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1.
Jagadish Singh 《Astrophysics and Space Science》2012,342(2):303-308
This paper studies the motion of an infinitesimal body near the out-of-plane equilibrium points, L 6,7, in the perturbed restricted three-body problem. The problem is perturbed in the sense that the primaries of the system are oblate spheroids as well as sources of radiation and small perturbations are give to the Coriolis and centrifugal forces. It locates the positions and examines the stability of L 6,7 with a particular application to the binary system Struve 2398. It is observed that their positions are affected by the radiation, oblateness and a small perturbation in the centrifugal force, but is unaffected by that of the Coriolis force. They are also found to be unstable. 相似文献
2.
Jagadish Singh 《Astrophysics and Space Science》2013,346(1):41-50
This study explores the effects of small perturbations in the Coriolis and centrifugal forces, radiation pressures and triaxiality of the two stars (primaries) on the position and stability of an infinitesimal mass (third body) in the framework of the planar circular restricted three-body problem (R3BP). it is observed that the positions of the usual five (three collinear and two triangular) equilibrium points are affected by the radiation, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. The collinear points are found to remain unstable, while the triangular points are seen to be stable for 0<μ<μ c and unstable for $\mu_{c} \le\mu\le\frac{1}{2}$ , where μ c is the critical mass ratio influenced by the small perturbations in the Coriolis and centrifugal forces, radiation and triaxiality. It is also noticed that the former one and all the latter three posses stabilizing and destabilizing behavior respectively. Therefore, the overall effect is that the size of the region of stability decreases with increase in the values of the parameters involved. 相似文献
3.
This paper examines the motion of a test particle in the vicinity of the triangular points L 4,5 by considering the more massive primary as a source of radiation in the framework of the relativistic restricted three-body problem (R3BP). It is found that the position and stability of the triangular point are affected by both the relativistic factor and radiation pressure. 相似文献
4.
We consider the primaries of the circular restricted three-body problem (CR3BP) to be luminous and investigate the influences of small perturbations in the Coriolis and centrifugal forces together with Poynting-Robertson (P-R) drag from both primaries on the triangular points. It is seen, both analytically and numerically, that the positions of triangular points are affected by the radiation pressures, P-R drag and a small perturbation in the centrifugal force. This has been shown for the binary systems Luyten 726-8 and Kruger 60.1. These perturbing forces do not influence the nature of the stability of triangular points in the presence of P-R drag. They remain unstable in the linear sense. 相似文献
5.
This paper presents a generalized problem of the restricted three body studied in Abdul Raheem and Singh with the inclusion that the third body is an oblate spheroidal test particle of infinitesimally mass. The positions and stability of the equilibrium point of this problem is studied for a model in which the primaries is the binary system Struve 2398 (Gliese 725) in the constellation Draco; which consist of a pair of radiating oblate stars. It is seen that additional equilibrium points exist on the line collinear with the primaries, for some combined parameters of the problem. Hence, there can be up to five collinear equilibrium points. Two triangular points exist and depends on the oblateness of the participating bodies, radiation pressure of the primaries and a small perturbation in the centrifugal force. The stability analysis ensures that, the collinear equilibrium points are unstable in the linear sense while the triangular points are stable under certain conditions. Illustrative numerical exploration is given to indicate significant improvement of the problem in Abdul Raheem and Singh. 相似文献
6.
In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with. 相似文献
7.
《New Astronomy》2015
This paper examines the existence and linear stability of equilibrium points in the perturbed Robe’s circular restricted three-body problem under the assumption that the hydrostatic equilibrium figure of the first primary is an oblate spheroid. The problem is perturbed in the sense that small perturbations are given to the Coriolis and centrifugal forces are being considered. Results of the analysis found two axial equilibrium points on the line joining the centre of both primaries. It is further observed that under certain conditions, points on the circle within the first primary are also equilibrium points. And a special case where the density of the fluid and that of the infinitesimal mass are equal (D = 0) is discussed. The linear stability of this configuration is examined; it is observed that the first axial point is unstable while the second one is conditionally stable and the circular points are unstable. 相似文献
8.
The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977)
restricted problem of three bodies’ has been studied. In this problem one body,m
1, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ
1. The second one,m
2, is a mass point outside the shell andm
3 is a small solid sphere of densityϱ
3 supposed to be moving inside the shell subject to the attraction ofm
2 and buoyancy force due to fluidϱ
1. Here we assumem
3 to be an infinitesimal mass and the orbit of the massm
2 to be circular, and we also suppose the densitiesϱ
1, andϱ
3 to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0). 相似文献
9.
This paper examines the effect of a constant κ of a particular integral of the Gylden-Meshcherskii problem on the stability of the triangular points in the restricted three-body
problem under the influence of small perturbations in the Coriolis and centrifugal forces, together with the effects of radiation
pressure of the bigger primary, when the masses of the primaries vary in accordance with the unified Meshcherskii law. The
triangular points of the autonomized system are found to be conditionally stable due to κ. We observed further that the stabilizing or destabilizing tendency of the Coriolis and centrifugal forces is controlled
by κ, while the destabilizing effects of the radiation pressure remain unchanged but can be made strong or weak due to κ. The condition that the region of stability is increasing, decreasing or does not exist depend on this constant. The motion
around the triangular points L
4,5 varying with time is studied using the Lyapunov Characteristic Numbers, and are found to be generally unstable. 相似文献
10.
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis
and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that
the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of
equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen
that the triangular points are stable for 0<μ<μ
c
and unstable for
mc ￡ m < \frac12\mu_{c}\le\mu <\frac{1}{2}, where μ
c
is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that
collinear points remain unstable. 相似文献
11.
This paper investigates the periodic orbits around the triangular equilibrium points for 0<μ<μ c , where μ c is the critical mass value, under the combined influence of small perturbations in the Coriolis and the centrifugal forces respectively, together with the effects of oblateness and radiation pressures of the primaries. It is found that the perturbing forces affect the period, orientation and the eccentricities of the long and short periodic orbits. 相似文献
12.
Navin Chandra 《Planetary and Space Science》2004,52(8):747-760
The non-linear stability of the triangular libration point L4 of the restricted three-body problem is studied under the presence of third- and fourth-order resonances, when the more massive primary is a triaxial rigid body and source of radiation. In this study, Markeev's theorems are applied with the help of Moser's theorem. It is found that the stability of the triangular libration point is unstable in the third-order resonance case and in the fourth-order resonance case, this is stable or unstable depending on A1 and A2, and a source of radiation parameter α, where A1, A2 depend upon the lengths of the semi-axes of the triaxial rigid body. 相似文献
13.
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable. 相似文献
14.
This paper investigates the combined effect of small perturbations ε,ε′ in the Coriolis and centrifugal forces, radiation pressure q i , and changing oblateness of the primaries A i (t) (i=1,2) on the stability of equilibrium points in the restricted three body problem in which the primaries is a supergiant eclipsing binary system which consists of a pair of bright oblate stars having the appearance of a giant peanut in space and their masses assumed to vary with time in the absence of reactive forces. The equations of motion are derived and the equilibrium points are obtained. For the autonomized system, it is seen that there are more than a pair of the triangular points as κ→∞; κ being the arbitrary sum of the masses of the primaries. In the case of the collinear points, two additional equilibrium points exist on the line joining the primaries when simultaneously κ+ε′<0 and both primaries are oblate, i.e., 0<α i ?1. So there are five collinear equilibrium points in this case. Two non-planar equilibrium points exist for κ>1. Hence, there are at least nine equilibrium points of the system. The stability of these points is explored analytically and numerically. It is seen that the collinear and triangular points are stable with respect to certain conditions controlled by κ while the non-planar equilibrium points are unstable. 相似文献
15.
The existence and stability of a test particle around the equilibrium points in the restricted three-body problem is generalized
to include the effect of variations in oblateness of the first primary, small perturbations ϵ and ϵ′ given in the Coriolis and centrifugal forces α and β respectively, and radiation pressure of the second primary; in the case when the primaries vary their masses with time in
accordance with the combined Meshcherskii law. For the autonomized system, we use a numerical evidence to compute the positions
of the collinear points L
2κ
, which exist for 0<κ<∞, where κ is a constant of a particular integral of the Gylden-Meshcherskii problem; oblateness of the first primary; radiation pressure
of the second primary; the mass parameter ν and small perturbation in the centrifugal force. Real out of plane equilibrium points exist only for κ>1, provided the abscissae
x < \fracn(k-1)b\xi<\frac{\nu(\kappa-1)}{\beta}. In the case of the triangular points, it is seen that these points exist for ϵ′<κ<∞ and are affected by the oblateness term, radiation pressure and the mass parameter. The linear stability of these equilibrium
points is examined. It is seen that the collinear points L
2κ
are stable for very small κ and the involved parameters, while the out of plane equilibrium points are unstable. The conditional stability of the triangular
points depends on all the system parameters. Further, it is seen in the case of the triangular points, that the stabilizing
or destabilizing behavior of the oblateness coefficient is controlled by κ, while those of the small perturbations depends on κ and whether these perturbations are positive or negative. However, the destabilizing behavior of the radiation pressure remains
unaltered but grows weak or strong with increase or decrease in κ. This study reveals that oblateness coefficient can exhibit a stabilizing tendency in a certain range of κ, as against the findings of the RTBP with constant masses. Interestingly, in the region of stable motion, these parameters
are void for
k = \frac43\kappa=\frac{4}{3}. The decrease, increase or non existence in the region of stability of the triangular points depends on κ, oblateness of the first primary, small perturbations and the radiation pressure of the second body, as it is seen that the
increasing region of stability becomes decreasing, while the decreasing region becomes increasing due to the inclusion of
oblateness of the first primary. 相似文献
16.
The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied.
It is found that L4,5 are unstable in the whole range 0 ≤ μ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable
for 0 < μ < μ0, where μ is the mass parameter and μ0 = 0.03852....
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
Most existing satellite relative motion theories utilize mean elements, and therefore cannot be used for calculating long-term bounded perturbed relative orbits. The goal of the current paper is to find an integrable approximation for the relative motion problem under the J 2 perturbation, which is adequate for long-term prediction of bounded relative orbits with arbitrary inclinations. To that end, a radial intermediary Hamiltonian is utilized. The intermediary Hamiltonian retains the original structure of the full J 2 Hamiltonian, excluding the latitude dependence. This formalism provides integrability via separation, a fact that is utilized for finding periodic relative orbits in a local-vertical local-horizontal frame and determine an initialization scheme that yields long-term boundedness of the relative distance. Numerical experiments show that the intermediary-based computation of orbits provides long-term bounded orbits in the full J 2 problem for various inclinations. In addition, a test case is shown in which the radial intermediary-based initial conditions of the chief and deputy satellites yield bounded relative distance in a high-precision orbit propagator. 相似文献
18.
The photogravitational restricted three bodies within the framework of the post-Newtonian approximation is carried out. The mass of the primaries are assumed changed under the effect of continuous radiation process and oblateness effects of the two primaries. New perturbed locations of the triangular points are computed. In order to introduce a semi-analytical view, A Mathematica program is constructed so as to draw the locations of triangular points versus the whole range of the mass ratio μ taking into account the photo-gravitational effects, the relativistic corrections and/or oblateness effects. All the obtained figures are analyzed. 相似文献
19.
B. Ishwar 《Celestial Mechanics and Dynamical Astronomy》1996,65(3):253-289
The non-linear stability of the triangular equilibrium point L
4 in the generalized restricted three-body problem has been examined. The problem is generalized in the sense that the infinitesimal body and one of the primaries have been taken as oblate spheroids. It is found that the triangular equilibrium point is stable in the range of linear stability except for three mass ratios. 相似文献
20.
We consider the self-similar problem of a supernova explosion in a radially inhomogeneous medium by taking into account the generation of accelerated relativistic particles. The initial density of the medium is assumed to decrease with distance from the explosion center as a power law, ρ 0 = A/r θ. We use a two-fluid approach in which the total pressure in the medium is the sum of the circumstellar gas pressure and the relativistic particle pressure. The relativistic particle pressure at the shock front is specified as an external parameter. This approach is applicable in the case where the diffusion coefficient of accelerated particles is small and the thickness of the shock front is much smaller than its radius. We have numerically solved a system of ordinary differential equations for the dimensionless quantities that describe the velocity and density behind the shock front as well as the nonrelativistic gas and relativistic particle pressures for various parameters of the inhomogeneity of the medium and various compression ratios of the medium at the shock front. We have established that the shock acceleration of cosmic rays affects most strongly the formation of a supernova shell (making it thinner) in a homogeneous circumstellar medium. A decrease in the circumstellar matter density with distance from the explosion center causes the effect of shock-accelerated relativistic particles on the supernova shell formation to weaken considerably. Inhomogeneity of the medium makes the shell thicker and less dense, while an increase in the compression ratio of the medium at the shock front causes the shell to become thinner and denser. As the relativistic particle density increases, the effect of circumstellar matter inhomogeneity on the shell formation becomes weaker. 相似文献