A Rigorous Conceptual Framework Linking Self-Rotation to Orbital Stability and Spacetime Curvature in Celestial Bodies: The Role of Frame-Dragging, Geodesic Paths, and Low-Pressure Spacetime Environments

This rigorous conceptual paper advances a novel theoretical framework asserting that the self-rotation (spin) of celestial bodies, including planets and stars, plays a critical role in sustaining their orbital paths through the generation of spacetime curvature via frame-dragging effects, as predicted by general relativity. We postulate that the cessation of self-rotation could destabilize these paths, potentially transforming stable orbiting bodies into rogue, free-floating entities. Grounded in the principles of general relativity, this framework integrates the geodesic equations, Kerr metrics, and gravitomagnetic phenomena to model the interplay between spin and orbital dynamics. The analysis is bolstered by precise mathematical derivations, Python-based numerical simulations incorporating verified observational data from missions such as Gravity Probe B and recent rogue planet surveys by JWST and Euclid, advanced sensitivity and uncertainty analyses employing Bayesian inference and quantitative statistics, and explicit falsifiability criteria. High-fidelity TikZ visualizations depict spacetime curvature, geodesic trajectories, and simulation outputs. Additionally, we explore the implications of planetary rotation on habitability, including magnetic field generation, atmospheric circulation, and climate stability. This multidisciplinary integration—spanning general relativity, astrophysics, computational physics, statistical modeling, and astrobiology—provides a deep, multidimensional, and empirically substantiated perspective on orbital stability and planetary habitability, challenging conventional views and offering testable predictions for future observations.