Averaged Disturbing Function for the Saturn–Titan–Hyperion 4:3 Resonance

Abstract The averaged disturbing function for the Saturn–Titan–Hyperion system near the 4:3 mean-motion resonance is presented, following the formalism of C. D. Murray & S. F. Dermott. Secular and first-order resonant terms are explicitly derived, with direct and indirect contributions separated. Using current orbital elements, numerical coefficients confirm the system’s proximity to resonance. Resonant angles are defined and used to express the perturbative terms. A graphical representation illustrates the relative strengths and phase behaviors of each term, providing insights into the dynamical coupling between Titan and Hyperion.