On relative periodic solutions of the planar general three-body problem

Details On relative periodic solutions of the planar general three-body problem On relative periodic solutions of the planar general three-body problem

Dec 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..12..439b&link_type=abstract

Celestial Mechanics, vol. 12, Dec. 1975, p. 439-462.

Physics

13

Orbital Mechanics, Periodic Functions, Solar Orbits, Three Body Problem, Circular Orbits, Equations Of Motion, Orbital Elements, Solar System, Tables (Data)

Scientific paper

We describe two relatively simple reductions to order 6 for the planar general three-body problem. We also show that this reduction leads to the distinction between two types of periodic solutions: absolute or relative periodic solutions. An algorithm for obtaining relative periodic solutions using heliocentric coordinates is then described. It is concluded from the periodicity conditions that relative periodic solutions must form families with a single parameter. Finally, two such families have been obtained numerically and are described in some detail.

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