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

Abstract: We consider the plane circular restricted three-body problem. It is described by the autonomous Hamiltonian system with two degrees of freedom and one small parameter μ ∈ [0,1/2] which is the mass ratio of the two massive bodies. Periodic solutions to this problem form two-parameter families. We propose methods of computation of symmetric periodic solutions for all values of parameter μ. Each solution has 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 three coordinate systems: one 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 explicitly.Note: Research direction:Mathematical problems and theory of numerical method