Preprint Derives Asymmetric Ranging Equation for Arbitrary Satellite Trajectories in Curved Spacetime

Bogdan Dimitrov extends prior elliptic-integral solutions for Keplerian orbits to arbitrary space trajectories by intersecting null cones in curved spacetime. The work introduces space-time and geodesic distances that retain physical meaning beyond planar cases and proves the forward geodesic distance exceeds the return path solely due to the satellites' non-inertial reference frames. No numerical integration or hardware validation is presented; the derivation remains purely analytic.

Current GNSS timing corrections treat uplink and downlink symmetrically at the nanosecond level. The new asymmetry implies that dense low-Earth-orbit meshes planned for 6G/7G could accumulate tens of picoseconds of unmodeled error per hop, directly affecting positioning accuracy for autonomous vehicles and financial timestamping that millions rely on daily.

The paper correctly flags the physical origin of irreversibility yet omits any comparison against existing post-Newtonian GPS models or Monte-Carlo error budgets, leaving open whether the effect exceeds current clock and orbit uncertainties. A follow-on simulation campaign using real ephemerides would be required to quantify operational impact.

Integration into constellation simulators is the immediate next step; without it the framework stays theoretical despite its potential relevance to next-generation satellite networks.