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The causes for the existing deficiencies in the determination of the attitude of the ROSAT satellite were investigated by a collaboration of DASA, GSOC, and MPE. In order to develop possible improvements detailed studies of the precision achievable in position measurements by the star trackers on the one hand and by the X-ray system on the other hand were performed. The comparison of the two systems showed that each subsystem by itself fulfills the specification but that the complete ROSAT system falls short of fulfilling it. Although only a small improvement of the attitude solution was achieved the performed tasks were essential for an optimal calibration of the X-ray system. The gained insights into the properties of the attitude variations will in some suitable cases make it possible to develop empirical correction procedures for the scientific evaluation of the X-ray data.