Families of periodic orbits about Lagrangian points L1, L2 and L3 with continuation method

Abstract

This study deals the impact of radiation pressure and albedo from the respective primaries in the context of regularized periodic motion of infinitesimal mass under the frame of restricted three body problem with the help of continuation method. The effect of these perturbing parameters on the orbital properties about the collinear Lagrangian points and their stability property are investigated. An expansion in the structure of Lyapunov orbits are found due to radiation pressure effect and albedo whereas crossing of stability bounds (±1) occurs in the continuation process of Lyapunov orbits indicating the presence of halo bifurcation. This occurrence of halo bifurcation leads to the origin of halo periodic orbits from Lyapunov periodic orbits at different values of radiation parameter ( q ) and albedo ( Q A ). From these bifurcating orbits, families of halo periodic orbits are determined using continuation in radiation parameter and albedo, respectively. Due to the existence of one of the stability index ( ν ), which is either greater than 1 or less than ​− ​1, periodic orbits become unstable. • Regularized restricted three body problem with radiation pressure and albedo are discussed. • Numerical computation of periodic orbits about collinear equilibrium points are discussed. • The parametric evolution of periodic orbit as the function of radiation and albedo parameter are presented. • Families of periodic orbits are found with the help of continuation in radiation and albedo parameter.