Quadrature errors in the partial derivatives required for the direct recovery of gravity anomalies from satellite observations
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Date
1972-12
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Ohio State University. Division of Geodetic Science
Abstract
The equations of motion of a geodetic satellite in the earth's gravitational field expressed by gravity anomalies require the evaluation, amongst others, of the partial derivatives of the disturbing force with respect to individual gravity anomalies. These derivatives would be in error if evaluated using coordinates at the center points of the mean gravity anomaly blocks. This report discusses how these blocks should be subdivided so that the partial derivatives could be numerically evaluated for each subdivision, and then finally meaned to give the value representative of the whole blocks, with accuracies better than 2 - 3% for all blocks. The number of subdivisions is large for the blocks nearest to the satellite subpoint and decreases away from it. The actual values of this spherical distance and the actual subdivision of the mean gravity anomaly blocks has been determined numerically for 184 15° x 15° equal area blocks. Satellite heights above the earth of 400 km, 800 km and 1600 km have been considered. The computer times for the suggested scheme have been compared with alternative solutions.
Description
Prepared for National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland: Grant No. NGR 36-008-161, OSURF Project No. 3210