Systematic study of the connections between the collinear libration points of a coherent Sun-Earth-Moon restricted four-body model
- Paper number
IAC-17,C1,8,2,x38625
- Author
Mr. Bastien Le Bihan, ISAE - Institut Supérieur de l'Aéronautique et de l'Espace, France
- Coauthor
Prof. Josep J. Masdemont, Universitat Politecnica de Catalunya (UPC), Spain
- Coauthor
Prof. Gerard Gomez, University of Barcelona, Spain
- Coauthor
Prof. Stéphanie Lizy-Destrez, SUPAERO- Ecole Nationale Supérieure de l'Aéronautique et de l'Espace, France
- Year
2017
- Abstract
\newcommand{\scf}[1]{{\mdseries\textsc{#1}}} \newcommand*{\crtbp}{\scf{crtbp}} \newcommand*{\crtbps}{{\mdseries\textsc{crtbp}}s} \newcommand*{\qbcp}{\scf{qbcp}} \newcommand*{\emo}{\scf{em}} \newcommand*{\sem}{\scf{sem}} \newcommand*{\se}{\scf{se}} \newcommand{\li}[2]{{\mdseries\textsc{#1}}$_{#2}$} \newcommand{\emlo}{\li{eml}{1}} \newcommand{\emlt}{\li{eml}{2}} \newcommand{\semlo}{\li{seml}{1}} \newcommand{\semlt}{\li{seml}{2}} \newcommand{\selo}{\li{sel}{1}} \newcommand{\selt}{\li{sel}{2}} The dynamics about the libration regions of the Sun-Earth (\se) and Earth-Moon (\emo)systems have been used for the last decades in several missions, both for nominal orbit determination and transfer trajectory design. Beyond such approaches, the gravitational influence of the Earth, the Sun, and the Moon can be combined to produce efficient transfers in the extended Sun-Earth-Moon-spacecraft (\sem) system. Historically, the latter system has been approximated as two coupled Circular Restricted Three Body Problems (\crtbp), the Sun-Earth and Earth-Moon systems, with their associated libration points, \li{sel}{i} and \li{eml}{i}, $i = 1, \dots, 5$. The hyperbolic manifolds of the orbits about \emlt~and \li{sel}{1,2} provide dynamical channels that can be suitably combined to produce low-energy trajectories. This so-called \emph{coupled \crtbp approximation} has been previously used to compute various types of connections, including low-energy Earth-Moon transfers, Earth-to-\emlt~trajectories, and free \li{sel}{1,2}-to-\emlt~transfers. The later type is of particular interest to better understand the natural coupling between the two systems that underlies all these low-energy transfers. The coupled \crtbp~approximation relies on the fact that the dynamics associated with the \emo and \se subsystems are partially preserved in the four-body context. However, for every computed trajectory, this option requires both a specific Sun-Earth-Moon configuration and an arbitrary connection between the two \crtbps, which prevents the use of this model as a basis for a systematic search. In this paper, free \li{sel}{1,2}-to-\emlt~transfers are consistently obtained for the first time in a single, coherent model of the Sun-Earth-Moon system called the Quasi-Bicircular model. The sets of staging orbits and their associated hyperbolic manifolds are obtained semi-analytically at both ends of the transfer, using the \emph{pa\-ra\-me\-te\-ri\-za\-ti\-on method}, taking into account the explicit time-dependency of the dynamics. A systematic search for connections is then performed in the parameterization space: initial conditions on the center-unstable manifold at \emlt~are propagated forward in time and projected on the center manifold at \li{sel}{1,2}. A transfer is found each time that the distance of projection is close to zero. These solutions are refined solving a two-point boundary value problem, for which the boundary conditions are easily written in the parameterization space. This process can be coupled with a continuation procedure to easily obtain families of natural connections. Both planar and three-dimensional transfers are obtained. Finally, the resulting trajectories are refined to JPL ephemerides.- Abstract document
- Manuscript document
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