In this paper, we treat the practical problem of tracking the attitude and angular velocity of a spacecraft in the presence of gravity and disturbance moments. Autonomous trajectory tracking in the presence of disturbance moments is a challenging problem for robotic spacecraft, besides autonomous aerial and ground vehicles. The approach used here achieves almost global stable trajectory tracking by using a globally defined dynamics model that includes a moment on the vehicle created by a gravity potential and a disturbance moment that vanishes when the required angular velocity to be tracked is zero. The feedback control law is also globally defined. In the presence of the particular type of disturbance moments considered, this control law achieves almost global asymptotic tracking. Lyapunov-type methods on the nonlinear space of rigid body rotations are used to analyze the properties of the closed loop system and show near global stability and asymptotic convergence to the desired attitude and angular velocity trajectory. The treatment in this paper utilizes concepts from geometric mechanics to treat the dynamics of the feedback system in a global manner.