Dynamic analysis of Lyapunov and Halo orbits in the Proxima Centauri system

This article investigates the state of an infinitesimal third body within the Proxima Centauri–Proxima Centauri \( b \) dynamical system. Within this framework, the authors discover the Lagrange points \(\mathtt {L_i} \ (i = 1, 2, 3, 4, 5)\) and trace the zero velocity curves to facilitate motion analysis. The study primarily focuses on the stability analysis and construction of planar Lyapunov orbits around the collinear Lagrange points \(\mathtt {L_1}\) and \(\mathtt {L_2}\). Additionally, the spatial problem is explored by computing families of Halo orbits and procuring invariant tube manifolds associated with them, precisely mapping the possible regions of motion that emanate from these orbits. The orbits are generated using a robust differential correction and numerical integration scheme. The results contribute to our knowledge of the gravitational dynamics at work and provide important data that could potentially guide future expeditions to this exotic exoplanetary system.