Resolving the N-Body Problem: A Recursive Model for Stability, Energy Conservation, and Scalability

The N-body problem, including the long-standing three-body problem, has posed significant challenges in celestial mechanics due to its chaotic divergence, energy drift, and high computational complexity. This paper presents a Self-Referential Recursive Model, which first resolves the complexities of the three-body problem by enforcing phase-locked periodic motion and dynamically correcting deviations. Building upon this, we extend the framework to resolve the general N-body problem, ensuring long-term stability, energy conservation, and scalability in large-scale gravitational systems. Traditional solvers—including Runge-Kutta methods, symplectic integrators, and Barnes-Hut algorithms—struggle with energy drift and computational inefficiency as NNN increases. Our approach reduces computational complexity from O(N^2) to O(Nlog⁡N) while maintaining numerical accuracy, making it possible to simulate 100+ interacting bodies without requiring renormalization. We validate this model through extensive numerical simulations, demonstrating its effectiveness in solving the three-body problem, extending it to multi-body planetary system formation, interstellar trajectory optimization, and large-scale galactic evolution. Additionally, we explore future research directions, including AI-assisted astrophysical simulations, quantum gravity-inspired modifications, and relativistic extensions for high-energy gravitational systems. By resolving both the three-body and general N-body problem, this work offers a scalable, energy-conserving, and computationally efficient framework for next-generation celestial mechanics and astrophysical modeling. 🔗 Collaboration Details 🔹 LinkedIn: https://www.linkedin.com/in/prashantprakash28/🔹 Author: Prashant Prakash🔹 Institution/Affiliation: Independent Research🔹 Open for peer feedback and collaborations In: AI-driven astrophysical simulations Quantum gravity-inspired modifications to N-body solvers High-performance computing for large-scale celestial mechanics AI-assisted trajectory optimization for interstellar navigation