Investigating the albedo effects on the dynamics of infinitesimal mass in the elliptic Sitnikov five-body problem

Abstract

In this paper, we aim to showcase the significant impacts of albedo and eccentricity of the primaries on the infinitesimal mass within the elliptic case of the Sitnikov five-body problem. The Van der Pol transformation and averaging technique were employed to formulate the averaged equations of motion for the infinitesimal mass. Subsequently, the Hamiltonian equations of motion were derived using the action angle variables $I$ and $\theta$. Additionally, we obtained $\theta$ in terms of the Jacobi elliptic function $sn$ through a canonical transformation. The investigation utilized the first return map to explore various orbits such as regular, periodic, quasi-periodic, chaotic, or stochastic in the presence of albedo and eccentricity. It was observed that chaotic and stochastic regions emerged as the albedo effect increased, disrupting the periodic tubes and islands. Moreover, by escalating the albedo effect and eccentricity of the primaries, several families of periodic orbits were revealed.