The control of a spacecraft hovering over a rotating small body, such as an asteroid or comet, is analyzed. The effect of closed-loop control strategies on the overall stability of hovering spacecraft trajectories is considered. We characterize the ability of one-dimensional altimetry measurements to stabilize a hovering spacecraft and nd some ideal control methodologies that yield stable hovering trajectories. These ideas are developed for the ideal case of a uniformly rotating spherical small

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... body and then are applied to a rotating ellipsoid and a rotating model of the asteroid Castalia. Application of this control approach to hovering over a nonuniformly rotating body is also analyzed. Finally, the stability of translational motions over an asteroid with active hovering control is studied and shown to be similar, in some cases, to hovering over a uniformly rotating body. The necessary modi cations to the measurement and control laws for these more general cases are characterized as well.