NDLI: Lunar capture trajectories and homoclinic connections through isomorphic mapping

Content Provider	Springer Nature Link
Author	Giancotti, Marco Pontani, Mauro Teofilatto, Paolo
Copyright Year	2012
Abstract	Analysis and design of low-energy transfers to the Moon has been a subject of great interest for many decades. This paper is concerned with a topological study of such transfers, with emphasis to trajectories that allow performing lunar capture and those that exhibit homoclinic connections, in the context of the circular restricted three-body problem. A fundamental theorem stated by Conley locates capture trajectories in the phase space and can be condensed in a sentence: “if a crossing asymptotic orbit exists then near any such there is a capture orbit”. In this work this fundamental theoretical assertion is used together with an original cylindrical isomorphic mapping of the phase space associated with the third body dynamics. For a given energy level, the stable and unstable invariant manifolds of the periodic Lyapunov orbit around the collinear interior Lagrange point are computed and represented in cylindrical coordinates as tubes that emanate from the transformed periodic orbit. These tubes exhibit complex geometrical features. Their intersections correspond to homoclinic orbits and determine the topological separation of long-term lunar capture orbits from short-duration capture trajectories. The isomorphic mapping is proven to allow a deep insight on the chaotic motion that characterizes the dynamics of the circular restricted three-body, and suggests an interesting interpretation, and together corroboration, of Conley’s assertion on the topological location of lunar capture orbits. Moreover, an alternative three-dimensional representation of the phase space is profitably employed to identify convenient lunar periodic orbits that can be entered with modest propellant consumption, starting from the Lyapunov orbit.
Starting Page	55
Ending Page	76
Page Count	22
File Format	PDF
ISSN	09232958
Journal	Celestial Mechanics and Dynamical Astronomy
Volume Number	114
Issue Number	1-2
e-ISSN	15729478
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-08-14
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Restricted three-body problem Homoclinic connection Permanent capture orbits Earth–Moon transfer Low energy transfers Poincaré section Lagrange points Lyapunov orbits Invariant manifolds Chaos Conley’s theorem Geophysics/Geodesy Aerospace Technology and Astronautics Astrophysics and Astroparticles Dynamical Systems and Ergodic Theory Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mathematical Physics Astronomy and Astrophysics Modeling and Simulation Computational Mathematics Space and Planetary Science

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