Along-Track Boundedness Condition for Spacecraft Relative Motion Around a Slowly Rotating Asteroid

In this paper, the closed-form along-track boundedness condition for spacecraft relative motion around a slowly rotating asteroid is presented. As opposed to the previously proposed criteria where three necessary constraints must be satisfied, the current approach only requires to enforce one constraint to suppress the along-track drift, thus allowing two additional degrees of freedom in spacecraft formation design. In particular, to adapt the derived results applicable for formation with a relatively large size, the boundedness condition via first-order analysis is then extended to obtain a second-order result. In the latter case, the value of mean semimajor axis difference is found to be the root of a quadratic (algebraic) equation. Moreover, an optimal single-impulse maneuver is analyzed, by means of which the bounded relative motion can be guaranteed in the presence of initialization errors. Illustrative examples are provided to validate the analytical results.