On the Stability of the Satellite Systems

Abstract

It is proved by the criterion of Hill for the stability of the motion of the Moon based on the Jacobi integral that the motion of the satellites in our solar system is stable under the restriction that the deviation of the actual orbit from Hill's intermediary orbit does not grow large enough to escape from the oval of zero-velocity. The motion of Phoebe and Triton is stable even though it is in retrograde motion. We can not ascertain on this criterion the stability of the outermost four satellites of Jupiter VIII, IX, XI, and XII which are in retrograde motion. Even from this circumstance we are inclined to think that these four satellites are quite different in their genesis from the outer satellites of Jupiter VI, VII and X.