A Universal Computational Framework for Relativistic Time Offsets of Rotating Celestial Bodies

Quantifying relativistic time offsets across diverse gravitational environments, from planetary surfaces to rapidly rotating black holes, remains a fundamental challenge in relativistic astrophysics. We present a universal analytical and computational framework that unifies the treatment of proper time differentials induced by gravity, rotation, and spacetime curvature for all rotating celestial bodies. The formulation incorporates three key effects: gravitational potential including all zonal harmonics to arbitrary order, special relativistic kinetic effects from rotational motion, and a frame-dragging correction derived from the weak-field Kerr metric. We introduce a Universal Coordinate System (UCS) that standardizes positional references across rotating spheroids and curved spacetime geometries. Our framework is validated through over 100,000 high-precision simulations, benchmarked against NASA's SPICE Toolkit ephemerides and IERS Earth orientation data. The formula reproduces known limits such as Schwarzschild and Kerr while enabling new applications in strongly gravitating and rapidly rotating regimes. This work provides a unified, closed-form, computationally efficient tool for relativistic time offset evaluation, with implications for space-based clock synchronization, precision astrometry, and fundamental tests of general relativity.