Infinitesimal orbits around lagrange points in the elliptic, restricted three-body problem

Abstract

This study presents a method of obtaining asymptotic approximations for motions near a Lagrange point in the planar, elliptic, restricted three-body problem by using a yon Zeipel-type method. The calculations are carded out for a second-order escape solution in the proximity of the equilateral Lagrange point, L4, where the primaries' orbital eccentricity is taken as the small parameter ¢.

Effects of radiation on stability of triangular equilibrium points in elliptic restricted three body problem

“…The analytical investigation concerning the structure of asymptotic perturbative approximation for small amplitude motions has been "performed by Selaru and Cucu-Dumitrescu [14], [15]", provided the third point mass lies in the neighbourhood of a Lagrangian equilateral points in the planer , elliptical restricted three bodies. Non-linear stability of the triangular equilibrium points of the elliptical restricted three body problem was "studied by Gyorgrey [16], Kumar and Choudhary [17], Erdi [18]".…”

“…Furthermore, the nonlinear stability of the infinitesimal in the orbits or the size of the stable region around L 4 was "studied by Gyorgrey [16]" and the parametric resonance stability around L 4, in elliptical restricted three body problem was "studied by Erdi [18]". The influence of the eccentricity of the orbit of the primary bodies with or without radiation pressure on the existence of the equilibrium points and there stability was "discussed to some extent by Khasan [12], [13], Pinyol [19], Floria [20], Halan and Rana [21], Markeev [22], Selaru and Dumitrescu [14], [15], Nayayan and Ramesh [23], [24]". The stability of triangular points in the elliptical restricted three body problem under radiating and oblate primaries was "studied by Singh and Umar [25], [26]".…”

A study of libration points in CR3BP under albedo effect

“…are discussed by Danby [22]; Selaru D. et.al. [24]; Markellos et al [25]; Subbarao and Sharma [26]; Khanna and Bhatnagar [27,29]; Roberts G.E. [33]; Oberti and Vienne [34]; Perdiou et.…”

A general solution to non-collinear equilibria in terms of largest root (κ) of confocal oblate spheroid

“…[10]; El-Shaboury [11]; Bhatnagar et al [12]; Selaru D. et.al. [13]; Markellos et al [14]; Subbarao and Sharma [15]; Khanna and Bhatnagar [16,17]; Roberts G.E. [18]; Oberti and Vienne [19]; Sosnytskyi [20]; Perdiou et.…”