On the existence of the ?out of plane? equilibrium points in the photogravitational restricted three-body problem

“…These are the functions of q 1 , A 2 and M b , which are similar to those of Szebehely (1967), Ragos and Zafiropoulos (1995), Jiang and Yeh (2006) and others.…”

Section: Triangular Equilibrium Pointsmentioning

confidence: 89%

Linear stability of equilibrium points in the generalized photogravitational Chermnykh’s problem

Kushvah

2008

Astrophys Space Sci

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The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided μ < μ Routh = 0.0385201. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem.

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“…This problem was first formulated by [31,32], and in 1937 Robertson modified Poynting's idea by basing his argument on Einstein's relativity theory from which he formulated a new radiation force. Subsequent examinations of the problem by researchers [23,10,33,34,35,25,26] have shown that P-R drag has a destabilizing effect on the stability of triangular equilibrium points. The authors of [23] modelled a problem in which the bigger primary is an intense emitter of radiation with [6] as the classical case.…”

Section: Introductionmentioning

confidence: 99%

“…[33] investigated the location and linear stability of the five Lagrangian points when the third body is acted upon by various drag forces, and these forces are seen to have destabilizing tendencies. The motion of the test particle in the vicinity of two radiating bodies, having PR-drags was examined by [34] and they established numerically the positions of the triangular equilibrium points lying outside the orbital plane. These points are seen to be unstable due to the presence of PR-drags.…”

Section: Introductionmentioning

confidence: 99%

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

Singh

Simeon

2017

IFSL

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Abstract. This paper explores the motion of an infinitesimal body around the triangular equilibrium points in the framework of circular restricted three-body problem (CR3BP) with the postulation that the primaries are triaxial rigid bodies, radiating in nature and are also under the influence of Poynting-Robertson (P-R) drag. We study the linear stability of these triangular points and for the numerical application, the binary stars Kruger 60 (AB) and Archird have been considered. These triangular points are not only perceived to move towards the line joining the primaries in the direction of the bigger primary with increasing triaxiality, they are also unstable owing to the destabilizing influence of P-R drag.

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On the existence of the ?out of plane? equilibrium points in the photogravitational restricted three-body problem

Cited by 31 publications

References 13 publications

Linearization of the Hamiltonian in the generalized photogravitational Chermnykh’s problem

Linearization of the Hamiltonian in the generalized photogravitational Chermnykh’s problem

Linear stability of equilibrium points in the generalized photogravitational Chermnykh’s problem

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

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