共查询到20条相似文献，搜索用时 15 毫秒
1.
In this paper we have deduced the differential equations of motion of the restricted problem of three bodies with decreasing mass, under the assumption that the mass of the satellite varies with respect to time. We have applied Jeans law and the space time transformation contrast to the transformation of Meshcherskii. The space time transformation is applicable only in the special casen=1,k=0,q=1/2. The equations of motion of our problem differ from the equations of motion of the restricted three body problem with constant mass only by small perturbing forces. 相似文献
2.
The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more realistic model in which a disk, with power-law density profile, is rotating around the common center of mass of the system. Then, we analyze the periodic motion in the neighborhood of Lagrangian equilibrium points for the value of mass parameter $0<\mu\leq\frac{1}{2}$ . Periodic orbits of the infinitesimal mass in the vicinity of equilibrium are studied analytically and numerically. In spite of the periodic orbits, we have found some other kind of orbits like hyperbolic, asymptotic etc. The effects of radiation factor as well as oblateness coefficients on the motion of infinitesimal mass in the neighborhood of equilibrium points are also examined. The stability criteria of the orbits is examined with the help of Poincaré surfaces of section (PSS) and found that stability regions depend on the Jacobi constant as well as other parameters. 相似文献
3.
4.
The self-similar model of a shock wave, produced on account of an instantaneous release of energy in an inhomogeneous self-gravitating gaseous mass, has been discussed with the help of equations of motion and equilibrium conditions. The disturbances are headed by a shock of variable strength. The variation of velocity density, pressure, and mass have been discussed for the different values of strength of the shock. 相似文献
5.
《New Astronomy》2021
In the present work, we shall show an exhaustive numerical analysis of the dynamical behavior of the test particle in the modified restricted three-body problem with variable mass in which the extra effect of the three-body interaction is also taken into account. This additional force ingredient appears in the potential of the classical problem as a new extra term. As the main results, we determine the motion for test particle, under the effect of three-body interaction, which varies its mass according to Jeans’ law (Jeans (1928)). The number and existence of the libration points along with their stability have been investigated as the function of value of the parameters which occur due to variable mass of the test particle. Moreover, the regions of the possible motion are also unveiled where the test particle is free to move. Furthermore, the multivariate version of the Newton-Raphson (NR) iterative scheme is used to determine the outcomes of the used parameters on the topology of the basins of convergence (BoC) linked to the libration points. The numerical analysis shows that the topology of the basins of convergence linked with the libration points is highly influenced by the used parameters. Moreover, we perform a systematic analysis to unveil how the regions of convergence are related with the number of required iterations and also with the corresponding probability distributions. 相似文献
6.
对金斯定则的几点认识 总被引：1，自引：0，他引：1
用物理学基本定律可导出金斯经验定则,它似应称为金斯定则,该定则的速度、高度或能量等表述完全等效,可随意选用,用能量观点更容易解释此定则,满足金斯定则只是给定的粒子成为具有稠密大气的行星或卫星的主要大气成分的必要条件,该定则的适应范围可用方程或其图像表示,也能用诺模图确定,它适用于太阳系内的行星,卫星,小行星,流星体和像柯伊伯带天体与半人马族星这样的外太阳系天体,此定则现在仍有普遍的现实意义。 相似文献
7.
Mohan Ananda 《Celestial Mechanics and Dynamical Astronomy》1975,12(4):495-511
Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, we extend this technique to mass points and mass discs in the gravity field. This required the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing. 相似文献
8.
双黑洞组成的近密双星系统并合是激光干涉仪引力波天文台等地基引力波探测器的主要探测对象。随着探测器灵敏度的提高,大量该类信号的探测将成为进一步研究黑洞物理的有效工具。但是目前对双黑洞系统的起源机制和内禀参数分布等物理问题的研究还不够深入,例如由引力波探测得到的黑洞质量分布与X射线双星观测的结果存在较大差异,还未有很好的理论模型可解释该结果。目前普遍认为双黑洞系统主要有两种起源:大质量双星演化机制和动力学起源机制。基于这两类起源的双黑洞系统在质量、自旋分布等方面存在差异。因此可在贝叶斯理论框架下,利用引力波信号携带的波源质量和自旋等信息,推断波源起源,计算不同起源的双黑洞系统所占比例,以及检验质量自旋等参数分布的差异。 相似文献
9.
We have analyzed the motion of an infinitesimal mass in the restricted four-body problem with solar wind drag. It is assumed that the forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and found the Jacobi integral, zero velocity surfaces, and particular solutions of the system. It is found that three collinear points are real when the radiation factor 0<β<0.1 whereas only one real point is obtained when 0.125<β<0.2. The stability property of the system is examined with the help of Poincaré surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded. 相似文献
10.
The equilibrium-configurations of the Magnetic-Binary problem are investigated in the case of equatorial motion. The law of this constrained motion is derived and then the procedure for localizing the equilibrium points is developed. The type of equilibrium is also studied by means of the known method of variational equations. 相似文献
11.
Demetrios Gn. Fakis Tilemahos J. Kalvouridis 《Celestial Mechanics and Dynamical Astronomy》2013,116(3):229-240
This study outlines some aspects of the dynamics of a small body under the action of a Maxwell-type N-body system with a spheroidal central body. The non-sphericity of the central primary is described by means of a corrective term in the Newton’s law of gravitation and is taken into account during the derivation of the equations of motion of the small body, improving in this way, previous treatments. Based on this new consideration we investigate the equilibrium locations of the small body and their parametric dependence, as well as the zero-velocity curves and surfaces for the planar motion, and the evolution of the regions where this motion is permitted when the Jacobian constant varies. 相似文献
12.
The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability. 相似文献
13.
We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center
of mass of the system with perturbed mean motion. Using analytical and numerical methods, we have found equilibrium points
and examined their linear stability. We have also found the zero velocity surface for the present model. In addition to five
equilibrium points there exists a new equilibrium point on the line joining the two primaries. It is found that L
1 and L
3 are stable for some values of inner and outer radius of the disk while other collinear points are unstable, but L
4 is conditionally stable for mass ratio less than that of Routh’s critical value. Lastly, we have studied the effects of radiation
pressure, oblateness and mass of the disk on the motion and stability of equilibrium points. 相似文献
14.
In this article we study for first time the motion of charged particleswith neglected mass under the influence of Lorentz and Coulomb forces offour moving celestial bodies. For this problem we give the equations ofmotion, variational equations and energy integral. Also we give theequilibrium configurations demonstrating an extensive numericalinvestigation of the equilibrium points with comments about theirappearance. 相似文献
15.
V. I. Ferronsky S. A. Denisik S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1984,32(2):173-183
Generalized Jacobi's equation is derived by introducing the friction force into the equations of motion of mass points constituting the system.The exact solution of the equation of virial oscillations of celestial bodies written for non-conservative systems is obtained using non-linear time scale in the course of the change of variables for a particular friction force law.The nature of the undamped virial oscillations of celestial bodies is though to be related to the system unstability near the state determined by the virial theorem. Thus, the friction force changes its sign near the unstable equilibrium state and due to dissipation of energy during evolution of the system the undamped virial oscillations can be described as self-exited oscillations. 相似文献
16.
R. P. Prajapati R. K. Pensia S. Kaothekar R. K. Chhajlani 《Astrophysics and Space Science》2010,327(1):139-154
The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous,
viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron
inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of
relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The
conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that
the presence of arbitrary radiative heat-loss functions and thermal conductivity modifies the fundamental Jeans criterion
of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode
of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that
the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite
electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical
resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the
curves we find that the presence of thermal conductivity, finite electrical resistivity and density-dependent heat-loss function
has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability.
The effect of arbitrary heat-loss functions is also studied on the growth rate of a radiative instability. 相似文献
17.
G. Djurašević 《Astrophysics and Space Science》1986,124(1):5-25
The well-known problem of reckoning the critical surfaces (equipotential zero-velocity surfaces) in the close binary systems is approached by an independent method. The formulation of the problem is based on the assumptions of the binary's matter consisting of ionized hydrogen, the system possessing black-body radiation, a potential magnetic field, being in adiabatic equilibrium. Total pressure and total internal energy are examined. The model, implying synchronous rotation of the components, is described by hydromagnetic equations. For a statical case, however, it is representable by the equation of motion alone. Next, the temperature field is reproduced whereby the ratioP
r/Pg= is playing part of a free parameter. The resulting potential functions, applied to particular binaries, furnish the Lagrangian collinear points, critical surfaces and potentials over them in terms of . The families of surfaces thus obtained, compared with those springing from the Roche model, differ qualitatively in their geometry, position of the collinear equilibrium points, number of possible equilibrium states and the values of critical potentials. At identifying the allowed and forbidden regions of the gas motion new areas have been disclosed across which the gas outflow can take place and more possibilities of shell forming both around the individual components and the system as a whole. As the gas enthalpy and radiation are increased, the surfaces' geometry is undergoing changes. The method enables the intensity of gas velocity to be ascertained at any point in the system.The results of the method outlined here complement the picture of possible equilibrium states in the close binary systems in the presence of radiation and magnetic field. 相似文献
18.
《New Astronomy》2021
This paper examines the effects of triaxiality of both the primaries on the position and stability of the oblate infinitesimal mass in the neighborhood of triangular equilibrium points in the framework of Elliptical restricted three body problem. We have found the solutions for the locations of triangular equilibrium points. We have investigated the stability of infinitesimal mass around the triangular equilibrium points.It is observed that the infinitesimal motion around triangular equilibrium points are stable under certain condition with respect to triaxiality of primaries. We have applied the method of averaging used by Grebenivok, throughout the analysis of the stability of the infinitesimal mass around the triangular equilibrium points. We have exploited simulation technique using MATLAB 15 to analyze the stability of the system. The critical mass ratio depends on the triaxiality, oblateness, semi- major axis and eccentricity of the elliptical orbits. 相似文献
19.
We consider the problem of the motion of a zero-mass body in the vicinity of a system of three gravitating bodies forming a central configuration.We study the case where two gravitating bodies of equal mass lie on the same straight line and rotate around the central body with the same angular velocity. Equations for calculating the equilibrium positions in this system have been derived. The stability of the equilibrium points for a system of three gravitating bodies is investigated. We show that, as in the case of libration points for two bodies, the collinear points are unstable; for the triangular points, there exists a ratio of the mass of the central body to the masses of the extreme bodies, 11.720349, at which stability is observed. 相似文献
20.
《New Astronomy》2024
We numerically study a version of the synchronous circular restricted three-body problem, where an infinitesimal mass body is moving under the Newtonian gravitational forces of two massive bodies. The primary body is an oblate spheroid while the secondary is an elongated asteroid of a combination of two equal masses forming a rotating dipole which is synchronous to the rotation of the primaries of the classic circular restricted three-body problem. In this paper, we systematically examine the existence, positions, and linear stability of the equilibrium points for various combinations of the model's parameters. We observe that the perturbing forces have significant effects on the positions and stability of the equilibrium points as well as the regions where the motion of the particle is allowed. The allowed regions of motion as determined by the zero-velocity surface and the corresponding isoenergetic curves as well as the positions of the equilibrium points are given. Finally, we numerically study the binary system Luhman-16 by computing the positions of the equilibria and their stability as well as the allowed regions of motion of the particle. The corresponding families of periodic orbits emanating from the collinear equilibrium points are computed along with their stability properties. 相似文献