In this paper, two different discrete schemes of the second-order linear time-varying system represented by the linearized satellite magnetic attitude control motion equation are obtained by Euler method. Then, the controllability and observability conditions of a new discrete second-order linear time-varying system are proposed and the validity of these conditions is further verified by some numerical examples. Next, the theoretical results are applied to investigate the controllability and observability of the discretized satellite magnetic control system. Different periods $\tau$ are chosen to investigate the effect on the controllability and observability of the resulting discrete system. The corresponding conclusions are obtained.