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One of the most important parameters in satellite communication links, particularly in low earth orbits (LEO) and elliptical orbits is Doppler frequency shift (DFS) and Doppler frequency rate (DFR) at communication channels. This paper analyzes Doppler frequency effects in various satellite orbits. For this purpose, a new orbit generator is presented for accurate simulation of satellite orbits. The non-spherical mass distribution turbulence of the earth and its effects on Doppler shift calculations is considered and simulation results of Doppler frequency shift for an elliptical LEO satellite in L-band is presented.