Three-body orbital stability criteria for circular orbits

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Abstract
Previous investigations of the stability of hierarchical three-body systems by Harrington and by Black and his collaborators give conflicting results. A new numerical examination of such systems and the corresponding stability criteria indicate that the Black functions give the general qualitative behavior for very large and very small values of the third component; while for the range close to the equal-mass case the Harrington criterion is the more appropriate. Neither criterion was found to be satisfactory but it was found that the new results obtained are, however, in very good quantitative agreement with those obtained from the analytical c2H method. This suggests that this criterion has a wider range of validity than previously suspected. Boundaries of stability are derived for the satellite, inner planet and outer planet mass combinations. The numerical results show a larger range of stable orbits in the outer planet case where the restricted model gives inconclusive results.

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