The objective of this research is to study the optimal rendezvous of a chaser spacecraft with a target spacecraft. The problem is modeled in two ways. First, a linearized model using the Clohessy-Wiltshire (CW) equations is used as an approximation to the relative dynamics. Second, a full nonlinear model is used. The results for minimum-fuel and minimum-time trajectories is studied for both models and the solutions are compared. An analysis is performed to determine the effect of neglecting the nonlinear contributions in the model when using the linearized approximation of the relative dynamics.