Sagnac and Rotation Terms in Continental-Scale Clock Comparisons: Magnitudes and Correction Accuracy

Comparing clocks across a continent on a rotating Earth requires rotation terms that are large compared with the precision of the clocks themselves. The Sagnac term for an east-west link is not a subtle correction; mishandled, it overwhelms the potential signal entirely. This paper estimates the term for four baselines at mid-latitude, states the geometric approximation used, and converts the term into an equivalent fractional frequency over a day, so the accuracy with which Earth rotation and link geometry must be known becomes explicit. The computed results, taken from the deposited script, are as follows in summary: The computed rows entry 1 baseline_km is 500. The computed rows entry 1 sagnac_ns is 0.136. The computed rows entry 1 frac_equiv_1day is 1.57e-15. The computed rows entry 2 baseline_km is 1000. The computed rows entry 2 sagnac_ns is 0.541. The computed rows entry 2 frac_equiv_1day is 6.26e-15. The computed rows entry 3 baseline_km is 2000. The computed rows entry 3 sagnac_ns is 2.14. The computed rows entry 3 frac_equiv_1day is 2.47e-14. The computed rows entry 4 baseline_km is 3000. The computed rows entry 4 sagnac_ns is 4.71. The computed rows entry 4 frac_equiv_1day is 5.45e-14. The study is a computation from stated assumptions, not a measurement, and its figures should be read at the precision those assumptions support.