In this paper, we modify and apply a robust almost global attitude tracking control scheme to the model of a small satellite. The control scheme, which has been reported in prior literature, is modified to take into account the actuator constraints and actuator configuration of this satellite, which are based on a small satellite currently being developed at the University of Hawaii. The actuators consist of three magnetic torquers and one small reaction wheel. The mass and inertia properties correspond to the known values for this satellite. The satellite is in circular low earth orbit of altitude 600 km and its dynamics model includes gravity, atmospheric and geomagnetic effects. The control strategy used here achieves almost global asymptotically stable attitude trajectory tracking, which implies that the desired attitude trajectory is tracked from all initial conditions on the state except for those that lie on a zero-volume subset within the state space. The continuous feedback control law is also globally defined. Feedback control gains are continuously varied based on known actuator constraints and tracking errors. The almost global asymptotic tracking property can be shown using a generalized Lyapunov analysis on the nonlinear state space of the attitude dynamics. The control torque obtained from this almost-globally-stabilizing feedback control law is partitioned so that each actuator generates a part of this control torque that is within its saturation limits. The control law for the reaction wheel has a singularity when the reaction wheel axis is perpendicular to the local geomagnetic field. To avoid actuator saturation, the control inputs to the actuators are kept constant whenever any actuator reaches a certain fraction of its saturation value. Numerical simulation results for two de-tumbling maneuvers, one where the control law singularity does not appear and one where it does, confirm that the desired attitude trajectory is tracked almost globally.