The subject of this paper is an antenna tracking system used to maintain an antenna on board a geosynchronous (GEO) satellite, pointed towards a low earth orbit (LEO) satellite. The tracking system uses the BPSK modulated signals transmitted from the LEO satellite. The signal is received by an electronically switched antenna beam. A suitable processing of the received signal level then generates an error voltage which drives a tracking loop. The measurement of the received signal level is implemented by a power detector. Analysis of the antenna tracking algorithm is carried out and the performance is given in terms of linearized mean-square tracking error. The mean-square tracking error is related to the antenna beam parameters, to the closed loop bandwidth and to the statistics of the power measurement process. In particular, it is shown that a key parameter for the tracking loop performance is the signal-to-noise ratio (SNR) at the power detector output, which is inversely proportional to the variance of the pointing error, and a theory has been developed to find an accurate expression for the SNR.