Hill stability of satellite orbits

Szebehely's criterion for Hill stability of satellites is derived from Hill's problem and a more exact result is obtained. Direct, Hill stable, circular satellites can exist almost twice as far from the planet as retrograde satellites. For direct satellites the new result agrees with Kuiper's empirical estimate that such satellites are stable up to a distance of half the radius of action of the planet. Comparison with the results of numerical experiments shows that Hill 'stability is valid for direct satellites but meaningless for retrograde satellites. Further accuracy for the maximum distance of Hill stable orbits is obtained from the restricted problem formulation. This provides estimates for planetary distances in double star systems.