Observation and stabilization problems for a rigid body rotating about its mass centre in a time-periodic magnetic field is considered. The moment of the applied forces about the mass centre is a vector product of the field and the vector of control. The only measurement is of the field and its time derivatives in the body co-ordinates. The model describes the angular motion of a satellite in the geomagnetic field with the control carried out by a magnetic moment of current coils (magnetorquers) mounted on the satellite body. It is shown that generically the knowledge of the field and its derivatives is sufficient for the attitude determination. A problem of stabilization along one direction is considered. The stabilizer constructed in this work drives the system to a given motion from all initial points that do not belong to an unstable manifold. It is shown that all stabilizers have such a manifold of initial conditions.