Investigation of Finite-Element Representations of the Geopotential
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As alternatives to lengthy series expansions for globally valid approximations of the earth’s gravity field, piecewise approximation methods are evaluated. A single global equation is retained only for the point mass and second zonal terms of the geopotential; all finer structure undulations are modeled by a global family of locally valid functions. A degree 23 spherical harmonic series for the geopotential is replaced by finite-element approximations within the spherical shell out to 1.2 earth radii. This example application demonstrates conclusively the feasibility and desirability of the finite-element approach. An order of magnitude reduction in the calculation time for gravitational acceleration is realized over conventional calculations with spherical harmonic recursions. © 1976 American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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