Summary
A typical geodetic satellite orbit has been computed by numerical integration for a period of thirty hours. The gravitational potential of a standard orbit was represented by the SAO 1969 Standard Earth potential coefficients taken to degree 18. Other orbits were generated using the generalized Stokes' equations and the coating method applied to gravity anomalies and surface densities, in 5°, 10°, 15° and 30° equal-area blocks, derived from the given potential coefficients. The differences between these orbits yield the position differences to be expected when representing the potential field by using gravity data instead of potential coefficients. Using 10°, 15°, and 30° blocks and the generalized Stokes' equations, the position error at the end of thirty hours was 89 meters, 224 meters, and 2060 meters respectively. This error is primarily due to the integration error in computing the gravitational field by summation over a finite number of areas.
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Rapp, R.H. Satellite orbit computations using gravity anomalies. Stud Geophys Geod 16, 1–9 (1972). https://doi.org/10.1007/BF01614228
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DOI: https://doi.org/10.1007/BF01614228