Invariant manifolds and transport in a Sun-perturbed Earth-Moon system
[eng] This dissertation is devoted to the analysis of the motion of small bodies, like asteroids, in the neighbourhood of the Earth-Moon system from a celestial mechanics approach. This is an extensive area of research where probably, the most extended simplified mathematical model is the well-known...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/190643 |
| Acceso en línea: | https://hdl.handle.net/2445/190643 http://hdl.handle.net/10803/675932 |
| Access Level: | acceso abierto |
| Palabra clave: | Mecànica celeste Problema dels tres cossos Invariants Asteroides Meteorits Lluna Celestial mechanics Three-body problem Asteroids Meteorites Moon |
| Sumario: | [eng] This dissertation is devoted to the analysis of the motion of small bodies, like asteroids, in the neighbourhood of the Earth-Moon system from a celestial mechanics approach. This is an extensive area of research where probably, the most extended simplified mathematical model is the well-known autonomous Hamiltonian system the Restricted Three-Body Problem (RTBP). Many modifications to this model have been proposed, looking for a more accurate description of the system. One of the simplest ways of introducing additional physical effects is through time-periodic perturbations, such that such that the new non-autonomous system is close to the autonomous one, and it has many periodic or quasi-periodic solutions. If these solutions are hyperbolic, they have stable/unstable invariant manifolds, such that stable manifolds approach the quasi-periodic solutions forward in time, meanwhile unstable manifolds do it backward in time, constituting the skeleton for the dynamical transport phenomena we are interested in. Notice that one dimension can be reduced by defining a suitable temporal Poincar´e map. Therefore, our aim is to compute the quasi-periodic solutions and their manifolds in this map. Most of the effort of this dissertation is addressed to the Bicircular Problem (BCP), in which the Earth and Moon are treated as the primaries in the RTBP and the gravitational field of the Sun is introduced as a time-periodic forcing of the RTBP. In particular, we have extensively analysed the horizontal family of two dimensional quasi-periodic solutions in the neighbourhood of the collinear unstable equilibrium point L3. We found that diverse trajectories connecting the Earth, the Moon and the outside Earth-Moon system are governed by L3 dynamics. Big attention is paid to the trajectories coming from the Moon towards the Earth, since they may give an insight of the travel that lunar meteorites perform before landing in our planet. These results have been translated and compared with those of a realistic model based on JPL (Jet Propulsion Laboratory) ephemeris, showing a good agreement between the results obtained. We also have proposed and carried out a strategy for capturing a Near Earth Asteroid (NEA) using the stable invariant manifolds of the horizontal family of quasi-periodic orbits around L3 in the BCP. To this aim the high order parametrization of the stable/unstable invariant manifolds is introduced, for which computation we have employed the jet transport technique. Finally, the strategy is applied to the NEA 2006 RH120. The contributions to the BCP presented in this dissertation include two other applications. The first one is devoted to the study of the unstable behaviour near the triangular points, meanwhile the second is devoted to a family of stable invariant curves around the Moon that are close to a resonance, promoting the appearance of chaotic motion. The last part of the dissertation is focused on the effective computation of the high or- der parametrization of the stable and unstable invariant manifolds associated with reducible invariant tori of any high dimension. To this aim, we resort on the reducible system, that offers a high degree of parallelization of the computations. Besides, we explain how to com- bine the presented methods with multiple shooting techniques to accurately compute highly unstable invariant objects. Finally, we apply the developed algorithms to compute the high order parametrization of the manifolds associated to L1 and L2 in an Earth-Moon system that includes five time-periodic forcings regarded to four physical features of the system, besides the solar gravitational field. |
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