Periodic Solutions of the Restricted Three-Body Problem for Small μ
We consider the plane circular restricted three-body problem for small mass ratios μ of principal bodies. Using Power Geometry, we found all limit problems for μ → 0: the two-body problem, Hill's problem, intermediate Henon's problem, and the main limit problem. In each of these problems we isolated solutions that are the limits of periodic solutions of the restricted problem as μ → 0, as well as limits of the families of periodic solutions (which are called the generating families). Using generating families, for small μ > 0, we studied the family h which begins as retrograde circular orbits of infinitely small radius around the body of bigger mass. We demonstrated that, as μ increases, the structure of the family h does not undergo significant changes.
Mathematical problems and theory of numerical methods