The purpose of this paper is to present a modified cross-product unloading law that can be used to provide an open-loop compensation control design to counteract the predominant effects of the gravity gradient torque. The modified cross-product unloading law, is successfully applied to a three-axis stabilized, nadir-pointed LEO spacecraft with two-gimbals solar array. The variation of the two solar array orientations can significantly change the spacecraft's moment of inertia during the nominal operation mode, which can produce significant momentum accumulation in the roll-yaw body plane and cause large yaw pointing error. A rigorous study of momentum management performance capability has been conducted by using a high-fidelity performance simulation software that contains models of four environmental disturbance torque (gravity gradient, aerodynamic, solar, and magnetic). The simulation results show that the proposed momentum unloading control law has enabled a substantial reduction in the maximum accumulated roll momentum, which results in improving the pointing accuracy of the LEO spacecraft enormously.