Periodic orbits around the collinear equilibrium points for binary Sirius, Procyon, Luhman 16,α-Centuari and Luyten 726-8 systems: the spatial case

Abstract

An investigation of three-dimensional periodic orbits and their stability emanating from the collinear equilibrium points of the restricted three-body problem with oblate and radiating primaries is presented. A simulation is done by using five binary systems: Sirius, Procyon, Luhman 16, α-Centuari and Luyten 726-8. Firstly, based on the topological degree theory, the total number of the collinear equilibrium points for the five binary systems were obtained and then, their positions were determined numerically. The linear stability of these equilibrium points was also examined and found to be unstable in the Lyapunov sense. An analytical approximation of three-dimensional periodic solutions around them was established via the Lindstedt-Poincaré local analysis. Finally, using the analytical solution to obtain starting orbits, the families of three-dimensional periodic orbits emanating from these equilibria have been continued numerically.

Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

“…Das et al [18] investigated the field of the radiating binary stellar system in the circular RTBP. Singh et al [19] found three-dimensional periodic orbits around the collinear equilibrium points of the RTBP with oblate and radiating primaries. Singh and Umar [20] found that the positions of the third particle depended on the oblateness, radiation coefficients of the primaries, and the eccentricity of their orbits in the elliptic RTBP.…”

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

“…When considering multiple perturbation factors, Singh et al did a great deal of work on the libration points and their stability of various restricted three-body models (see References [33][34][35][36][37][38][39][40][41]). These factors mainly include the oblateness of the primaries [35][36][37][38]40,41], the oblateness of the third body [37], and the small perturbation in centrifugal force and Coriolis force [35][36][37][38][39][40][41], the radiation pressure of the primaries [33][34][35][36][37][38][39][40][41], the changing mass of the primaries over time based on the Meshcherskii law [34][35][36], the changing mass of the third body governed by Jeans law [42], the triaxiality of the primaries [39]. Basic references on oblateness, Coriolis and centrifugal forces, and radiation pressure can be found in References [43][44][45][46][47].…”