Considers the problem of spacecraft formation flying in the presence of periodic disturbances. In particular, the nonlinear position dynamics of a follower spacecraft relative to a leader spacecraft are utilized to develop a learning controller which accounts for the periodic disturbances entering the system model. Using a Lyapunov-based approach, a full state feedback control law, a parameter update algorithm, and a disturbance estimate rule are designed which facilitate the tracking of given reference trajectories in the presence of unknown spacecraft masses. Illustrative simulations are included to demonstrate the efficacy of the proposed controller.