Bounded relative orbits about asteroids for formation flying and applications

• We consider two spacecraft flying in a formation about the asteroid 4179 Toutatis.
• We derive first order conditions that minimize the drift between the satellites.
• We find a full family of stable periodic orbits about the target asteroid.
• We compute quasi-periodic invariant tori and use them to initialize the formation.
• Numerical simulations prove that the satellites stay bounded for long time spans.

The relative motion about 4179 Toutatis is studied in order to investigate the feasibility of formation flying as an alternative concept for future asteroid exploration missions. In particular, the existence of quasi-frozen orbits about slowly rotating bodies allows us to compute families of periodic orbits in the body-fixed frame of the asteroid. Since these periodic orbits are of the center×center type, quasi-periodic invariant tori are calculated via fully numerical procedures and used to initialize spacecraft formations about the central body. Numerical simulations show that the resulting in-plane and out-of-plane relative trajectories remain bounded over long time spans; i.e., more than 30 days.