The inertial pointing problem of a rigid satellite by solely magnetic torqueing is considered in this paper. To ensure globally uniformly ultimately bounded motion about the reference in inertial space, a sliding mode attitude control law, which consists of equivalent and reaching control terms, based on a novel time-varying sliding manifold is designed. The originality of the sliding manifold relies on the inclusion of two time-integral terms. The usage of the proposed sliding manifold makes the application of the equivalent control method to the considered problem possible, and it is proven that the state trajectories reach the newly designed sliding manifold in finite time even under the effect of four realistically modeled disturbance components and parametric uncertainty of all inertia matrix entries. For the constructed purely magnetic attitude control system, stability and existence of the sliding mode as well as state trajectories' finite time convergence to the sliding manifold are demonstrated via Lyapunov function techniques. The results of a simulation example verify the robust stability of the designed attitude control system. The steady state performance of the attitude control system is evaluated in the altitude range of low-Earth-orbits. (C) 2018 Elsevier Masson SAS. All rights reserved.