This project focuses on the study previous to the development of an Attitude Determination and Control System (ADCS) of a small space telescope, the Humble Space Telescope (hST). The ADCS is essential for the telescope operation as it must guarantee a good observation of the space regions of interest. The proposed system is based on the use of quaternions to lighten the computational weight. The QUEST (Quaternion Estimator) algorithm will be used for the attitude determination from the vector observations made with the sensors, mainly star trackers. The control part will be done by means of a PD (Proportional Derivative) controller using a control law based on the error quaternion between the actual and the desired attitude. The stability of the proposed control law will be verified by a Lyapunov study. An empirical study of the effect of the propotional and derivative gains on the system's response will be carried out. The main hardware for the control part will be reaction wheels, combined with the use of magnetorquers for the desaturation of the reaction wheels. The numerical simulations that are going to be conducted will verify the viability of the proposed system.