Exploring the Impact of a Three-Body Interaction Added to the Gravitational Potential Function in the Restricted Three-Body Problem

Consider a binary star system (e.g., pulsar-white dwarf, pulsar-pulsar) with a significantly smaller companion, such as an exoplanet, in orbit about the binary. Given the absence of experimental data gathered within the vicinity of the binary, it is possible that the gravitational field within this system might not be accurately modeled by well-known pairwise gravitational forces. In this research, the presence of an additional three-body interaction is considered. Many-body forces are not an entirely new concept; in fact, the importance of three-body interactions in accurately modeling force fields on the atomic scale is well established in nuclear physics. On a much larger scale, the motion of a small body orbiting a binary star system serves as a new and interesting application for determining the characteristics of a three-body interaction. In this investigation, frequency analysis is used to study its effect on possible orbits of the exoplanet. When weighted appropriately, the three-body force contribution is found to significantly alter the stability, form and existence of periodic and quasi-periodic orbits available at various energy levels. Physically, this means that exoplanets could follow orbits that cannot be accurately recovered using traditional inverse-square gravitational forces.