Abstract
Abstract In this paper, we discuss in brief some basic issues of quantum space gravimetry, related to standard approach of geodesy which is based on the Newton model of gravity and Euclidean geometry. We emphasize the need to apply relativistic gravity in practical high-precision geodesy. Here we do not intend to solve the existing hard experimental and theoretical problems, being essential for the topic: development of quantum gravity, physics of dark matter and dark energy, novel physical principles of extended general relativity, in particular, a nonlinear superposition principle in general relativity and its extensions, and so on. Rather, we point out the fundamental unsolved problems, which are substantial for quantum space gravimetry and future practical high-precision geodesy. We outline the possible ways for their study and decision. Thus, to some extend, the present paper is a program for further developments, not a presentation of the fnal solutions. Our goal is to warn corresponding scientifc community about the ultimate necessity for going outside the frameworks of the formulated more than three century ago, and used up to now in geodesy, Newton gravity, together with Euclidian geometry. At present, in the emerging high-precision geodesy one must replace them with modern models of gravity and corresponding non-Euclidean geometry. Without using and further development of those issues, the interpretation of data obtained from high-precision measurements by satellites for geodetic use seems to be quite problematic, uncertain, and may be misleading for practitioners.
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