Generalized out-of-plane equilibrium points in the frame of elliptic restricted three-body problem: Impact of oblate primary and luminous-triaxial secondary

Abstract

This paper studies the motion of a third body near the 1 st family of the out-of-plane equilibrium points, L 6,7 , in the elliptic restricted problem of three bodies under an oblate primary and a radiating-triaxial secondary. It is seen that the pair of points (𝜉 0 , 0, ±𝜁 0 ) which correspond to the positions of the 1 st family of the out-of-plane equilibrium points, L 6,7 , are affected by the oblateness of the primary, radiation pressure and triaxiality of the secondary, semimajor axis, and eccentricity of the orbits of the principal bodies. But the point ±𝜁 0 is unaffected by the semimajor axis and eccentricity of the orbits of the principal bodies. The effects of the parameters involved in this problem are shown on the topologies of the zero-velocity curves for the binary systems PSR 1903+0327 and DP-Leonis. An investigation of the stability of the out-of-plane equilibrium points, L 6,7 numerically, shows that they can be stable for 0.32 ≤ 𝜇≤ 0.5 and for very low eccentricity. L 6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.