The Gravitational Shadow: Random Matrix Theory Reveals Universal Level Repulsion in Planetary Orbital Architecture

A random matrix theory (RMT) program has shown that single-source, charge-and-release systems across the Earth sciences exhibit Wigner-Dyson level repulsion in the timing of their events, while superpositions of many independent sources collapse to Poisson. Here we carry the program into celestial mechanics, where the charge-and-release process is gravitational accretion: a forming planet clears its feeding zone (its Hill sphere and resonance-swept neighborhood), casting a gravitational shadow that forbids other bodies from occupying nearby orbits. We test whether this clearing imprints level repulsion on the logarithmic spacing of orbital semi-major axes. Two methodological traps are handled explicitly. The Titius-Bode trap (planetary log-a is near-geometric, so a naive spacing ratio is inflated by periodicity, not repulsion) is removed by local unfolding of each system. The resonance trap (mean-motion-resonant chains lock into exactly geometric spacing) is flagged by a post-unfolding coefficient of variation below 0.15. After unfolding, the Solar System eight planets show genuine repulsion (r-bar = 0.632), while the Galilean moons are correctly flagged as resonance-locked (CV = 0.09, Laplace 1:2:4 resonance) and excluded. Pooling 320 Kepler and transit multi-planet systems (1130 planets), each unfolded in its own frame, yields r-bar = 0.674 (95 percent CI 0.68 to 0.72), GUE-class repulsion that is stronger than the Solar System and stronger than any Earth system in the program. This contradicts the naive prediction of Poisson collapse: pooling does not randomize, because each planetary system is internally repulsive and we preserve that structure by unfolding each system in its own frame. The collapse is recovered only when the per-system frames are destroyed. Globally mixing all 1130 planets into a single catalog drives r-bar down to 0.437, and an independent-clock null gives 0.396. Level repulsion in orbital architecture is therefore a local-spacetime property: within a single gravitational well it is universal and GUE-strong, but mixing many independent wells with different stellar masses, formation histories, and dynamical clocks erases it. The above-GUE rigidity characterizes the dynamically cold, tightly packed systems of the Kepler dichotomy, plausibly the maximum-packing limit of planetary formation. Why orbital clearing lands in a more rigid universality class (closer to GUE) than the terrestrial charge-and-release systems (near GOE) is flagged as an open theoretical problem. The gravitational shadow is the spatial analog of the temporal charge-and-release mechanism, and r-bar measures the rigidity of orbital clearing. This is the eighth system in a unified RMT program and the first to extend it from temporal to spatial, and from terrestrial to cosmic, charge-and-release.