Abstract
The restricted three body problem is treated in the framework of the post-Newtonian approximation of general relativity. The equations of motion are linear zed around the libration points L4,5. Locations of the equilibrium points L4,5 are obtained. Existence and stability of these points are investigated. The relativistic correction to the classical mass ratio is determined.
Highlights
In any assumed isolated two-body massive orbiting system, there are five equilibrium points, Li,i = 1, 2, 3, 4,5, these points usually called Lagrangian or Libration points
The restricted three body problem (RTBP in brief) is defined as a system consisting of two massive bodies, the primaries, revolving in a circular orbits around their centre of mass, and a third body of infinitesimally small mass which moves in the primaries orbital plane
The existence stability of the triangular points L4,5 in the relativistic RTBP is studied [9], they concluded that L4,5 always unstable in the whole range 0 ≤ μ ≤ 0.5 in contrast to the previous results of the classical RTBP where they are stable for 0 ≤ μ ≤ μ0, where μ is the mass ratio and μ0 = 0.03852
Summary
Conclusion is that in the planar case the triangular points L4,5 are always stable within some domain of mass ratio. The triangular points are stable in the linear system for the values of the mass ratio in the interval (0, μ) where μ = 0.038521 is the Routhian value, is shown[3]. The existence stability of the triangular points L4,5 in the relativistic RTBP is studied [9], they concluded that L4,5 always unstable in the whole range 0 ≤ μ ≤ 0.5 in contrast to the previous results of the classical RTBP where they are stable for 0 ≤ μ ≤ μ0 , where μ is the mass ratio and μ0 = 0.03852 .
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