Computer Science – Numerical Analysis
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..18..185s&link_type=abstract
Celestial Mechanics, vol. 18, Aug. 1978, p. 185-194.
Computer Science
Numerical Analysis
5
Angular Velocity, Celestial Mechanics, Lagrangian Equilibrium Points, Oblate Spheroids, Three Body Problem, Numerical Analysis, Orbital Mechanics, Taylor Series
Scientific paper
In the three-dimensional restricted three-body problem, it is known that there exists a near one-to-one commensurability ratio between the planar angular frequencies and the corresponding angular frequency in the z-direction at the three collinear equilibria (L1,2,3), which is significant for small and practically important values of the mass parameter (mu). When the more massive primary is treated as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries, it is established that oblateness induces a one-to-one commensurability at the exterior point L3 (to the right of the more massive primary) and the interior point L2 for mu between zero and 1/2 and that at L1 no such commensurability exists. However, the values of the oblateness coefficient involved at L2 are too high to have any practical significance, while the smallness of those at L3 for small values of mu may be useful for generating periodic orbits of the third kind.
Rao V. S. P.
Sharma Raj Kumar
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