Why the Laplace Resonant Angle is So Special

Abstract

We analyze adjacent local pairs of mean-motion resonances (MMRs) between three orbiting bodies designed to produce a Laplace resonant phase angle φ L or one of its multiples N φ L, where integer N ≥ 2. This assumption yields a concrete pattern of Laplace resonances, very few of which (with angles φ L and 2φ L) have been observed in actual (extra)solar subsystems. All other MMRs face issues of proximity or remoteness of the orbits (they are too close or too far apart). We highlight one as yet unobservable MMR in each N-sequence for which these issues appear to be less acute.