Hill-Type Stability and Hierarchical Stability of the General Three-Body Problem

Abstract

Systematic numerical experiments show that the Hill-type stability criterion does not indicate, in the case of the initially elliptic coplanar three-body problem, a practical hierarchical stability. In some situations, this analytical criterion seems to be too restrictive, so that empirical stability regions exist outside the Hill-type stability regions; in other situations, however, it can be shown that specific instabilities occur frequently inside the Hill-type stability regions.