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Fermi coordinates and static observer in Schwarzschild spacetime

In this paper we construct the Fermi coordinates along any arbitrary line in simple analytical way without use the orthogonal frames and their parallel transport. In this manner we extend the Eddington approach to the construction of the Fermi metric in terms of the Riemann tensor. In the second part of the present article we show how the proposed approach works practically by applying it for deriving the Fermi coordinates for the static observer in the Schwarzschild spacetime.