A simple criterion for determining the dynamical stability of three-body systems

Coplanar, prograde three-body systems (TBS) are discussed, emphasizing the specification of general criteria for determining whether such systems are dynamically stable. It is shown that the Graziani-Black (1981) criteria provide a quantitatively accurate characterization of the onset of dynamic instability for values of the dimensionless mass ranging from one millionth to one million. Harrington's (1977) general criterion and the Graziani-Black criterion are compared with results from analytic work that spans a 12-orders-of-magnitude variation in the mass ratios of the TBS components. Comparison of the Graziani-Black criteria with data for eight well-studied triple-star systems indicates that the observed lower limit for the ratio of periastron distance of the tertiary orbit to the semimajor axis of the binary orbit is due to dynamical instability rather than to cosmogonic processes.