Hill stability of the general problem of three bodies

We discuss Hill stability in the general three-body problem. The Hill curves in the general problem are the same as in the planar problem. We show that the bifurcation points correspond to the five equilibrium solutions, and derive the criterion for stability in the general case. Application of this criterion to 19 natural satellites of the Solar system leads to the result that, apart from Neptune 1, all the other 18 satellites are unstable in the sense of Hill. The dominant factor in producing this result is the finite eccentricity of the planetary orbits around the Sun.