Tajudeen Oluwafemi Amuda
Articles written in Journal of Astrophysics and Astronomy
Volume 36 Issue 2 June 2015 pp 291-305
Out-of-Plane Equilibrium Points in the Photogravitational CR3BP with Oblateness and P-R Drag
Jagadish Singh Tajudeen Oluwafemi Amuda
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 𝐿_{6,7} 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.
Volume 40 Issue 1 February 2019 Article ID 0005
JAGADISH SINGH TAJUDEEN OLUWAFEMI AMUDA
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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