Spin-Axis Organization and Orbital Spacing in Planetary Systems: A Phenomenological Radial-Wave Framework for Orbital Spacing and Obliquity

Planetary obliquities—the angles between planetary spin axes and their orbital-plane normals—and the spacing of planetary orbits both exhibit structured yet diverse distributions across the Solar System and exoplanetary systems. Standard explanations attribute axial tilts to primordial angular momentum, stochastic giant impacts, tidal evolution, and long-term gravitational perturbations, while orbital spacing is commonly associated with disk evolution, migration, and dynamical stability. While these mechanisms account for many observed features, the combined distribution of obliquities and orbital distances suggests the possibility of additional large-scale structural organization in rotating gravitational systems. In this work, a phenomenological framework referred to as Radial Waves is introduced to provide a geometric interpretation of both orbital spacing and spin-axis orientation. Within this framework, rotational symmetry in approximately spherical gravitational systems gives rise to structured radial modulation patterns. These patterns are not introduced as new physical fields or propagating waves, but as geometric representations of organized dynamical structure. Orbital radii and planetary obliquities are interpreted as responses to position within this radial structure, with low-obliquity states associated with radial troughs and higher tilts associated with crest regions. The model also suggests a tendency toward increasing orbital spacing with distance, consistent with expanding radial wavelength. The proposed formulation does not modify classical gravitational theory, conservation laws, or established models of planetary formation and evolution. Instead, it provides a phenomenological geometric framework for interpreting the joint organization of orbital spacing and planetary obliquity. Possible implications for planetary-system architecture are briefly discussed.