Abstract
This paper investigates the positions and stability of libration points in the framework of the circular restricted three-body problem for the systems: Luyten726-8 and HD98800. The position of the third body lie in the plane almost directly above and below the center of the oblate primary. It is found that radiations and oblateness of the primary have destabilizing effects; the presence of any one or more of the latter makes weak the stabilizing ability of the former, consequently the overall effect is that the range of stability of the libration points decreases. Considering the range of stability and instability, that is and , the libration points are respectively stable and unstable for HD98800 and Luyten 762-8 systems. Our results show that, all the roots are real, and for each set of values, there exist at least a positive real part and hence in the Lyapunov sense, the stability of the libration points are unstable for the systems HD98800 and Luyten 762-8.
Highlights
The masses of the planets compared to its approximate circular motion around the Sun and the small masses of asteroids and the satellites of planets constitute the restricted problem
Triangular equilibrium solution becomes unstable in the absence of the coriolis force, the exponential terms with real characteristic exponents replaced the oscillatory solution of the linearized equations of motion (Wintner 1941)
The change ε in the coriolis force is related to the critical mass parameter μc value by the expression μc Triangular equilibrium points’ stability of the photogravitational
Summary
The masses of the planets compared to its approximate circular motion around the Sun and the small masses of asteroids and the satellites of planets constitute the restricted problem. The change ε in the coriolis force is related to the critical mass parameter μc value by the expression μc Triangular equilibrium points’ stability of the photogravitational
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