Low-fuel transfers from Mars to quasi-satellite orbits around Phobos exploiting manifolds of tori

Abstract

Quasi-satellite orbits (QSOs) are considered by JAXA’s MMX mission, in which CNES is involved, 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, generically lose periodicity once the eccentricity of Phobos’ orbit is taken into account. In this case, QSOs are replaced by quasi-periodic tori. Recent work on MMX project includes, among many others, station-keeping strategies around QSOs exploiting invariant tori in the elliptic Hill problem. In the present paper, a resonant QSO will be first computed in the Mars-Phobos circular restricted three-body problem. Then, by continuation on the eccentricity of the secondary, this QSO will be converted into a periodic resonant QSO in the Mars-Phobos elliptic restricted three-body problem. The latter problem is more precise than the Hill problem at far distance from the secondary and thus more adapted to handle Mars-Phobos transfers. Notice that considering resonant orbits enables to preserve the periodicity of the QSOs when the eccentricity is nonzero. Then, a family of invariant tori surrounding the resonant QSO in the Elliptic Restricted Three-Body Problem will be obtained by continuation on the frequency. In the next step, stable invariant manifolds emanating from the tori will be computed. Finally, two-impulse transfers between a parking orbit around Mars and the tori surrounding the QSO will be presented with the objective to minimize the total velocity increment. Interesting transfer trajectories will be shown allowing for a ballistic approach to Phobos. These trajectories lead to a reduction in the total velocity increment in comparison with classical Mars to QSOs transfers. Here, instead of targeting directly the resonant QSO, the spacecraft will reach first an invariant manifold before coasting along this manifold until encountering a torus surrounding the QSO. Thus, the spacecraft will reach a quasi-periodic QSO inside the torus that is close to the periodic resonant QSO.