Analytic continuation of circular and elliptic Kepler motion to the general 3-body problem

The existence of families of periodic solutions of the general planetary 3-body problem in which one of the orbits is ellipic is shown. Each family derives from uncoupled circular and elliptic Kepler motion in a given resonance, with the eccentricity of the elliptic orbit as the parameter. The standard method of Poincare's analytic continuation cannot be directly applied due to the vanishing of a determinant, so a strong form of the implicit function theorem is used.