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This paper presents a method for determining the orbit of a satellite by observing, in the course of a single pass, the Doppler shift in the frequency of a CW signal transmitted from the ground and reflected by the satellite to one or more ground-based receivers at remote sites. The method is sufficiently general that, with minor modification, it may be applied to any type of satellite or ICBM tracking measurements. The computation consists of improving approximations for initial position and velocity components by successive differential corrections which are obtained from a least squares treatment of an over-determined system of condition equations while imposing elliptic motion as a constraint. Methods for obtaining approximations for the initial position and velocity components are likewise discussed. Results are presented for computations with typical input data.