Equilibrium Points and Networks of Periodic Orbits in the Pseudo-Newtonian Planar Circular Restricted Three-body Problem

We explore a pseudo-Newtonian planar circular restricted three-body problem in which the primaries are modeled using an approximate gravitational potential up to the second nonvanishing term of the Fodor-Hoenselaers-Perjes expansion. We aim to understand how the main free parameters of the system affect its dynamical properties. In particular, we determine how the mass of the primaries as well as the transition parameters affect not only the properties of the points of equilibrium (total number, locations, and linear stability) but also the networks of simple symmetric periodic orbits. Our results show that, under this approach, significant variations are observed in the fixed points (number and stability) and periodic orbits of the planar circular restricted three-body problem, even when small contributions of the non-Newtonian terms are considered. We also provide direct applications of the new model potential in real observable binary stellar systems.