Leveraging manifolds of tori associated with quasi-satellite orbits to design low-fuel mars-phobos transfers
- Paper number
IAC-20,C1,6,2,x56354
- Author
Dr. Marc Jorba-Cuscó, France, Centre National d'Etudes Spatiales (CNES)
- Coauthor
Dr. Richard Epenoy, France, Centre National d'Etudes Spatiales (CNES)
- Year
2020
- Abstract
Quasi-Satellite Orbits (QSOs) are considered by JAXA’s MMX mission, in which CNES is involved [1], for the scientific observation of the Martian moon Phobos prior to landing and sample return operations. These periodic orbits, originally defined in the Mars-Phobos Circular Restricted Three-Body Problem, generally lose periodicity once the eccentricity of Phobos’ orbit is taken into account. In this case, QSOs are replaced by quasi-periodic tori [2]. Recent work on MMX project include, amongst many others, station-keeping strategies around QSOs exploiting invariant tori [3]. This study has been carried out considering the elliptical Hill problem.\\ \indent In this work, we first compute a resonant QSO in the Mars-Phobos Circular Restricted Three-Body Problem. Then, by continuation on the eccentricity of the secondary, we build a family of periodic QSOs parametrized by the eccentricity in the Elliptic Restricted Three-Body Problem. Notice that considering resonant orbits enables us to preserve the periodicity of the QSOs when the eccentricity is non-zero. After reaching the eccentricity of Phobos, we build a family of invariant tori by continuation on the frequency till convergence to the target torus. The tori are computed here in the Elliptic Restricted Three-Body Problem. As a matter of fact, the later model is more precise than the Hill problem at far distance from the secondary and thus more adapted to handle Mars-Phobos transfers. In the next step, we compute the stable invariant manifold emanating from the target torus. Finally, we build nearly-ballistic two-impulse transfers between a parking orbit around Mars and different points on the manifold trying to minimize the total delta-v. Interesting transfer trajectories will be shown allowing for a ballistic capture by Phobos. Here, instead of targeting directly a QSO as done in [4], the spacecraft reaches first the invariant manifold before coasting along the manifold until encountering the target torus.\\ \textbf{References}\\ [1] Elisabet Canalias, Laurence Lorda, Julien Laurent-Varin, “Design of Realistic Trajectories for the Exploration of Phobos", \textit{AIAA Space Flight Mechanics Meeting}, 8-12 January 2018, Kissimmee, USA.\\[-0.25cm] [2] Àngel Jorba and Jordi Villanueva, “On the Persistence of Lower Dimensional Invariant Tori under Quasi-Periodic Perturbations”, \textit{Journal of Nonlinear Science}, Vol. 7, pp. 427-473, 1997.\\[-0.25cm] [3] Nicola Baresi, Diogene Alessandro dei Tos, Hitoshi Ikeda, Yasuhiro Kawakatsu, “Orbit Design and Maintenance in the Elliptical Hill Problem with Applications to the Phobos Sample Return Mission MMX”, Paper IAC-19-C1.4.7, $70^{th}$ \textit{International Astronautical Congress}, 21-25 October 2019, Washington D.C., USA.\\[-0.25cm] [4] Kenta Oshima and Tomohiro Yanao, “Spatial Unstable Periodic Quasi-Satellite Orbits and their Applications to Spacecraft Trajectories”, \textit{Celestial Mechanics and Dynamical Astronomy}, 131:23, 2019.- Abstract document
- Manuscript document
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