The problem of planning a safe trajectory for a free-flying robot to approach an uncontrolled spinning satellite is addressed. First, a heuristic plan is presented for a simple planar case, which constructs a collision-free path within realistic system constraints. Second, a general numerical optimization technique for planning a safe spatial trajectory is presented. In it, the approach path is parameterized and a cost function based on performance metrics is minimized in order to find the optimal path. The results are analyzed, and it is shown that optimization techniques can be used to produce a far safer approach trajectory than the heuristic method.