https://doi.org/10.1140/epjp/s13360-025-06936-3
Regular Article
Dynamic analysis of Lyapunov and Halo orbits in the Proxima Centauri system
1
Department of Mathematics, Hansraj College, University of Delhi, New Delhi, India
2
Department of Physics, Hansraj College, University of Delhi, New Delhi, India
3
Department of Mathematics, Sri Aurobindo College, University of Delhi, Delhi, India
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Received:
31
May
2025
Accepted:
6
October
2025
Published online:
17
October
2025
Abstract
This article investigates the state of an infinitesimal third body within the Proxima Centauri–Proxima Centauri 
dynamical system. Within this framework, the authors discover the Lagrange points 
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 
and 
. 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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
