Statistics – Computation
Scientific paper
Apr 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008sosyr..42..154b&link_type=abstract
Solar System Research, Volume 42, Issue 2, pp.154-176
Statistics
Computation
3
95.10.Ce, Celestial Mechanics
Scientific paper
We consider the planar circular restricted three-body problem. It is described by an autonomous Hamiltonian system with two degrees of freedom and one parameter μ ∈ [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 examples, we consider the family c, which begins at the fixed collinear point L 1, and the family i, which begins with direct circular orbits of an infinitely small radius around the primary P 1 of a bigger mass. We give a complete description of the generating families c and i for μ = 0.
Bruno Aleksandr D.
Varin Victor P.
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