A Unified Shear-Driven Model for Planetary Obliquities in the Outer Solar System

The origin of planetary obliquities across the outer Solar System remains a long-standing dynamical puzzle. The canonical giant impact hypothesis can reproduce individual spin states in isolation, but cannot fully account for the continuous radial distribution of obliquities from Jupiter to Pluto within a single self-consistent framework. This work presents a deterministic steady-state model based on continuous medium gradient shear coupled with solar tidal binding. In this model, the final obliquity of a planet is determined by the interplay between local shear stress from the protoplanetary disk, solar tidal binding torque, and planetary torsional inertia. We identify a prominent shear stress peak at 12.5 AU beyond Saturn’s orbit, shaped by the superposition of Jupiter’s far-field density perturbation and the Sun’s radial density gradient near the primordial condensation front. A dimensionless obliquity locking parameter Λ is introduced to quantify the relative strength of shear versus binding, unifying the observed obliquity sequence across five bodies into three distinct dynamical regimes. We further show that the steady obliquity corresponds to the global minimum of a composite potential energy surface, toward which the system spontaneously evolves via macroscopic dissipative processes. The model consistently explains the small obliquities of Jupiter and Saturn, the extreme 97.8◦ tilt of Uranus, the moderate 28.3◦ obliquity of Neptune, and the very high 122.5◦ obliquity of Pluto. These results suggest that planetary obliquities are natural outcomes of continuousmedium self-healing dynamics in the protoplanetary disk, offering a deterministic alternative to the stochastic giant impact hypothesis. This framework also provides falsifiable predictions for obliquity distributions in exoplanetary systems.