Orbital Stability and Gravitational Dominance Across Planetary Systems: A Hill-Radius Scaling Approach

Determining the extent of orbital stability in multi-body gravitational systems remains a fundamental challenge in celestial dynamics. In this study, we analyze how gravitational dominance transitions with distance by directly comparing the local influence of a celestial body to that of the Sun. A numerical simulation framework is developed in which distances are normalized by the Hill radius, enabling a unified comparison across systems that differ by orders of magnitude in mass and scale. The analysis includes Earth, Mars, Jupiter, and the near-Earth asteroid 101955 Bennu, providing a broad range of gravitational environments. The results show that Hill-radius normalization reveals a consistent scaled pattern in stability behavior across all cases, with similar profile shapes and well-defined transition regions separating body-dominated and solar-dominated regimes. For Earth and Mars, these transitions occur at approximately 0.17 and 0.12 Hill radii, respectively, while Jupiter maintains stability out to nearly 0.45 Hill radii; in contrast, no stability boundary is detected for Bennu within the sampled range. These findings indicate that Hill-radius scaling provides a robust and physically meaningful framework for comparing gravitational environments, while deviations in low-mass regimes suggest that additional dynamical factors influence orbital stability beyond simple scaling.