This paper presents a generalized problem of the photogravitational restricted three body, where both the primaries are radiating; in the sense that the eccentricity of the orbits and the oblateness due to both the primaries and infinitesimal are considered. The positions and stability of the equilibrium points of this problem are studied. The stability analysis ensures that, the collinear equilibrium points are unstable in the linear sense while the stability condition for the triangular points is obtained. For illustrative numerical exploration four binary system: Luyten-726, Kruger-60 and Alpha-Centauri are considered, the location and stability of their planar equilibrium points are studied semi-analytically.
The present paper models the restricted three body problem, considering the generalization that the orbits of the primaries are taken to be elliptic and the two primaries are considered to be sources of radiation and all three participating bodies are considered as oblate spheroids. Hamiltonian of the problema is derived and then normalized using well-established normalization techniques. The range of values of µ and e for the linear stability of triangular equilibrium points have been found in presence of resonance. The stability of some of the cases of third order resonances has been simulated and explored graphically. The linear stability is observed in the resonance cases 3λ2 = −1, 3λ2 = −2 and λ1 + 2λ2 = 0, where as the triangular points are found to be linearly unstable in the case λ1 − 2λ2 = 2.
This work deals with the nonlinear stability of the elliptical restricted three-body problem with oblate and radiating primaries and the oblate infinitesimal. The stability has been analyzed for the resonance cases around ω1=2ω2 and ω1=3ω2 and also the nonresonance cases. It was observed that the motion of the infinitesimal in this system shows instable behavior when considered in the third order resonance. However, for the fourth order resonance the stability is shown for some mass parameters. The motion in the case of nonresonance was found to be unstable. The problem has been numerically applied to study the movement of the infinitesimal around two binary systems, Luyten-726 and Sirius.
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