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.

JAXA的MMX任务（涉及CNES）考虑了准卫星轨道（QSO），以便在着陆和返回样品之前对火星上的火卫一进行科学观测。这些周期性轨道最初在Mars-Phobos圆形受限三体问题中定义，一旦考虑了Phobos轨道的离心率，通常会失去周期性。在这种情况下，将QSO替换为准周期的花托。关于MMX项目的最新工作，除其他外，还包括围绕QSO的站台保持策略，这些策略在椭圆山问题中利用不变的花托。在本文中，将首先在Mars-Phobos圆形受限三体问题中计算共振QSO。然后，通过继续次级的偏心，在Mars-Phobos椭圆受限三体问题中，该QSO将转换为周期共振QSO。与希尔问题相比，后一个问题比希尔问题更精确，并且距离次要问题较远，因此更适合处理Mars-Phobos转移。注意，当偏心率不为零时，考虑共振轨道可以保留QSO的周期性。然后，将通过在频率上继续获得在椭圆限制三体问题中围绕共振QSO的不变托勒族。在下一步中，将计算从花托发出的稳定不变流形。最后，将提出火星周围的停放轨道与QSO周围的花托之间的两次脉冲转移，目的是使总速度增量最小化。有趣的转移轨迹将被显示，从而可以对火卫一采取弹道方法。与经典的火星到QSO的传输相比，这些轨迹导致总速度增量的减小。在这里，代替直接瞄准共振QSO，航天器将首先到达不变歧管，然后沿该歧管滑行，直到遇到围绕QSO的圆环。因此，航天器将在圆环内部到达接近周期共振QSO的准周期QSO。航天器将首先到达不变歧管，然后沿该歧管滑行，直到遇到围绕QSO的圆环。因此，航天器将在圆环内部到达接近周期共振QSO的准周期QSO。航天器将首先到达不变歧管，然后沿该歧管滑行，直到遇到围绕QSO的圆环。因此，航天器将在圆环内部到达接近周期共振QSO的准周期QSO。