The propeller and the frog

TL;DR

This paper introduces the 'frog' resonance, a new co-orbital resonance explaining non-Keplerian motions of propellers in planetary rings, with predictions matching observed libration periods.

Contribution

The paper proposes and characterizes the 'frog' resonance, a novel co-orbital resonance mechanism for propeller moonlets in planetary rings, distinct from traditional horseshoe and tadpole orbits.

Findings

Predicts a libration period of ~4 years for Blériot propeller.

Explains observed non-Keplerian motions of propellers.

Provides a theoretical framework for ring-moonlet interactions.

Abstract

"Propellers" in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller, and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of the co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the "frog" resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Bl\'eriot in Saturn's A ring, our theory predicts a libration period of ~4 years, similar to the ~3.7 year period over which Bl\'eriot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.