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The paper contains the formulation of an analytical expression of the TCP throughput and the packet loss probability over geostationary satellite channels on the basis of the state-of-the-art in the field. This work is based on the most important literature about TCP modeling and analysis. The expression obtained, in closed form, is a function of the bandwidth and buffer queues size available at the satellite gateway. Performance analysis is provided in terms of throughput and packet loss probability. Analytical results are compared with the tests obtained through a satellite network emulator already validated in the literature.