Methods of harmonic synthesis for global geopotential models and their first-, second- and third-order gradients |
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Authors: | E Fantino S Casotto |
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Institution: | (1) Dipartimento di Astronomia, Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padua, Italy;(2) Center for Space Studies (CISAS) “G. Colombo”, Università di Padova, Via Venezia 15, 35131 Padua, Italy |
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Abstract: | Four widely used algorithms for the computation of the Earth’s gravitational potential and its first-, second- and third-order
gradients are examined: the traditional increasing degree recursion in associated Legendre functions and its variant based
on the Clenshaw summation, plus the methods of Pines and Cunningham–Metris, which are free from the singularities that distinguish
the first two methods at the geographic poles. All four methods are reorganized with the lumped coefficients approach, which
in the cases of Pines and Cunningham–Metris requires a complete revision of the algorithms. The characteristics of the four
methods are studied and described, and numerical tests are performed to assess and compare their precision, accuracy, and
efficiency. In general the performance levels of all four codes exhibit large improvements over previously published versions.
From the point of view of numerical precision, away from the geographic poles Clenshaw and Legendre offer an overall better
quality. Furthermore, Pines and Cunningham–Metris are affected by an intrinsic loss of precision at the equator and suffer
from additional deterioration when the gravity gradients components are rotated into the East-North-Up topocentric reference
system.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. |
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Keywords: | Geopotential Spherical harmonics Gravity tensors Gravitational gradients Associated Legendre functions Helmholtz polynomials Clenshaw summation |
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