Abstract
This paper studies the motion of a third body near the 1st family of the out-of-plane equilibrium points, L6,7, 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 (ξ0,0,±ζ0) which correspond to the positions of the 1st family of the out-of-plane equilibrium points, L6,7, 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 ±ζ0 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, L6,7 numerically, shows that they can be stable for 0.32≤μ≤0.5 and for very low eccentricity. L6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.
Highlights
The motion of a body is influenced by the mutual gravitational attraction from other bodies
Our aim in this paper is to study the existence and stability of the out-of-plane equilibrium points under an oblate primary and a luminous-triaxial secondary in the ER3BP with application to the binary systems DP-Leonis and PSR 1903-0327
This article is organized in 7 sections as follows: the first section is the introduction; the equations of motion are given in Section 2; Section 3 contains the surface of zero-velocity curves (ZVC) in the (ξ−ζ) plane; the positions and stability of the out-of-plane equilibrium points are treated in Sections 4 and 5, respectively; Section 6 contains numerical application, while Section 7 is the discussion which concludes the study
Summary
The motion of a body is influenced by the mutual gravitational attraction from other bodies. Reference [16] proved the existence of a second family of the out-of-plane equilibrium points L8,9 when the principal bodies are both luminous under certain condition (i.e., the relation between the mass and radiation pressure parameters). They studied the stability for μ = 0.5 and μ = 0.2. [26] investigated the influence of PoyntingRobertson drag and oblateness on the existence and stability of the out-of-plane equilibrium points in the spatial elliptic restricted three-body problem This article is organized in 7 sections as follows: the first section is the introduction; the equations of motion are given in Section 2; Section 3 contains the surface of zero-velocity curves (ZVC) in the (ξ−ζ) plane; the positions and stability of the out-of-plane equilibrium points are treated in Sections 4 and 5, respectively; Section 6 contains numerical application, while Section 7 is the discussion which concludes the study
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