  A simple question of celestial mechanics is investigated: in what regions of
phase space near a binary system can planets persist for long times? The
planets are taken to be test particles moving in the field of an eccentric
binary system. A range of values of the binary eccentricity and mass ratio is
studied, and both the case of planets orbiting close to one of the stars, and
that of planets outside the binary orbiting the system's center of mass, are
examined. From the results, empirical expressions are developed for both 1) the
largest orbit around each of the stars, and 2) the smallest orbit around the
binary system as a whole, in which test particles survive the length of the
integration (10^4 binary periods). The empirical expressions developed, which
are roughly linear in both the mass ratio mu and the binary eccentricity e, are
determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both
regions, and can be used to guide searches for planets in binary systems. After
considering the case of a single low-mass planet in binary systems, the
stability of a mutually-interacting system of planets orbiting one star of a
binary system is examined, though in less detail.
