Propulsive spacecraft enable scientific discovery and exploration of the worlds beyond Earth. Au- tonomous spacecraft have landed on Earth, the Moon, Mars, Mercury, Venus, Titan, asteroids, and a comet. Recently discovered planetary pits allow access to subsurface voids valuable for scientific discov- ery and sustained exploration. With recent advancements in embedded convex optimization software and trajectory optimization theory, increasingly sophisticated autonomous missions will be able to safely and efficiently reach these unexplored destinations. This thesis develops and tests an algorithm for fuel-optimal landing into planetary pits. By represent- ing the safe regions outside and inside a planetary pit as distinct convex spaces, techniques for optimal guidance based on convex optimization are extended to find trajectories into pits. A search routine for time of flight and time of entry into the pit finds globally fuel-optimal landing trajectories. This time search softens constraints on maximum thrust and landed vehicle mass to reliably find solutions without sensitivity to initialization. The algorithm is implemented within a modeling language and uses an em- bedded solver for convex optimization. The resulting implementation is therefore practical and effective for use in future missions. The algorithm is tested in simulated landing scenarios that vary vehicle parameters, mission con- straints, and pit dimensions. The feasibility and optimality of generated trajectory solutions are ex- amined along with algorithm runtime. This research determines that fuel-optimal guidance capable of landing within planetary pits is viable for future missions.