Periodic orbits of the third kind in the restricted three-body problem with oblateness

Details Periodic orbits of the third kind in the restricted three-body problem with oblateness Periodic orbits of the third kind in the restricted three-body problem with oblateness

Apr 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990ap%26ss.166..211s&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 166, no. 2, April 1990, p. 211-218.

Astronomy and Astrophysics

Astrophysics

2

Oblate Spheroids, Orbital Elements, Three Body Problem, Orbit Perturbation, Periodic Functions, Secular Variations

Scientific paper

By use of the secular perturbing potential due to oblateness, the existence of periodic orbits of the third kind is established through Poincare's method of analytic continuation in the three-dimensional, restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. For two sets of the canonical variables, the singularities are found at the inclinations i = 68.5833, 111.4167 deg, while for the other two sets of the canonical variables, the singularities are at i = 55.3854, 103.575 deg.

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