自旋产生的四极矩对轨道运动不产生影响。     

The Gravitational Effects of a Celestial Body with Magnetic Charge and Moment

The gravitational effects (precession of charge-less particles and deflec-tion of light)in the gravitational field of a celestial body with magnetic charge and moment(CM)are investigated.We found that the magnetic charge always weak-ens the pure Schwarzschild effects,while the magnetic dipole moment deforms the effects in a more complicated way.     

Gravitational potential of solid bodies in the solar system

The gravitational potential of a solid body is expanded without approximation in any moving reference frame, in terms of harmonic coefficients relative to fixed axis in the body.     

Spiral structure and hydrodynamic gravitational resonance

A persistent and large scale galactic spiral structure might be the result of resonant excitation of density waves, forced in the low viscosity interstellar gas, by the gravitational field of an asymmetric stellar structure (galactic nucleus, condensation, companion galaxy, etc.) rotating like a rigid body around the galactic centre. This paper deals with this problem in the simple case of a homogeneous plane viscous medium of infinite extent, in a state of rigid body rotation. Numerical estimates are given in the case of density waves excited by the gravitational field of a central dumb-bell. They show that the mechanism of hydrodynamic gravitational resonance is worthy of a further, more realistic, treatment.     

On the possibility of generating gravitational radiation by the sun

In the present paper the gravitational radiation emitted from large solar energetic flares and from the Sun as a whole in the course of the generation shock waves and quadrupole oscillations of the solar body are studied. The expected densities of the energy fluxes of the gravitational radiation at the distance of the Earth are calculated.     

Asymptotic stability of synchronous orbits for a gravitating viscoelastic sphere

We study the dynamics of a viscoelastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. We work in the quadrupole approximation. We consider the solution in which the center of mass of the body moves on a circular orbit, and the body rotates in a synchronous way about its axis, so that it always shows the same face to the planet as the Moon does with the Earth. We prove that if any internal deformation of the body dissipates some energy, then such an orbit is locally asymptotically stable. The proof is based on the construction of a suitable system of coordinates and on the use of LaSalle??s principle. A large part of the paper is devoted to the analysis of the kinematics of an elastic body interacting with a gravitational field. We think this could have some interest in itself.     

Black hole stability

A vector theory of electromagnetism and gravitation has indicated a possible equivalence of gravitational energy and electric charge. If true, the resulting electromagnetic and gravitational forces within a stationary, gravitationally collapsed body of radiusR=GM/c ² are everywhere in balance within the body, if it has a radial mass density distribution proportional to 1/r ². In addition, radial perturbation of such a body will result in a force imbalance which is restorative. Hence, the equilibrium is stable.     

Relativistic gravitational potential and its relation to mass-energy

From the general theory of relativity a relation is deduced between the mass of a particle and the gravitational field at the position of the particle. For this purpose the fall of a particle of negligible mass in the gravitational field of a massive body is used. After establishing the relativistic potential and its relationship to the rest mass of the particle, we show, assuming conservation of mass-energy, that the difference between two potential-levels depends upon the value of the radial metric coefficient at the position of an observer. Further, it is proved that the relativistic potential is compatible with the general concept of the potential also from the standpoint of kinematics. In the third section it is shown that, although the mass-energy of a body is a function of the distance from it, this does not influence the relativistic potential of the body itself. From this conclusion it follows that the mass-energy of a particle in a gravitational field is anisotropic; isotropic is the mass only. Further, the possibility of an incidental feed-back between two masses is ruled out, and the law of the composition of the relativistic gravitational potentials is deduced. Finally, it is shown, by means of a simple model, that local inhomogeneities in the ideal fluid filling the Universe have negligible influence on the total potential in large regions.     

Mutual gravitational potential and torque of solid bodies via inertia integrals

The mutual gravitational potential and the mutual gravitational torque of two bodies of arbitrary shape are expanded to the fourth order. The derivations are based on Cartesian coordinates, inertia integrals with relation to the principal reference frames of each body, and the relative rotation matrix. The current formulation is convenient to utilize in high precision problems in rotational dynamics.     

Application of the Gauss' Method to the Stellar Three Body Problem

In this paper, we deal with the stellar three body problem, that is one star is far away from the other two stars. The outer orbit is assumed to be Keplerian. To analyze the effect of the distant star on the orbit of the close stars, we use the Gauss method; this method consist in replacing the gravitational attraction of the third star by the gravitational attraction of an infinitesimal non-homogeneous elliptic ring. We obtain the force vector for the Gauss method in terms of elliptic integrals. Finally we compare the results obtained by this model with the classical third body model. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the gravitational stability of satellite-orbiting objects: A reply to T. Gold

The stability of a satellite-orbiting object under the disturbing influence of the parent planet can be assessed by comparison with analogous three-body systems. The changes in the eccentricity and semimajor axis of a satellite-orbiting object (disturbed by the planet) and a planetary satellite (disturbed by the sun) scale equally if the dimensions of the systems are scaled by the sphere of influence of the orbited body. Thus, the apparent gravitational stability of planetary satellites supports theories of the gravitational stability of satellite-orbiting objects.     

Relativistic dynamical friction in a collisional fluid

The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is calculated for straight-line motion and circular motion, generalizing previous results by several authors. Possible applications to the study of extreme mass-ratio inspirals around strongly accreting supermassive black holes are suggested.     

On stability of orbit of artificial moon moving around a small celestial body perturbed by an external body

We examine the stability of the orbit of an artificial moon of a small celestial body in the presence of an external massive perturbing body in terms of the restricted three-body problem. The orbit of this moon is shown to be dependent on the shape of the small body and central gravitational field of the external body. We study how these factors interact with each other and how they affect the stability of the orbit.     

Hydromagnetic buoyancy force in the solar atmosphere

An extraneous magnetized body, either a flux tube or a plasmoid, immersed in the solar atmosphere is subjected to a hydromagnetic buoyancy force. It results from the peripheral inhomogeneity of ambient hydromagnetic pressure, which is caused or enhanced by the presence of the extraneous body. This extra-caused force acts at various mass elements of the immersed body through its distribution as a nearly uniform force density, just like the gravitational force. Since hydromagnetic buoyancy force comprises hydrostatic buoyancy force, hydrodynamic lift force, and magnetostatic diamagnetic force, this constitutes a magnetohydrodynamic generalization of Archimedes' principle which deals with hydrostatic buoyancy force.In the solar atmosphere hydromagnetic buoyancy force has an obliquely upward direction, with a component in the direction opposite to the downward gravity. It provides an upward force to counterbalance or even to exceed the downward gravitational force. Such an upward force is the dynamic cause for the stationary equilibrium of quiescent prominences and outward motion of coronal transients.     

Angular momentum and gyroscope in flat space-time theory of gravitation

The study of a previously proposed theory of gravitation in flat space-time (Petry, 1981a) is continued. A conservation law for the angular momentum is derived. Additional to the usual form, there must be added a term coming from the spin of the gravitational field. The equations of motion and of spin angular momentum for a spinning test particle in a gravitational field are given. An approximation of the equations of the spin angular momentum in the rest frame of the test particle is studied. For a gyroscope in an orbit of a rotating massive body (e.g., the Earth) the precession of the spin axis agrees with the result of Einstein's general theory of relativity.     

引力坍缩能形成环星系吗?

大部分环星系是由星系相互作用、引力响应的演化形成．但是，这并不是形成环星系的唯一方式．孤立星系的引力坍缩也可能形成环星系．本文进行引力坍缩的数值模拟试验，计算结果也显示出较好的环形结构．     

The multipolar structure of the gravitational radiation from a rotating body

We give the metric coefficients of the retarded field of non-plane gravitational waves from a multipolar source at infinity, and hence the expression for the power of the multipole radiation from a slowly rotating body. When specific calculations are made for the quadrupole radiation, we find that the radiation from a rotating body has a strong directivity. Our calculated results for the total power of two pulsars are in good agreement with previous estimates.