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

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

May 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..95...27b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 95, Issue 1-4, pp. 27-54

Astronomy and Astrophysics

Astronomy

8

Restricted Three-Body Problem, Periodic Solutions, Two-Parameter Families

Scientific paper

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 μ in [0,1/2] 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 P 1 of bigger mass. For this family, we cite detailed data for μ = 0 and μ ≈ 10^{-3} and give a brief description of its evolution as μ increases up to μ = 1/2.

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