Investigation of the Stability of a Test Particle in the Vicinity of Collinear Points with the Additional Influence of an Oblate Primary and a Triaxial-Stellar Companion in the Frame of ER3BP

Abstract

We investigate in the elliptic framework of the restricted three-body problem, the motion around the collinear points of an infinitesimal particle in the vicinity of an oblate primary and a triaxial stellar companion. The locations of the collinear points are affected by the eccentricity of the orbits, oblateness of the primary body and the triaxiality and luminosity of the secondary. A numerical analysis of the effects of the parameters on the positions of collinear points of CEN X-4 and PSR J1903+0327 reveals a general shift away from the smaller primary with increase in eccentricity and triaxiality factors and a shift towards the smaller primary with increase in the semi-major axis and oblateness of the primary on L1. The collinear points remain unstable in spite of the introduction of these parameters.

Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

“…In this section, we apply the data (barrowed from NASA ADS and [7]) of the binaries PSR 1903+0327 and DP-Leonis Advances in Astronomy 9 (Table 1) to the analytical results obtained in the previous sections under the assumption that the primary body is an oblate spheroid while the secondary body is a luminoustriaxial body both moving in elliptic Keplerian orbits. The positions of the out-of-plane equilibrium points (Equation (19)) together with the roots of the characteristic equation (Equation 20) are computed (for some assumed values of the potential of the system under consideration) in Tables 2-4 for PSR 1903+0327 and in Tables 5-7 for DP-Leonis with the help of the Wolfram Mathematica 10.3.…”

“…Over decades, the study of the existence of some families of particular solutions in both circular and elliptic R3BP has received the attention of various researchers like [1][2][3][4][5][6][7][8][9][10][11][12][13] among others.…”