Future missions involving in-space servicing, repair, inspection, or rendezvous and docking require algorithms for safe, autonomous proximity operations. Algorithms for relative navigation, safe separation, and circumnavigation trajectory design are presented. The algorithms rely on safe, natural motion trajectories and covariance information from relative navigation to minimize the probability of spacecraft collision. The algorithms are described in the context of a space inspection mission where two attached spacecraft separate and one circumnavigates the other. These algorithms can also be applied to a variety of rendezvous or other proximity operations missions, whether autonomous or manually operated.