Stable or nearly stable orbits do not generally possess well-distinguished manifold structures that assist in designing trajectories for departing from or arriving onto a periodic orbit. For some potential missions, the orbits of interest are selected as nearly stable to reduce the possibility of rapid departure. However, the linearly stable nature of these orbits is also a drawback for their timely insertion into or departure from the orbit. Stable or nearly stable near rectilinear halo orbits (NRHOs), distant retrograde orbits (DROs), and lunar orbits offer potential long-horizon trajectories for exploration missions and demand efficient operations. The current investigation focuses on leveraging stretching directions as a tool for departure and trajectory design applications. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information for efficient departure from the orbit. Similarly, maximum stretching in reverse time enables arrival with a minimal maneuver magnitude.