Analytical derivation of star sensor accuracies due to centroid error

An analytical expression for the boresight rotation accuracy of a star sensor is derived. This error is computed as a function of the distance of the star measurement on the detector to its centre. The note also obtains the ratio between the cross-axis error and the boresight rotation error. The analytical findings are seen to be in agreement with the experimental findings in the literature. Numerical experiments illustrate the rotation accuracies for star sensors with different fields of view.