Long-Term Stability of Planets in Binary Systems

A simple question of celestial mechanics is investigated: in what regions ofphase space near a binary system can planets persist for long times? Theplanets are taken to be test particles moving in the field of an eccentricbinary system. A range of values of the binary eccentricity and mass ratio isstudied, and both the case of planets orbiting close to one of the stars, andthat of planets outside the binary orbiting the system's center of mass, areexamined. From the results, empirical expressions are developed for both 1) thelargest orbit around each of the stars, and 2) the smallest orbit around thebinary system as a whole, in which test particles survive the length of theintegration (10^4 binary periods). The empirical expressions developed, whichare roughly linear in both the mass ratio mu and the binary eccentricity e, aredetermined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in bothregions, and can be used to guide searches for planets in binary systems. Afterconsidering the case of a single low-mass planet in binary systems, thestability of a mutually-interacting system of planets orbiting one star of abinary system is examined, though in less detail.Comment: 19 pages, 5 figures, 7 tables, accepted by the Astronomical Journa