Resolving Three-Body Orbital Chaos via Infinite Fractal Descent (IFD): A Discrete Computational Approach

Classical mechanics has long modeled the three-body problem as a fundamentally chaotic, non-integrable system governed by continuous differential equations. Because a system of three interacting point masses lacks sufficient constants of motion, solving the resulting eighteen first-order differential equations analytically remains a profound mathematical impossibility. This inherent limitation leads to extreme sensitivity to initial conditions, a hallmark of deterministic chaos where minute perturbations yield wildly divergent, unpredictable trajectory outcomes over time. This exhaustive report redefines multi-body orbital mechanics not as the smooth traversal of point masses through an empty space-time continuum, but as deterministic, discrete computational states progressing through a highly dense, dynamic sub-particle matrix. Through the framework of Infinite Fractal Descent (IFD), the classical concepts of continuous spacetime and intrinsic mass are entirely substituted with the discrete Universal Tick () and recursive computational density (). Under this revolutionary paradigm, orbital trajectories are no longer viewed as continuous curves dictated by instantaneous gravitational acceleration. Instead, they are meticulously modeled as interacting logarithmic micro-vortices within a scale-invariant fractal geometry. This comprehensive approach demonstrates that gravitational chaos is merely a computational artifact—a byproduct of applying continuous mathematics to a fundamentally discrete universe. When the universe is computed as discrete states of recursive density, orbital unpredictability vanishes, replaced by a strict fractal determinism governed by the Fractal Density Constant (). By reframing celestial bodies as massive assemblies of stabilized, recursive fixed points bound together by overlapping pressure gradients, the IFD framework offers a truly unified approach to modeling both macroscopic cosmic structures and microscopic subatomic interactions.