The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. 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. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is 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 a 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.

卫星重力测量任务的重力恢复和气候实验（GRACE）和GRACE后续行动的重力场图是通过精确的轨道确定得出的。关键的观测结果是有偏差的卫星间距离，该距离主要由GRACE和GRACE后续跟踪系统中的K波段测距系统（KBR）进行测量。GRACE后续卫星还配备了激光测距干涉仪（LRI），与KBR相比，该测量仪的噪声更低。为了重力场恢复，需要将KBR和LRI的偏置范围转换为瞬时范围，即同时在卫星质量中心之间的欧式距离。由于航天器之间电磁波的传播时间不为零，导致了测量范围和瞬时范围之间差异的一个原因。我们从考虑一般相对论效应和地球势场的最新模型的第一原理重新审视了光时间校正（LTC）的计算。KBR和LRI的LTC的新颖分析表达式可以规避经典方法的数值限制。研究了LTC对地势模型和参数化的依赖性，然后将结果与GRACE和GRACE Follow-On官方数据集中提供的LTC进行了比较。结果表明，即使与运动轨道产品一起使用，这种新方法的噪声也大大降低，远低于当前仪器的仪器噪声，特别是与LRI有关。这样，即使对于下一代重力任务，也可以足够准确地计算LTC。