  The gravity field maps of the satellite gravimetry missions GRACE (Gravity
Recovery and Climate Experiment) 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 non-zero 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.
