Hill Radius, Space-Phase Dominance, and Planetary Precession in the SP3 Framework

The Hill radius is an empirical boundary observed throughout celestial mechanics, markingthe distance at which one body’s influence over nearby trajectories yields to that of a moremassive neighbor. Importantly, the Hill radius is defined by observed stability behaviorrather than by allegiance to any particular theory of gravity. This paper reformulates the Hillradius within the SP3 framework, interpreting it as a boundary of relative space-phasedominance between a planet and the Sun. Building on this reinterpretation, we examineplanetary perihelion precession—most prominently Mercury’s—as a subtle manifestationof temporary imbalance in space-phase dominance during closest approach. The extremesmallness of observed precession is shown to be evidence not of weak planetarycoherence, but of its strength: planets remain stably confined to deeply conditioned orbitalgrooves generated by billions of revolutions. The Sun’s space-phase influence, whileomnipresent, is insufficient to dislodge these grooves, producing only minute cumulativeeffects under extreme proximity.