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A scheme for estimating the angular velocity of a spacecraft without rate gyros is presented. It is based upon a nonlinear estimator whose inputs are measured inertial vectors and their calculated time derivatives relative to vehicle axes. It works for all spacecraft attitudes and requires no knowledge of attitude. It can use measurements from a variety of onboard sensors like Sun sensors, star trackers, or magnetometers, and in concert. It can also use look angle measurements from onboard tracking antennas for tracking and data relay satellites or global positioning system satellites. In this paper, it is applied to a Sun point scheme on the Hubble Space Telescope assuming all or most of its onboard rate gyros have failed. Simulation results are presented for verification.