Long-Term Orbital Stabilization in Three-Body Systems via a Scale-Tension Restoring Force (Part II)

In Part I of this series, we introduced a vortex-inspired short-range repulsionterm that regularizes gravitational N -body dynamics by preventing close-encountersingularities. However, removing the r → 0 divergence does not by itself ensure long-term stability: chaotic three-body systems remain prone to energetic exchanges thateject one component to infinity, leaving a bound binary.In this paper (Part II), we introduce a complementary mechanism—a scale-tension restoring force that acts as an effective “tether” coupling each body tothe system barycenter through an extended geometric structure. The associatedconfining potential suppresses unbounded escape while preserving the system’s totalenergy.Numerical simulations of chaotic three-body configurations demonstrate thatthe combined model (vortex repulsion + scale tension) achieves: (i) zero ejectionevents over long integration times, (ii) bounded orbital radii with finite maximumexcursion, (iii) the emergence of quasi-periodic motion from initially chaotic con-ditions, and (iv) excellent conservation of energy and angular momentum relativeto pure Newtonian dynamics. These results suggest that hierarchical astrophysi-cal systems (triple stars, planetary systems, galactic cores) may be stabilized bygeometric structures beyond point-mass gravity.