Abstract
At different European institutes software has been developed for evaluation of the gravitational potential of the Earth using high degree spherical harmonic expansions. In this report the results of a comparison of a number of these software packages are presented. We compared the results for the second order derivatives (gravity gradients). It appeared that one of the most critical points in these computations is the definition of the coordinates, which should be as accurate as possible. Machine dependency and algorithm setup were of less importance, the former being only reflected in CPU timing results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
7 References
Balmino, G., Barriot, J.P., Valès, N. (1990) Nonsingular formulation of the gravity vector and gravity gradient tensor in spherical harmonics, Manuscripta Geodaetica 15: 11–16
CISI (1989) Study on precise gravity field determination methods and mission requirements, Final Report Phase A, ESA contract No. 7521/87/F/FL
Colombo, O.L. (1981) Numerical methods for harmonic analysis on the sphere, Dept. of Geod. Science, report no.310, Ohio State University, Columbus
Dornier (1988) ARISTOTELES Phase A study, Final Report, Estec contract No. 7528/88/NL/JS
Heiskanen, V., Moritz, H. (1967) Physical Geodesy, Freeman & Comp., San Francisco
Kaula, W.M. (1966) Theory of satellite geodesy, Blaisdell Publ. Comp., Waltham, Massachusetts
Koop, R., Stelpstra, D. (1989) On the computation of the gravitational potential and its first and second order derivatives, Manuscripta Geodaetica 14, 6: 373–382
Morgan, S.H., Paik, H.J. (Eds.) (1988) Superconducting Gravity Gradiometer Mission, Vol.II: Study Team Technical Report, NASA Technical Memorandum 4091
Paul, M.K. (1978) Recurrence relations for integrals of associated Legendre functions, Bulletin Bulletin Géodésique 52: 177–190
Thong, N.C., Grafarend, E.W. (1989) A spheroidal harmonic model of the terrestrial gravitational field, Manuscripta Geodaetica 14, 5: 285–304
Thong, N.C. (1989) Simulation of gradiometry using the spheroidal harmonic model of the gravitational field, Manuscripta Geodaetica 14, 6: 404–417
Tscherning, C.C. (1976) Computation of the second-order derivatives of the normal potential based on the representation by a Legendre series, Manuscripta Geodaetica 1: 71–92
Vermeer, M. (1989) FGI Studies on satellite gravity gradiometry. 1. Experiments with a 5-degree buried masses representation. Report 89:3 Finnish Geodetic Institute, Helsinki
Vermeer, M. (1990) Orbit integration with perturbing force interpolation from an OSU86F — based half — degree grid of geopotential partials, Manuscripta Geodaetica 15, 2: 83–96
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Balmino, G., Barriot, J., Koop, R. et al. Simulation of gravity gradients: a comparison study. Bulletin Géodésique 65, 218–229 (1991). https://doi.org/10.1007/BF00807265
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00807265