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

The Hill radius is an empirical boundary observed throughout celestial mechanics, marking
the distance at which one body’s influence over nearby trajectories yields to that of a more
massive neighbor. Importantly, the Hill radius is defined by observed stability behavior
rather than by allegiance to any particular theory of gravity. This paper reformulates the Hill
radius within the SP3 framework, interpreting it as a boundary of relative space-phase
dominance between a planet and the Sun. Building on this reinterpretation, we examine
planetary perihelion precession—most prominently Mercury’s—as a subtle manifestation
of temporary imbalance in space-phase dominance during closest approach. The extreme
smallness of observed precession is shown to be evidence not of weak planetary
coherence, but of its strength: planets remain stably confined to deeply conditioned orbital
grooves generated by billions of revolutions. The Sun’s space-phase influence, while
omnipresent, is insufficient to dislodge these grooves, producing only minute cumulative
effects under extreme proximity.