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Meeting ID: 916 6441 7222
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For more than a century the gravitational field of the Earth has been modeled in terms of gravitational potential, V, and/or its gradient, g, which is gravitational acceleration. As far back as Laplace it has been supposed that such models can be constructed using spherical harmonic expansions (SHEs) complete through some maximum degree and order N. The higher the value of truncation degree N, the greater the spatial resolution of the model. As early as 1961, geodesists began to worry about the mathematical foundations of such models. They were concerned that the SHEs would not converge at or near the Earth’s surface. But in 1969 T. Krarup argued that non-convergence was a non-problem in practice, and his argument was endorsed and popularized by H. Moritz, especially in his celebrated 1980 book on theoretical physical geodesy. Nevertheless, later studies of a numerical character seemed to suggest that divergence of SHEs was, in fact, a problem. A team of OSU mathematicians and geodesists recently revisited this problem and produced two mathematical proofs that SHEs will never converge at or near the surface of the Earth, and they demonstrated that this would lead to model prediction errors growing exponentially with distance beneath the Brillouin sphere, the smallest sphere that contains the solid Earth. I will explain and illustrate these findings, and point out that these limitations on the predictive skill of global gravity models have very important implications for inertial navigation, atomic timekeeping, and future technologies such as quantum networking.