Periodic and quasi-periodic motion around equilibrium points in a planar heterogeneous photogravitational restricted three-body problem with albedo effect

Abstract

This study investigates the planar motion of an infinitesimal particle in a heterogeneous photogravitational restricted three-body problem, where the more massive primary is assumed to be radiating while the less massive primary possesses a layered heterogeneous internal structure along with albedo-induced perturbative effects. Building upon the previously established equilibrium framework, the present work focuses on the orbital dynamics around both collinear and non-collinear equilibrium points. The local dynamics near the collinear equilibria are analyzed through linearization, revealing oscillatory components that permit the construction of small-amplitude periodic trajectories despite the inherent instability of these points. The influence of the heterogeneity parameter and radiation pressure on the equilibrium locations, instability characteristics, oscillation frequencies, and orbital periods is examined numerically. For the non-collinear equilibrium points, the linear stability analysis yields two independent oscillatory modes, leading to the existence of bounded periodic motion. Numerical simulations demonstrate stable periodic trajectories around the triangular equilibrium points, together with significant parameter-dependent variations in orbital geometry and oscillatory frequencies. The superposition of the two characteristic modes further gives rise to quasi-periodic trajectories, highlighting the richer dynamical behavior near stable equilibrium configurations. The results show that internal heterogeneity and photogravitational perturbations substantially modify both the equilibrium structure and the local orbital dynamics compared with the classical restricted three-body problem. The present analysis provides useful insight into the motion of small particles in perturbed celestial systems influenced by radiation and structural inhomogeneity.