Convex optimization techniques have deterministic convergence properties, are self-starting, i.e., they do not require an initial guess, and have been tested in real-time environments. These optimization techniques are applied to the trajectory planning problem for orbital rendezvous and proximity operations. Spacecraft rendezvous, inspection, and final approach trajectories are considered. Optional trajectory constraints are considered including approach corridors, keep-out zones, and maximum thrust acceleration levels. Two linear dynamics models are investigated: Clohessy-Wiltshire dynamics to describe the relative motion in an LVLH frame, and a new relative orbital motion dynamics model to describe the motion relative to a spinning or uncontrolled spacecraft. In both cases, an algorithm based on convex optimization and a second-order cone program is developed and used to generate optimal rendezvous and proximity operation trajectories. Results for several scenarios are presented and implemented in a nonlinear orbital simulation.