Evaluation of the relativistic redshift for a spaceborne optical clock

Spaceborne optical clocks will play a significant role in the tests of fundamental physics. However, orbital motion and gravitational potential lead to the relativistic redshift (RRS), which introduces systematic errors in frequency measurements. Based on perturbation force models and orbital ephemeris data, we calculated the trajectory of the China Space Station (CSS), and evaluated the RRS of a strontium optical lattice clock aboard. The uncertainty of the RRS is estimated to be 3.3 x 10-17, and the instability reaches 3.57 x 10-19 at 104 s, which is comparable to the overall uncertainty and instability of the state-of-the-art ground-based optical clock. Therefore, according to our assessment, the evaluating method for the RRS of the optical clock in the CSS is feasible and effective, and the results can serve as a reference for dynamic frequency correction of spaceborne optical clocks.