Averaging Time Required for Millimetre Geoid Resolution With Optical Lattice Clocks

Millimetre resolution is often quoted as the promise of clock geodesy, but a resolution claim without an averaging time is incomplete. Frequency noise falls only as the square root of averaging time for white frequency noise, so the final decade is disproportionately expensive. This paper converts height targets into fractional frequency targets and then into averaging times for three realistic instability coefficients, showing where millimetre work is a day-scale measurement and where it becomes a month-scale campaign. The computed results, taken from the deposited script, are as follows in summary: The computed Sr_lattice_lab_1mm_s is 7.56e+06. The computed Sr_lattice_lab_1mm_days is 87.5. The computed Sr_lattice_lab_1cm_s is 7.56e+04. The computed Sr_lattice_lab_1cm_days is 0.875. The computed transportable_1mm_s is 8.4e+07. The computed transportable_1mm_days is 972. The computed transportable_1cm_s is 8.4e+05. The computed transportable_1cm_days is 9.72. The computed best_demonstrated_1mm_s is 1.89e+06. The computed best_demonstrated_1mm_days is 21.9. The computed best_demonstrated_1cm_s is 1.89e+04. The computed best_demonstrated_1cm_days is 0.219. The computed frac_1mm is 1.09e-19. The computed frac_1cm is 1.09e-18. The study is a computation from stated assumptions, not a measurement, and its figures should be read at the precision those assumptions support.