ON THE EXISTENCE AND STABILITY OF COLLINEAR EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL CIRCULAR RESTRICTED THREE-BODY
Abstract
We have studied the positions and stability of collinear equilibrium points in the circular restricted three-body problem for Luyten 726-8 and Achird systems. We observed that the location of the collinear equilibrium points L_i (i=1,2,3) changes positions due to the oblateness and radiating factors for the binary systems under review. The changes in the positions of the collinear equilibrium points does not change the status of the collinear equilibrium points as they remain unstable and unchanged. As the oblateness increases, the region of stability of the collinear equilibrium points decreases. It is found that, the positions of the collinear equilibrium points are greatly affected by the oblateness and radiation factors of both primaries for the aforementioned binary systems. Our study reviewed that, at least one characteristic root has a positive real part and a complex root which in the sense of Lyapunov, the stability of the collinear equilibrium points is unstable for the stated binary systems.
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