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The gravity field maps of the satellite gravimetry missions GRACE (GravityRecovery and Climate Experiment) and GRACE Follow-On are derived by means ofprecise orbit determination. The key observation is the biased inter-satelliterange, which is measured primarily by a K-Band Ranging system (KBR) in GRACEand GRACE Follow-On. The GRACE Follow-On satellites are additionally equippedwith a Laser Ranging Interferometer (LRI), which provides measurements withlower noise compared to the KBR. The biased range of KBR and LRI needs to beconverted for gravity field recovery into an instantaneous range, i.e. thebiased Euclidean distance between the satellites' center-of-mass at the sametime. One contributor to the difference between measured and instantaneousrange arises due to the non-zero travel time of electro-magnetic waves betweenthe spacecraft. We revisit the calculation of the light time correction (LTC)from first principles considering general relativistic effects andstate-of-the-art models of Earth's potential field. The novel analyticalexpressions for the LTC of KBR and LRI can circumvent numerical limitations ofthe classical approach. The dependency of the LTC on geopotential models and onthe parameterization is studied, and afterwards the results are comparedagainst the LTC provided in the official datasets of GRACE and GRACE Follow-On.It is shown that the new approach has a significantly lower noise, well belowthe instrument noise of current instruments, especially relevant for the LRI,and even if used with kinematic orbit products. This allows calculating the LTCaccurate enough even for the next generation of gravimetric missions.

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