Parameter Distribution of Small Periodic Librations about the Equilateral Points of the Elliptic Restricted Problem

Details Parameter Distribution of Small Periodic Librations about the Equilateral Points of the Elliptic Restricted Problem Parameter Distribution of Small Periodic Librations about the Equilateral Points of the Elliptic Restricted Problem

Sep 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...8..177r&link_type=abstract

Celestial Mechanics, Volume 8, Issue 2, pp.177-179

Physics

Scientific paper

As previously shown (Rabe, 1970), two classes of small periodic librations exist, in the plane, elliptic restricted problem, for an infinite sequence of easily specified oscillation frequenciesZ j . The present paper considers the dependence ofZ on the eccentricitye of the primary motion, in addition to its dependence on the mass parameter κ, and determines the resulting relations between κ ande, for any given periodic frequencyZ j . These relationships are obtained from the conditionD (Z j ,κ, e)=0, where the basic determinantD has been expanded up to terms of orderZ 20, κ5, ande 4.

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