<h2>AAS 99-159</h2>
<h2>Stability of Hovering Orbits around Small Bodies                                                                                                 </h2>
<h4>D.J. Scheeres                                                                                                                                                                       </h4>
                                                                                                                                                                          
<h2> Abstract </h2>
Hovering trajectories at asteroids and comets have been proposed for a number of space science missions. We analyze two different options for hovering over a small body: inertially fixed hovering and body fixed hovering. The guidance laws for such hovering orbits are discussed and their dynamic stability investigated. The nature of their stability properties will impact he design and application of measurement and control strategies. For each case we analyze the stability of the hovering orbits over a point mass, and idealized 2nd degree and order gravity field in uniform rotation, and over the measured asteroid shape of Castalia with a uniform rotation of 4.07 hours. Fundamental differences are seen between the stability properties of the inertially-fixed and body-fixed hovering orbits, and between hovering above a point mass and above a uniformly rotating non-spherical central body.