Minimal Velocity Surface in a Restricted Circular Three-Body Problem

Abstract

In a restricted circular three-body problem, the concept of the minimum velocity surface $\mathscr{S}$ is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of the Hill surface requires the occurrence of the Jacobi integral. The minimum velocity surface, apart from the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of motion of the main bodies. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained after a single averaging of the original system over the longitude of the main bodies. The properties of $\mathscr{S}$ are investigated. We highlight the most significant issues. The set of possible motions of the zero-mass body bounded by surface $\mathscr{S}$ is compact. As an example, surfaces $\mathscr{S}$ for four small moons of Pluto are considered within the averaged Pluto–Charon–small satellite problem. In all four cases, $\mathscr{S}$ is a topological torus with a small cross section, having a circumference in the plane of motion of the main bodies as the center line.