Exploring the influence of a three-body interaction added to the gravitational potential function in the circular restricted three-body problem: A numerical frequency analysis
Abstract
Many binary star systems (e.g., pulsar-white dwarf) are known to possess significantly smaller companions, such as an exoplanet, in large orbits about the binary. Given that binary star systems exist far from the Earth, the interactions comprising their dynamical environment are unknown. Fundamentally, the motion of the exoplanet may be modeled using pairwise point-mass gravitational contributions from each of the two stars, assumed to possess similar masses. In this investigation, however, a three-body interaction is also considered. This extra force contribution is selected to depend inversely upon the product of the distances between the three bodies. The resulting model is constructed to reduce to the well-known circular restricted three-body problem as the three-body interaction is scaled to zero. A numerical frequency analysis is employed to examine the properties and prevalence of retrograde periodic and quasi-periodic orbits in the exterior region in the circular restricted three-body problem for a large mass ratio. Using these results as a baseline, a similar analysis is completed for various constants scaling the three-body interaction. The influence of this additional contribution is explored using the computed fundamental frequencies, which reflect changes in the underlying ordered dynamics in the vicinity of the binary. Poincaré maps are employed to confirm and explore the results of the frequency analysis. The results from this preliminary investigation suggest that the dynamics of an exoplanet in a large orbit about a binary star system are significantly altered by the inclusion of a three-body interaction.
Degree
M.S.A.A.
Advisors
Howell, Purdue University.
Subject Area
Astrophysics
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