The paper deals with the attitude active control of a Low Earth Orbit nanosatellite, actuated with magnetorquers. The satellite is on a polar orbit and is subject to gradient gravity. Magnetic actuation is preferred for nanosatellite attitude control because of its relatively low cost, lightweight and low power consumption. The basic idea is to use the interaction between the magnetic field generated by the coils and the Earth's magnetic field. The developed control strategy is a Linear Quadratic controller for the three-axis stabilization of the satellite. This optimal controller is derived from a linear model of the system which is nonlinear and time-varying.Since magnetic actuation can lead to poor performances because only two axes can be controlled at each time instant, an hybrid actuation system with magnetorquers and reaction wheels is also investigated. Simulation results are provided in the case of a 2U CubeSat attitude stabilization to illustrate and compare the control strategy efficiency in three cases: (i) with magnetic torquers, (ii) with gyroscopic torquers and (iii) with the hybrid actuation system.