Combined effect of oblateness, radiation and a circular cluster of material points on the stability of triangular liberation points in the R3BP

Singh, Jagadish; Taura, Joel John

doi:10.1007/s10509-014-1860-8

Cited by 8 publications

(12 citation statements)

References 9 publications

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“…q = 1, σ 1 = σ 2 = 0, M b = 0), the value of μ c tallies with that of [36] when the primaries are spherical and the smaller primary is non luminous. In the presence of the triaxiality of the smaller primary only (i.e.…”

Section: Discussionmentioning

confidence: 61%

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

Singh

Taura

2015

Differ Equ Dyn Syst

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In this paper the equations of motion of the circular restricted three body problem is modified to include radiation of the bigger primary, triaxiality of the smaller primary; and gravitational potential created by a belt. We have obtained that due to the perturbations, the locations of the triangular libration points and their linear stability are affected. The points move towards the bigger primary due to the resultant effect of the perturbations. Triangular libration points are stable for 0 < μ < μ c and unstable for μ c ≤ μ ≤ 1 2 , where μ c is the critical mass ratio affected by the perturbations. The radiation of the bigger primary and triaxiality of the smaller primary have destabilizing propensities, whereas the potential created by the belt has stabilizing propensity. This model could be applied in the study of the motion of a dust particle near radiating -triaxial binary system surrounded by a belt.

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Section: Discussionmentioning

confidence: 61%

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

Singh

Taura

2015

Differ Equ Dyn Syst

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“…, where F r is the force caused by radiation pressure force and F g results due to gravitational force [2,7]. the term M b (r 2 +T 2 ) 1/2 is the potential due to the circular cluster of material points ( [7,8] and refs therein) where M b is the total mass of the circular cluster of material points.…”

Section: Equation Of Motionmentioning

confidence: 99%

“…We have also choose µ = 0.2 and varies the oblateness coefficients. The six non-collinear points have been represented in figures (1-2) and presented for better clarification in table (2)…”

Section: Case 1: Y = 0 (Collinear Points)mentioning

confidence: 99%

Effect of Oblateness, Radiation and a Circular Cluster of Material Points on the Stability of Equilibrium Points in the Restricted Four-Body Problem

Falaye

2014

Few-Body Syst

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Within the framework of restricted four-body problem, we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating-oblate spheroids surrounded by a circular cluster of material points. In our model, we assume that the two masses of the primaries m 2 and m 3 are equal to µ and the mass m 1 is 1 − 2µ. By using numerical approach, we have obtained the equilibrium points and examined their linear stability. The effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary, on the existence and linear stability of the libration point have been critically examine via numerical computation. The stability of these points examined shows that the collinear and the non-collinear equilibrium points are unstable. The result presented in this paper have practical application in astrophysics.

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“…In this study, they investigated the possible chaotic and regular orbits for the disc-star-planet system and found that the influence from the disc can alter locations of equilibrium points and the stability pattern. Singh and Taura 11 however investigated the motion in a generalized R3BP when both primaries are radiating and oblate together while also considering the effect of a gravitational potential caused by a massive belt.The stability analysis of the equilibrium points shows that collinear points remain unstable, while the triangular points are conditionally stable. Subsequently Suraj et al 12 , discussed the equilibrium solutions of the planar R3BP when both primaries are heterogeneous oblate spheroids with three layers of different densities and sources of radiation.…”

Section: Introductionmentioning

confidence: 99%

Motion around triangular points in the restricted three-body problem with radiating heterogeneous primaries surrounded by a belt

Singh

Haruna²

2020

Sci Rep

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The present paper studies the locations and linear stability of the triangular equilibrium points when both primaries are radiating and considered as heterogeneous spheroid with three layers of different densities. Additionally, we include the effects of small perturbations in the Coriolis and centrifugal forces and potential from a belt (circumbinary disc). It is observed that the positions of the triangular equilibrium points are substantially affected by all parameters (except a perturbation in Coriolis force) involved in the system.The stabilty of motion is found only when $$0 < \mu < \mu_{c}$$ 0 < μ < μ c , where $$\mu_{c}$$ μ c is the critical mass value which depends on the combined effect of radiation pressures and heterogeneity of the primaries, small perturbations and the potential from a belt.It is also seen that the Coriolis force and the belt have stabilizing effect,while the centrifugal force, radiation and heterogeineity of the primaries have destabilizing behaviour.The net effect is that the size of the region of stability decreases when the value of these parameters increases where $$\mu$$ μ is the mass ratio and $$k_{1} ,k_{2}$$ k 1 , k 2 characterize heterogeneity of both primaries. A practical application of this model could be the study of motion of a dust grain near the heterogeneous and luminous binary stars surrounded by a belt.Finally, we carried out and discuss numerical experiments aiming at computing the positions of triangular points and critical masses of three binary systems: Archid, Xi Booties and Kruger 60.

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Combined effect of oblateness, radiation and a circular cluster of material points on the stability of triangular liberation points in the R3BP

Cited by 8 publications

References 9 publications

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

Effect of Oblateness, Radiation and a Circular Cluster of Material Points on the Stability of Equilibrium Points in the Restricted Four-Body Problem

Motion around triangular points in the restricted three-body problem with radiating heterogeneous primaries surrounded by a belt

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