On the stability of close binaries in hierarchical three-body systems

The Hill-type stability (cf. closure of the zero-velocity curves in the circular restricted three-body problem) of general hierarchical three-body systems is examined analytically in the case where the total mass of the binary is small in comparison to the mass of the external body (e.g. systems of the type Planet-Satellite-Sun, Planet-Planet-Star, etc.). This is compared with results derived by Szebehely, Markellos and Roy in the Planet-Satellite-Sun case of the circular restricted three-body problem. It is demonstrated how the Hill-type stability is affected by the sense of revolution of the binary, i.e. corotational or contrarotational, and the mass ratio within the binary. The effect of the difference in longitudes of the bodies in their orbits is also examined.