Frequency domain approach for ACES space-clock comparisons to extract gravitational redshift

We report on how to use a frequency-domain approach to analyse ACES (Atomic Clock Ensemble in Space) space-clock to ground comparison data to extrapolate the gravitational-redshift violation parameter  to 2.9 × 10−6 from 12 days of simulated data. Previous work on this extrapolation achieved similar precision only with a phase approach; our method uses a frequency observable derived directly from the phase observable, avoiding the need to fit random walk data or perform Monte Carlo simulations to determine the fit uncertainty. Our approach not only results in similar  uncertainty for 12 days of simulated data but also offers new analytic expressions for how the uncertainty scales with data-length and a different framework for understanding the limits of the measurement. The new framework illustrates more readily how a 1 × 10−16 frequency offset between the space and ground clock leads to a bias (i.e. systematic uncertainty) in  comparable to its statistical uncertainty of 2.9 × 10−6. Overall, our approach provides an independent analysis method for the determining , particularly important for the overall rigor and validity of the ACES science return.