Stability in dynamical astronomy.
Hill's concept of stability is generalized and its relation to bifurcation theory is shown. A quantitative measure of stability is introduced that allows the comparison of the stability of different astronomical systems. Theoretical stability limits for triple stellar systems, for planetary systems, and for satellite systems are established. The measure of stability is evaluated for several known triple stellar systems as well as for the planets and for the natural satellites of the solar system. The model of the restricted problem of three bodies and values of the Jacobian constant are used to study planetary and satellite systems. The model of the general problem of three bodies is used to establish criteria for triple stellar systems.IN GENERAL, THE RESULTS SHOW A HIERARCHY OF STABILITY: the existing triple systems are more stable than the planetary orbits of the solar system. The satellites of the solar system are least stable; in fact, some of the satellites are close to the line of instability (the Earth's Moon) and some are actually unstable (the four outermost satellites of Jupiter).