Mathematics
Scientific paper
Aug 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981sjam...41..181p&link_type=abstract
SIAM Journal on Applied Mathematics, vol. 41, Aug. 1981, p. 181-202.
Mathematics
6
Branching (Mathematics), Orbit Perturbation, Orbital Mechanics, Three Body Problem, Approximation, Circular Orbits, Elliptical Orbits, Existence Theorems, Mass Ratios, Perturbation Theory
Scientific paper
The considered investigation has the objective to establish the existence and asymptotic approximation of two one-parameter families of periodic orbits of the circular planar restricted three-body problem with the small mass ratio greater than zero, periodic in rotating coordinates, and generated by a 1st species-2nd species bifurcation orbit for the small mass ratio equal zero. The periodic orbits considered approach either elliptical orbits with rational mean motion which are tangent to the unit circle (i.e. the moon's orbit) or a retrograde circular motion of unit radius as the mass ratio approaches zero. The investigation uses a singular perturbation method, similar to that employed by Perko (1974).
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