A theoretical investigation is made to explore the possibility of obtaining corrections to star catalogues from the observations of artificial satellites. A model is established to represent the system formed when such corrections are determined simultaneously with corrections to the geocentric position of the observer. The covariance matrix is established analytically for the two-dimensional case. The resulting correlations and weights are discussed. Since this method presents an independent way of obtaining the systematic errors in star catalogues, it is related to the measurement of all quantities which depend on star positions.