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Space Gradiometry on the Reference Ellipsoid


Campus Paris-Rive-Gauche


Séminaires du Campus spatial

Salle Paul Klee 454A, bat. Condorcet

Erik Grafarend

University of Stuttgart, Germany

Space Gradiometry with respect to the International Ellipsoid is an integral part of Space Geodesy. Here we introduce the gravitation tensor (tidal tensor, curvature tensor) in terms of ellipsoid harmonics introduced by Jacobi (1834). We fit the model of Somigliani-Pizzetti reference field in Jacobi ellipsoidal/shpheroidal coordinates. It balances the conservative parts of the gravitational functionals of second order and the centrifugal functionals of second order as well. We study the central question of how many terms of an ellipsoidal harmonic setup by degree/order are estimable. As a result we find singularities caused by degree/order of type zero/zero, one/minus one, zero, plus one (datum problem/gauge problem). A speciality is our analysis in terms of tensor-valued ellipsoidal harmonics. The treatment extends previous results projects in terms of spherical harmonics world-wide in use to the extent that the trace of the gravity tensor is not zero due to the rotation of the Earth or any other rotating planet.