Much effort in recent times has been devoted to the study of low energy transport in multibody gravitational systems. Despite continuing advancements in computational abilities, such studies can often be demanding or time consuming in the three-body and four-body settings. In this work, the Hamiltonian describing the planar circular restricted three-body problem is rewritten for systems having small mass parameters, resulting in a 2D symplectic twist map describing the evolution of a particle's Keplerian motion following successive close approaches with the secondary. This map, like the true dynamics, admits resonances and other invariant structures in its phase space to be analyzed. Particularly, the map contains rotational invariant circles reminiscent of McGehee's invariant tori blocking transport in the true phase space, adding a new quantitative description to existing chaotic zone estimates about the secondary. Used in a patched three-body setting, the map also serves as a tool for investigating transfer trajectories connecting loose captures about one secondary to the other without any propulsion systems. Any identified initial conditions resulting in such a transfer could then serve as initial guesses to be iterated upon in the continuous system. In this work, the projection of the McGehee torus within the interior realm is identified and quantified, and a transfer from Earth to Venus is exemplified. / Master of Science / The transport of a particle between celestial bodies, such as planets and moons, is an important phenomenon in astrodynamics. There are multiple ways to mediate this objective; commonly, the motion can be influenced directly via propulsion systems or, more exotically, by utilizing the passive dynamics admitted by the system (such as gravitational assists).
Gravitational assists are traditionally modelled using two-body dynamics. That is, a space- craft or particle performs a flyby within that body's sphere of influence where momentum is exchanged in the process. Doing so provides accurate and reliable results, but the design space effecting the desired outcome is limited when considering the space of all possibilities.
Utilizing three-body dynamics, however, provides a significant improvement in the fidelity and variety of trajectories over the two-body approach, and thus a broader space through which to search. Through a series of approximations from the three-body problem, a discrete map describing the evolution of nearly Keplerian orbits through successive close encounters with the body is formed. These encounters occur outside of the body's sphere of influence and are thus uniquely formed from three-body dynamics. The map enables computation of a trajectory's fate (in terms of transit) over numerical integration and also provides a boundary for which transit is no longer possible. Both of these features are explored to develop an algorithm able to rapidly supply guesses of initial conditions for a transfer in higher fidelity models and further develop the existing literature on the chaotic zone surrounding the body.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/110928 |
| Date | 23 June 2022 |
| Creators | Werner, Matthew Allan |
| Contributors | Aerospace and Ocean Engineering, Ross, Shane D., Fitzgerald, Riley McCrea, Schroeder, Kevin Kent |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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