A Unified Phenomenological Framework for Cross-Scale Gravitational Phenomena: Exact Analytical Prediction of the Quaoar Ring Anomaly

The classical Roche limit fails to explain the ring of trans-Neptunian object Quaoar, observed at 7.38 times its radius in 2023, while the density-based formula predicts only 2.5–3.5 R. This paper proposes a generalized Roche limit based on a field-gradient criterion. The core field is defined as KVc/r2KVc/r2, where VcVc is the characteristic velocity of the source. For Quaoar, its rapid rotation gives a 27× increase in VcVc, yielding a theoretical ring limit of 7.32R, matching the observation with <1% deviation. The same framework also covers atmospheric drag (via permeability coefficient η), multi-body trajectories (vector superposition), and black hole accretion scaling. Newtonian gravity GM/r2GM/r2 emerges as a special case under restricted conditions. This framework offers a unified, parameter-economic alternative for cross-scale gravitational phenomena.