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An attempt is made to define the initial conditions from which a Sun-pointing satellite with a simple on-off jet-control system is capable of acquiring attitude control. The control system was assumed to be stabilised by means of phase advance of the error signal rather than by the use of rate gyroscopes. The study was carried out mainly by digital computation. The maximum initial angular velocity from which satisfactory acquisition performance could be achieved increased with increasing available angular acceleration and fell as the inertia configuration was made more asymmetrical. The results are strictly applicable only to control systems of the type outlined above. Suggestions are made of alternative arrangements which might be worth study.