Revisiting the Light Time Correction in Gravimetric Missions Like GRACE and GRACE Follow-On

The satellite gravimetry missions GRACE (Gravity Recovery and Climate Experiment) and GRACE Follow-On provide the global and monthly gravity field for almost 17 years, which plays an irreplaceable role in understanding the mass transport of the Earth system. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. However, the measured biased range which is directly measured by the inter-satellite ranging systems differs from the instantaneous biased range which is usually required for gravity field recovery. The difference is called the Light Time Correction (LTC) and arises from the non-zero travel time of electromagnetic waves between the spacecraft. We re-analyzed the LTC calculation from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field, and different types of orbital data. By analyzing the iterative equations in the LTC calculation of KBR and LRI, a novel analytical expression method is obtained to avoid the numerical limitation of the classical method. The dependency of the LTC on geopotential models and on the parameterization is further studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.