Errors of Quadrature Connected with the Simple Layer Model of the Geopotential
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Errors of Quadrature Connected with the Simple Layer Model of the Geopotential

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    When using the simple layer model of the geopotential in satellite geodesy, one has to integrate over surface elements of the earth on which the density of the assumed constant. The integration is solved numerically by subdividing the elements and by assuming constant kernels of the integrals for the subdivisions. This quadrature causes errors that are investigated for a sphere with the mean earth radius. By assuming unit density for the surface layer, exact values of the gravitational potential of the sphere and its gradient can be computed and compared with the values obtained by quadrature. Different sizes of surface elements and different methods of subdivisions are investigated. The error of quadrature, of course, increases with size of the surface elements and decreases with the number of subdivisions. An efficient and accurate way of subdividing is the method presently applied in the analysis of satellite data.
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