Exploring the Influence of Oblateness on Asymptotic Orbits in the Hill Three-Body Problem
Year: 2025
Type: article
Abstract: We examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear equilibrium points. By systematically varying the oblateness parameter, we determine conditions for the existence and location of these orbits. Our results confirm the presence of both homoclinic orbits, where trajectories asymptotically connect an equilibrium point to itself, and heteroclinic orbits, which establish connections between two distinct equilibrium points, via their stable and unstable invariant manifolds, which are computed both analytically and numerically. To achieve precise computations, we employ differential correction techniques and leverage the system’s inherent symmetries. Numerical calculations are carried out for orbit multiplicities up to twelve, ensuring a comprehensive exploration of the dynamical properties.
Source: AppliedMath
Author: Vassilis S. Kalantonis
Institution: University of Patras
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W4408504813