Families of asymmetric periodic solutions of the restricted problem of three bodies for the sun-Jupiter mass ratio and their relationship with the symmetric families.

Details Families of asymmetric periodic solutions of the restricted problem of three bodies for the sun-Jupiter mass ratio and their relationship with the symmetric families. Families of asymmetric periodic solutions of the restricted problem of three bodies for the sun-Jupiter mass ratio and their relationship with the symmetric families.

Jan 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29...51t&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 29, Jan. 1983, p. 51-74.

Mathematics

7

Celestial Mechanics, Jupiter (Planet), Mass Ratios, Periodic Functions, Solar Planetary Interactions, Three Body Problem, Asymmetry, Branching (Mathematics), Eccentricity, Equations Of Motion, Numerical Integration, Orbital Elements, Orbital Mechanics

Scientific paper

Message derived a method to detect bifurcations of a family of asymmetric periodic solutions from a family of symmetric periodic solutions in the restricted problem of three bodies for the limiting case when the second body has zero mass. This is used to examine several small integer commensurabilities. A total of 21 exterior and 21 interior small integer commensurabilities are examined and bifurcations (two in number) are found to exist only for exterior commensurabilities (q+1):1, q = 1,2,...,7. On investigating other commensurabilities of this form for values of q up to 50 two bifurcations are still found to exist for each. For a Sun-Jupiter mass-ratio the complete family of asymmetric periodic solutions associated with q = 1,2,...,5, and the initial segments of the asymmetric family with q = 6,7,...,12, have been numerically determined.

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