Alps' Resonance Constant

This work introduces the Alps Resonance Constant, a novel universal resonance frequency (≈ 0.04995 cycles/day) observed in classical multi-body systems governed by elastic gravitational interactions. By integrating Newtonian gravity with a short-range attractive elastic force, the system transitions from chaotic to synchronized behavior. The resonance frequency remains invariant across systems with 5 to 20 bodies, regardless of initial conditions. This study provides theoretical background, numerical simulation results, and frequency-domain analyses to support the discovery of a new constant of motion in classical mechanics. The implications extend to dark matter modeling, satellite formation dynamics, and resonance-based stability in complex systems.