Gravitational Dominance in Planetary Systems: An Energy-Based Hill-Radius Scaling Approach

This study examines gravitational dominance in planetary systems using an energy-based formulation. The relative influence of a celestial body and the Sun is quantified through a ratio of gravitational potential energies, evaluated as a function of distance normalized by the Hill radius to enable comparison across systems with widely different masses. The analysis is applied to Jupiter, Earth, Mars, and the asteroid 101955 Bennu. An energy-defined dominance region is found only in sufficiently massive systems: Jupiter exhibits a clear transition within a small fraction of its Hill radius, whereas Earth and Mars do not reach this threshold, and Bennu remains entirely solar-dominated. These results show that Hill-radius normalization does not yield a universal description of gravitational dominance and that energy-based measures provide a more restrictive and physically grounded interpretation.