Physics
Scientific paper
Apr 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977primm..41q.234z&link_type=abstract
Prikladnaia Matematika i Mekhanika, vol. 41, Mar.-Apr. 1977, p. 234-244. In Russian.
Physics
Celestial Mechanics, Circular Orbits, Hill Method, Orbit Perturbation, Secular Variations, Three Body Problem, Earth Orbits, Hamiltonian Functions, Long Term Effects, Motion Stability, Orbital Mechanics
Scientific paper
The three-body problem for the case when the distance between two of the points is much smaller than the distance from their barycenter to the third point is considered. In first-order perturbation theory the secular evolution is determined from a system of equations with Hamiltonian averaged over the mean longitudes of the points. The averaged problem is integrated, and it is studied for all admissible values of the problem parameters. In particular, situations are found where the motion along planar circular orbits is unstable. The stability of planar circular inverse motions is also studied for arbitrary ratio of the semimajor axes. Relationships among the parameters under which such orbits are unstable are determined.
Lidov M. L.
Ziglin S. L.
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