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, κ⁵, ande ⁴.