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Relationships for rms angular errors are developed for certain common active space probe and satellite angle-tracking systems. The only source of error considered is the thermal and shot noise of the receiver, bandlimited by the tracking servo noise bandwidth. If additional smoothing after angular readout is performed, only the special case of many samples averaged over a time long compared to the reciprocal servo noise bandwidth is considered. These thermal-noise errors are by no means the usual practical accuracy limitations of an angle-tracking system. They do, however, set bounds on minimal signal strength allowable for the desired tracking accuracy. The received signals were assumed to be sinusoidal of constant peak amplitude with the information, if any, contained in phase or frequency modulation. This is the most common signal in space probe or satellite tracking.