Orbital relativistic correction resulting from the Earth’s oblateness term

Abstract In the IERS Conventions, the general relativistic (GR) corrections to the motion of artificial satellites assume that the Earth is a regular sphere. We found, however, that the missing orbital GR correction resulting from the Earth’s oblateness for low earth orbiters (LEO) is greater by a factor of three than the geodetic precession, i.e., the relativistic effect included in the IERS Conventions. We test the impact of the relativistic oblateness correction on the orbits of geodetic satellites, such as Starlette and LARES, as well as on GRACE-FO and the future MAGIC mission dedicated to the gravity field recovery. Moreover, we derive the gravity field based on GRACE-FO data to check the impact of the missing GR correction on GRACE products. We found that the GR oblateness correction induces accelerations of the order of 10 –10 m/s 2 , which is above the sensitivity of current LEO orbit determination procedures. This effect causes a secular rate of the ascending node up to 2 mm/day and introduces a systematic bias to the GRACE-derived C 20 values of 3.0·10 –12 . Neglecting GR oblateness correction results in biased estimates of the GRACE-based equivalent water heights at the millimeter level. Therefore, this correction should be considered in geodetic products based on LEO satellite observations that require accuracy at the level of millimeters.