Abstract
With improved observational capabilities, an increasing number of binary systems have been discovered both within the solar system and beyond. By characterizing the gravitational environment near a binary star, for example, potential motions of a nearby exoplanet may be explored. The path of this comparatively small body is influenced by an underlying dynamical structure of periodic orbits which can attract, bound or repel trajectories in their vicinity. In this investigation, stability analysis is employed to examine the evolution of selected families of periodic orbits near large mass ratio binary systems in two dynamical models: the circular restricted three-body problem and an expanded model that incorporates an additional autonomous force to examine theories for three-body gravitational interactions. Discrete variational mechanics is employed to determine the natural parameters corresponding to the existence of a given orbit geometry, facilitating exploration of the effect of an additional three-body interaction on nearby periodic orbits and the conditions for reproducibility in the natural gravitational environment. Any unique effects of the additional autonomous force contribution may impact the potential motion of an exoplanet as it orbits a binary star system.
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