Existence and stability of collinear points in elliptic restricted three body problem with radiating and oblate primaries

Abstract

The location of the collinear points in elliptical restricted three body problem, taking into account the effect of oblateness and radiation pressure of both primaries, has been obtained in this paper. Vinti's method has been exploited and the x-coordinates are obtained in the form of series solution. The linear stability has been investigated and it is found that the points are unstable in the Lyapunov's sense. The problem is also numerically explored taking into account two binary systems: Luyten-726 and Kruger-60.

Collinear libration points in the elliptic restricted three body problem (ER3BP) under radiating and triaxial primaries with gravitational potential from the belt

“…In their model ( Aliroma et al., 2019 ) showed that the stability region could depend mainly on the eccentricity of the orbits in addition to considered pertubations. Exploiting Vinti's method in which an oblate-spheroidal coordinate system was used to describe the orbital motion and obtaining x-corodinates in the form of series solution ( Chakraborty et al., 2016 ) investigated the linear stability of the collinear points using two binary system Luyten-726 and Kruger-60 and found them to be unstable.…”

Existence of Resonance Stability of Triangular Equilibrium Points for an Oblate Infinitesimal in Elliptical Restricted Three Body Problem with Radiating Oblate Primaries

“…In classical problems the primaries are taken strictly as spheres but some planets and stars are sufficiently oblate to make departure from sphericity significant in the study of celestial systems. The influence of eccentricity of the orbit of the primaries with or without radiation pressure, oblateness and triaxiality of the primaries was studied by many authors [1,3,7,13,15,16,18,20,21,24,29,34,36] and others. Kumar and Ishwar [16] investigated the stability of the collinear liberation points when both the primaries are oblate and radiating whereas Singh and Aishetu [30] studied the stability of the triangular equilibrium points when both the primaries are oblate and radiating.…”