Abstract: A triaxially stabilized earth oriented satellite is provided with an attitude control system. The attitude control system contains a controller, final control elements for generating control torques around each of three axes of a system of coordinates (principle axes x, y, z) fixed relative to the satellite. Additionally, the attitude control system comprises, as measuring transducers, exclusively a direction vector measurement device, like a magnetometer or star sensor, a sun sensor array and an earth sensor. The process of the invention makes use of the apparatus as noted above and includes the steps of:A. determining an estimate for the rotating velocity of the satellite from a direction vector measurement;B. searching for the sun, depending on the size of the field of view of the sensor, by one or two search rotations at right angles to the optical axis;C. adjusting the direction of the sun relative to the optical axis; andD. adjusting the direction vector measurement to a reference direction S.sub.