Three-body orbital stability criteria for circular retrograde orbits

Previous investigations of the stability of hierarchical three-body retrograde systems moving on circular orbits by various authors have led to conflicting results and conclusions. The problem is re-examined, and the new numerical results indicate that these retrograde systems are more stable than their prograde counterparts with the same mass combinations. Although this result is similar to that of Harrington, there is no quantitative agreement between the actual values, except for the equal-mass case where there is complete agreement. The analytical |c²H| method which provides a sufficient condition for stability is found to be a poor indicator of orbital stability in this case, unlike the situation found for comparable prograde systems by Donnison & Mikulskis. It is found that a functional form similar to that used by Black to fit prograde systems gives reasonable first approximations to the new results. The boundaries of stability are also examined for the inner-planet, outer-planet, and satellite mass combinations.