Parameter Distribution of Small Periodic Librations about the Equilateral Points of the Elliptic Restricted Problem
Abstract
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}, κ^{5}, ande ^{4}.
 Publication:

Celestial Mechanics
 Pub Date:
 September 1973
 DOI:
 10.1007/BF01231411
 Bibcode:
 1973CeMec...8..177R