Hill stability cannot be easily established in the classical 3-body problem with point masses, as sufficient energy for escape of one of the bodies can always be extracted from the gravitational potential energy. For the finite density, so-called Full 3-body problem the lower limits on the gravitational potential energy ensure that Hill stability can exist. For the equal mass Full 3-body problem this can be easily established, with the result that for any equal mass, finite density 3-body problem in or near a contact equilibrium, none of the components of the system can escape in the ensuing motion.
