Space gradiometry: tensor-valued ellipsoidal harmonics, the datum problem and application of the Lusternik–Schnirelmann category to construct a minimum atlas

Abstract

Our contribution deals with three topics, namely (1) the tensor of gravity gradients in ellipsoidal harmonics, (2) the corresponding datum problem and (3) the construction of a minimum atlas in terms of ellipsoidal harmonics of Jacobi type following the basic result of the theory of the Lusternik–Schnirelmann catagory. “Generally speaking, geodesy is a brilliant illustration of the possibilities of application of mathematics and how to apply it. It is true that it gives only approximations, but as far as geodetic investigation can be regarded as completed it always gives the measure for the approximation.” F. Klein, Elementarmathematik vom hoheren Standpunkt aus, 171 (1928) 3rd ed. Gottingen