Singularity Avoidance in Many-Body Gravitational Systems via a Vortex-Inspired Repulsion Term

The gravitational N-body problem, particularly for N >= 3, exhibits chaotic behavior and suffers from singularities when bodies approach collision (r -> 0). Traditional numerical methods employ ad-hoc softening parameters to regularize the potential, but these lack physical motivation. In this paper, we propose a physically motivated vortex repulsion term inspired by fluid dynamical considerations. By modeling gravitating bodies as composite vortex structures with intrinsic angular momentum, we derive a short-range repulsive force that scales as r^-3. Numerical simulations demonstrate that the proposed model (i) avoids singularities through elastic scattering, (ii) maintains long-term orbital stability with negligible energy error, and (iii) offers a robust alternative to artificial softening.