Formulation of testing gravitational redshift based on Laser Time link between China Space Station and a ground station

This paper presents a high-precision gravitational redshift test using the China Space Station (CSS) Laser Time Transfer (CLT) system. We develop a comprehensive observation equation based on a c⁻³ c - 3 order relativistic model for space-ground clock comparison. While the CSS optical clock system is currently in the orbital debugging phase, our simulation using actual CSS orbit data achieves a gravitational redshift verification precision of (1.8± 47)× 10⁻⁷ ( 1.8 ± 47 ) × 10 - 7 – approximately one order of magnitude improvement better than previous experiments. Our work represents the first application of laser-based time transfer for gravitational redshift verification at such precision, and the first use of the CSS CLT link for testing this fundamental aspect of General Relativity. Unlike microwave-based methods, our laser approach avoids ionospheric effects and first-order Doppler shifts. Residual analysis identifies tropospheric delay variations and atmospheric turbulence as the primary remaining uncertainty contributors. The achieved precision enables gravitational potential difference measurements with 0.1 m ² 2 /s ² 2 precision – offering new capabilities for both fundamental physics investigations and geodetic applications including intercontinental height transfer. This work establishes a new benchmark for high-precision tests of relativistic physics and demonstrates the transformative potential of space-based optical time transfer.