Distribution of families of periodic orbits of the Hill’s problem and some applications to space mission design

Hill’s variant of the restricted there-body problem is one of the most important models in Celestial Mechanics and astrodynamics, with various applications in spacecraft mission design. In this talk we discuss some statistics of distributions of families of the Hill’s problem periodic orbits by symmetry types and by global multiplicities. Description of singular generating solutions method is provided as well. Each generating solution is a finite sequence composed according to certain rules from a countable set of arcs of two types, joined at the origin of coordinates with hyperbolic conics.  Generating solution provides information on symmetry type, global multiplicity of the orbit and other characteristics of the corresponding periodic solutions of the generated family. According to obtained statistics it can be possible to state that families of symmetric periodic orbits of the Hill’s problem form such a backbone of regular dynamics of the Hill problem. Some applications of obtained results to constructing periodic orbits with prescribed properties are discussed as well.