  The design and scale of a future mission to directly image and characterize
potentially Earth-like planets will be impacted, to some degree, by the
expected yield of such planets. Recent efforts to increase the estimated
yields, by creating observation plans optimized for the detection and
characterization of Earth-twins, have focused solely on coronagraphic
instruments; starshade-based missions could benefit from a similar analysis.
Here we explore how to prioritize observations for a starshade given the
limiting resources of both fuel and time, present analytic expressions to
estimate fuel use, and provide efficient numerical techniques for maximizing
the yield of starshades. We implemented these techniques to create an
approximate design reference mission code for starshades and used this code to
investigate how exoEarth candidate yield responds to changes in mission,
instrument, and astrophysical parameters for missions with a single starshade.
We find that a starshade mission operates most efficiently somewhere between
the fuel- and exposure-time limited regimes, and as a result, is less sensitive
to photometric noise sources as well as parameters controlling the photon
collection rate in comparison to a coronagraph. We produced optimistic yield
curves for starshades, assuming our optimized observation plans are schedulable
and future starshades are not thrust-limited. Given these yield curves,
detecting and characterizing several dozen exoEarth candidates requires either
multiple starshades or an eta_Earth > ~0.3.
