Physics
Scientific paper
Sep 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974phdt........46k&link_type=abstract
Ph.D. Thesis New York Univ., New York.
Physics
4
Periodic Variations, Planets, Rotating Bodies, Satellite Orbits, Circular Orbits, Gravitational Fields, Poincare Problem
Scientific paper
Several types of satellite orbits around a rotating, nearly spherical, non-axially-symmetric planet are studied. The orbits studied have osculating ellipses of periods nearly commensurable with the planet's rotation period, and they are periodic or quasiperiodic in coordinates rotating with the planet. The following types of periodic orbit are found: (1) nearly circular orbits inclined to the equator, not at critical inclination, (2) noncircular orbits at critical inclination, and (3) noncircular orbits near the equatorial plane. Existence proofs proceed by Poincare's method of surface of section, with the implicit function theorem used in cases (1) and (3) and the Birkhoff fixed point theorem in case (2) to give the required fixed point. Linear orbital stability of orbits of types (1) and (3) is discussed; it is of particular interest that under certain circumstances resonance does not lead to instability.
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