The dynamical Hill stability has been derived for a full three-body system composed of a binary moving on an inclined elliptical orbit relative to a third body where the binary mass is very small compared with the mass of the third body. This physical situation arises in a number of important astronomical contexts including extrasolar planetary systems with a star–planet–moon configuration. The Hill stability criterion against disruption and component exchange was applied to all the known extrasolar planetary systems and the critical separation of a possible moon from the planet determined for moon/planet mass ratios of 0.1, 0.01 and 0.001 assuming that the moon moves on a circular orbit. It is clear that in those cases where the planet moves on a circular orbit about the central star, the critical separation of the moon from the planet does not change significantly as the value of the moon/planet mass ratio is reduced. In contrast, for eccentric systems there can be big changes in the critical separation as the mass ratio decreases. The variation in size depends crucially on the size of the eccentricity of the planetary orbit.
To determine the effect of an eccentrically orbiting moon, the Hill stability criterion was applied generally to the planet–moon binary for a range of moon/planet mass ratios assuming that the planet moved on a circular orbit around the central star. It was found that in all cases the critical distance ratio increased, and hence the regions of Hill stability decreased as the binary eccentricity increased and also as the inclination of the third body to the binary was increased. The stability increased slightly as the moon/planet ratio was decreased. Also as the binary/third body mass ratio decreased the effects of the moon/planet mass ratio became less important and the stability curves tended to merge. These types of changes make exchange or disruption of the component masses more likely.