TY - JOUR

T1 - Revisiting the light time correction in gravimetric missions like GRACE and GRACE follow-on

AU - Yan, Yihao

AU - Müller, Vitali

AU - Heinzel, Gerhard

AU - Zhong, Min

N1 - Funding Information: Yihao Yan acknowledges the China Scholarship Council for scholarship support and expresses his gratitude to the GRACE-Follow-On LRI group members at the Albert-Einstein-Institute in Hannover, Germany. The authors thank Changqing Wang for the support of validating some force models. This work was supported by the National Natural Science Foundation of China (Project No. 41704013). This work was supported by the Max-Planck-Society and the Chinese Academy of Sciences within the LEGACY (“Low-Frequency Gravitational Wave Astronomy in Space”) collaboration (M.IF.A.QOP18098) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967.

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

KW - General relativity

KW - GRACE follow-on

KW - K-band ranging

KW - Laser interferomery

KW - Light time correction

UR - http://www.scopus.com/inward/record.url?scp=85104101007&partnerID=8YFLogxK

U2 - 10.1007/s00190-021-01498-5

DO - 10.1007/s00190-021-01498-5

M3 - Article

AN - SCOPUS:85104101007

VL - 95

JO - Journal of Geodesy

JF - Journal of Geodesy

SN - 0949-7714

IS - 5

M1 - 48

ER -