Direction-Correlated Rate Residuals in Globally Synchronized Orbital Clocks

Modern timekeeping increasingly relies on globally synchronized clock networks, including satellite constellations and long-baseline time-transfer links. In such systems, relativistic corrections are applied relative to a shared coordinate time, implicitly assuming that all kinematic and gravitational contributions to clock rates are fully absorbed by standard modeling and synchronization procedures. In this work we propose a precision null test of that assumption. We parameterize a possible direction-correlated residual channel in orbital clock rates, proportional to the projection of the satellite’s velocity onto a fixed inertial direction. For circular motion at constant speed this channel produces a sinusoidal modulation of the fractional frequency with zero mean over a full orbit and an amplitude that depends sharply on orbital-plane geometry. Standard general relativity together with conventional synchronization corresponds to the null hypothesis that the coefficient of this channel is exactly zero. The presence or absence of such a sinusoidal rate residual therefore provides a well-defined experimental test in globally synchronized clock networks, complementary to established local tests of relativistic time dilation.