On families of periodic solutions of the restricted three-body problem

We consider the plane circular restricted three-body problem. It is described by an autonomous Hamiltonian system with two degrees of freedom and one parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \in [0,1/2]$$\end{document} which is the mass ratio of the two massive bodies. Periodic solutions of this problem form two-parameter families. We propose methods of computation of symmetric periodic solutions for all values of the parameter μ. Each solution has a period and two traces, namely, the plane and the vertical one. Two characteristics of a family, i.e., its intersection with the symmetry plane, are plotted in the four coordinate systems used in the investigations: two global and two local ones related to the two massive bodies. We also describe generating families, i.e., the limits of families as μ → 0, which are known almost explicitly. As an example, we consider the family h, which begins with retrograde circular orbits of infinitely small radius around the primary P1 of bigger mass. For this family, we cite detailed data for μ = 0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \approx 10^{-3}$$\end{document} and give a brief description of its evolution as μ increases up to μ = 1/2.