2024-03-28T14:44:03Zhttps://www.tdx.cat/oai/requestoai:www.tdx.cat:10803/21212023-06-09T10:55:26Zcom_10803_1col_10803_84
nam a 5i 4500
Transferències de baixa energia
Formació de cràters lunars
Sistemes dìnàmics
Problema Circular Restringit dels Tres Cossos (CR3
Control òptim
The Role and Usage of Libration Point Orbits in the Earth - Moon System
[Barcelona] :
Universitat de Barcelona,
2011
Accés lliure
http://hdl.handle.net/10803/2121
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9788469391051
Alessi, Elisa Maria,
autor
Tesi
Doctorat
Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
2010
Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
Tesis i dissertacions electròniques
Gómez Muntané, Gerardo,
supervisor acadèmic
Masdemont Soler, Josep,
supervisor acadèmic
TDX
In this dissertation, we show the effectiveness of the exploitation of the Circular Restricted Three - Body Problem (CR3BP) in the Earth - Moon framework. We study the motion of a massless particle under the gravitational attraction of Earth and Moon, either to design missions in the new era of lunar exploration and simulate the behaviour of minor bodies that get close to the Earth.<br/><br/>A fundamental role is played by the five equilibrium, or libration, points that appear in the rotating reference system. We focus on two, L(1) and L(2), unstable collinear libration points, taking advantage of the central and hyperbolic invariant manifolds, which exist in their neighborhood. Various types of periodic and quasi-periodic orbits, to be conceived as station locations for a spacecraft, occupy the central manifold. A stable and an unstable invariant manifold are associated with any of these orbits: they serve as channels to get far or close to the central orbits for t > / = 0. We exploit the corresponding dynamics to construct transfers from either Earth and Moon to a libration point orbit (LPO) and to investigate some paths that might guide asteroids impacting onto the Moon.<br/><br/>We are witnesses of a recent enthusiasm on a possible return to the Moon. Several space agencies have designed unmanned missions that have just achieved observations around the Moon, in view of a future human installation. Besides, the space tourism companies are planning to extend their potentiality by offering lunar trips. In this context, the neighborhood of L(1) seems to be an appropriate place to put a space hub. Instead, L(2) would be profitable to monitor the lunar farside.<br/><br/>In Chapter 1, we explain the CR3BP and how to compute, with different methodologies, central orbits along with their associated hyperbolic manifolds and the transit trajectories lying inside them. Then, two more elaborate dynamical systems are introduced, the Bicircular Restricted Four - Body Problem and the Restricted n - Body Problem.<br/><br/>In Chapter 2, we use the stable and the unstable manifolds associated with L1/L2 central orbits to connect the lunar surface with such LPOs. We see that almost no effort should be put to follow these transfers thanks tothe natural dynamics we consider.<br/><br/>In Chapter 3, we study how to depart from a nominal orbit around the Earth and arrive to a L1/L2 LPO. This case requires two maneuvers, one to leave the Low Earth Orbit and another to insert into the stable manifold associated with the given LPO.<br/><br/>In Chapter 4, we wonder how the above reference solutions can change whenever different forces are added to the dynamical model. We describe two possible approaches that can be implemented, namely an optimal control strategy and a multiple shooting procedure. The results demonstrate that also in the Earth - Moon framework the CR3BP gives solutions close to the ones to be used in reality.<br/>In Chapter 5, we cope with the collision of asteroids onto the Moon. Such phenomenon happens continuously on all the rocky bodies populating the Solar System, as it can be inferred from the craters that mould their surface, and it is widely studied by several branches of science, since it provides information on the target and on the impactors in dynamical, astronomical and geological terms.<br/><br/>We analyze the role played, in the creation of lunar impact craters, by low-energy transit trajectories which approach the neighborhood of L(2). It turns out that in the most likely case the collisions are focused on the apex of the Moon. Summing up the gravitational force exerted by the Sun, we notice that the relative Earth-Moon-Sun configuration can change dramatically the percentage and the region of impact.<br/><br/>KEYWORDS: Circular Restricted Three-Body Problem, Lunar Impact Dynamics, Low-Energy Transfers, Optimal Control
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