  We analyze the properties of searches devoted to finding planetary transits
by observing simple stellar systems, such as globular clusters, open clusters,
and the Galactic bulge. We develop the analytic tools necessary to predict the
number of planets that a survey will detect as a function of the parameters of
the system, the observational setup, site properties, and planet properties. We
find that the detection probability is generally maximized for I-band
observations. The signal-to-noise ratio of a planetary transit is weakly
dependent on the mass of the primary for sources with flux above the sky
background, and falls very sharply for sources below sky. Therefore the number
of detectable planets is roughly proportional to the number of stars with
fluxes above sky (and not necessarily the number of sources with photometric
error less a given threshold). In order to maximize the number of detections,
experiments should be tailored such that stars near sky are above the detection
threshold. Once this requirement is met, the number of detected planets is
relatively weakly dependent on the detection threshold, diameter of the
telescope, exposure time, seeing, age of the system, and planet radius. The
number of detected planets is a strongly decreasing function of the distance to
the system, implying that the nearest, richest clusters may prove to be optimal
targets.
