The last several decades have resulted in an unfortunate byproduct of space exploration and development: orbital debris. Satellites in Low Earth Orbit have been required to make an ever increasing number of course corrections in order to avoid collisions. Despite efforts to the contrary, collisions continue to occur, each time creating additional debris and increasing the requirement for the remaining satellites to maneuver. Every required maneuver decreases a satellite's service life. The purpose of this study is to develop a minimum thrust profile to maneuver an orbiting satellite out of its projected error ellipse before a collision occurs. For comparison, both the impulsive and continuous thrust cases were considered as well as in-plane versus out-of plane maneuvering. This study made use of the Radau Pseudospectral Method to develop this minimum thrust profile. This method was run in MATLAB(r) using General Pseudospectral Optimal Control Software (GPOPS-II). Once the optimal solution was obtained, Systems Tool Kit(r) was used to simulate the resulting calculated trajectories and confirm avoidance of the error ellipse