• Jagadish Singh

      Articles written in Journal of Astrophysics and Astronomy

    • Stability of Triangular Equilibrium Points in the Photogravitational Restricted Three-Body Problem with Oblateness and Potential from a Belt

      Jagadish Singh Joel John Taura

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      We have examined the effects of oblateness up to 𝐽4 of the less massive primary and gravitational potential from a circum-binary belt on the linear stability of triangular equilibrium points in the circular restricted three-body problem, when the more massive primary emits electromagnetic radiation impinging on the other bodies of the system. Using analytical and numerical methods, we have found the triangular equilibrium points and examined their linear stability. The triangular equilibrium points move towards the line joining the primaries in the presence of any of these perturbations, except in the presence of oblateness up to 𝐽4 where the points move away from the line joining the primaries. It is observed that the triangular points are stable for 0 < 𝜇 < 𝜇c and unstable for 𝜇c ≤ 𝜇 ≤ $\frac{1}{2}$, where 𝜇c is the critical mass ratio affected by the oblateness up to 𝐽4 of the less massive primary, electromagnetic radiation of the more massive primary and potential from the belt, all of which have destabilizing tendencies, except the coefficient 𝐽4 and the potential from the belt. A practical application of this model could be the study of motion of a dust particle near a radiating star and an oblate body surrounded by a belt.

    • On the Stability of 𝐿4,5 in the Relativistic R3BP with Radiating Secondary

      Jagadish Singh Nakone Bello

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      This paper discusses the motion of a test particle in the neighbourhood of the triangular points 𝐿4,5 by considering the less massive primary (secondary) as a source of radiation in the framework of the relativistic restricted three-body problem (R3BP). It is found that the positions and stability of the triangular point are affected by both relativistic and electromagnetic radiation factors. It turns out that both the coordinates of the infinitesimal mass are affected, contrary to the classical where this happens only for one coordinate. A practical application of this model could be the study of dynamical evolution of dust particles in orbits around a binary system with a dark degenerate first primary and a secondary stellar companion.

    • Effect of Perturbations in the Coriolis and Centrifugal Forces on the Stability of 𝐿4 in the Relativistic R3BP

      Jagadish Singh Nakone Bello

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      The centrifugal and Coriolis forces do not appear as a result of physically imposed forces, but are due to a special property of a rotation. Thus, these forces are called pseudo-forces or `fictitious forces’. They are merely an artifact of the rotation of the reference frame adopted. This paper studies the motion of a test particle in the neighbourhood of the triangular point 𝐿4 in the framework of the perturbed relativistic restricted three-body problem (R3BP) when small perturbations are conferred to the centrifugal and Coriolis forces. It is found that the position and stability of the triangular point are affected by both the relativistic factor and small perturbations in the Coriolis and centrifugal forces. As an application, the Sun–Earth system is considered.

    • Effects of Triaxiality, Oblateness and Gravitational Potential from a Belt on the Linear Stability of 𝐿4,5 in the Restricted Three-Body Problem

      Jagadish Singh Joel John Taura

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      In this paper we have considered the restricted three body problem (R3BP) in which the more massive primary is triaxial, the less massive primary and infinitesimal body are oblate spheroids, and are encompassed by a belt of homogenous material points. Analytically and numerically, we have studied the effects of triaxiality of the more massive primary, oblateness of both the less massive primary and infinitesimal body and the gravitational potential generated by the belt on the location of the triangular libration points 𝐿4,5 and their linear stability. 𝐿4,5 do not form equilateral triangles with the primaries in the presence of all or any of the aforementioned perturbations. Due to triaxiality of the more massive primary and oblateness of the infinitesimal body the triangular libration points are seen to move away from the line linking the primaries, whereas they shift closer to the line owing to the oblateness of the less massive primary and the potential from the belt. The range 0 < 𝜇 < 𝜇c of stability of the triangular points is reduced in the presence of any of the perturbations, except when considering the potential from the belt the range increases, where 𝜇c is the critical mass ratio. The oblateness of a test particle (of infinitesimal mass) shifts the location of its libration positions away from the primaries and reduces its range of stability.

    • Out-of-Plane Equilibrium Points in the Photogravitational CR3BP with Oblateness and P-R Drag

      Jagadish Singh Tajudeen Oluwafemi Amuda

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      This paper investigates the motion of a test particle around the out-of-plane equilibrium points in the circular photogravitational restricted three-body problem when the effect of radiation pressure from the smaller primary and its Poynting-Robertson (P-R) drag are taken into account, and the bigger primary is modeled as an oblate spheroid. These points lie in the 𝑥𝑧-plane almost directly above and below the center of the oblate primary. The equilibrium points are sought, and we observe that, there are two coordinate points 𝐿6,7 which depend on the oblateness of the bigger primary, and the radiation pressure force and P-R drag of the smaller primary. The positions and linear stability of the problem are investigated both analytically and numerically for the binary system Cen X-4. The out-of-plane equilibrium points are found to be unstable in the sense of Lyapunov due to the presence of a positive real root.

    • Stability analysis of triangular equilibrium points in restricted three-body problem under effects of circumbinary disc, radiation and drag forces

      JAGADISH SINGH TAJUDEEN OLUWAFEMI AMUDA

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      This paper examines the linear stability analysis around triangular equilibrium points of a test body in the gravitational field of a low-mass post-AGB binary system, enclosed by circumbinary disc and radiating with effective Poynting–Robertson (P–R) drag force. The equations of motion are derived and positions of triangular equilibrium points are located. These points are determined by; the circumbinary disc, radiation and P–R drag. In particular, for our numerical computations of triangular equilibrium points and the linear stability analysis, we have taken a pulsating star, IRAS 11472-0800 as the first primary, with a young white dwarf star; G29-38 as the second primary. We observe that the disc does not change the positions of the triangular points significantly, except on the y-axis. However, radiation, P–R drag and the mass parameter $\mu$ contributeeffectively in shifting the location of the triangular points. Regarding the stability analysis, it is seen that these points under the combined effects of radiation, P–R drag and the disc, are unstable in the linear sense due to at least a complex root having a positive real part. In order to discern the effects of the parameters on the stability outcome, we consider the range of the mass parameter to be in the region of the Routhonian critical mass (0.038520). It is seen that in the absence of radiation and the presence of the disc, when the mass parameter isless than the critical mass, all the roots are pure imaginary and the triangular point is stable. However, when $\mu = 0.038521$, the four roots are complex, but become pure imaginary quantities when the disc is present. This proofs that the disc is a stabilizing force. On introducing the radiation force, all earlier purely imaginary roots became complex roots in the entire range of the mass parameter. Hence, the component of the radiation force is strongly a destabilizing force and induces instability at the triangular points making it an unstable equilibriumpoint.

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