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Orbital relativistic correction resulting from the Earth's oblateness term

Sosnica, Krzysztof and Ga&lstrokdyn, Filip, 2025. Orbital relativistic correction resulting from the Earth's oblateness term. Journal of Geodesy, 99(7):52, doi:10.1007/s00190-025-01973-3.

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@ARTICLE{2025JGeod..99...52S,
       author = {{So{\'s}nica}, Krzysztof and {Ga{\l}dyn}, Filip},
        title = "{Orbital relativistic correction resulting from the Earth's oblateness term}",
      journal = {Journal of Geodesy},
     keywords = {Precise orbit determination, Quadruple term, General relativity, Artificial satellites, GRACE-FO, Engineering, Geomatic Engineering},
         year = 2025,
        month = jul,
       volume = {99},
       number = {7},
          eid = {52},
        pages = {52},
     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{\textperiodcentered}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.}",
          doi = {10.1007/s00190-025-01973-3},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2025JGeod..99...52S},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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