  For extrasolar planets with orbital periods, P>10 days, radial velocity
surveys find non-circular orbital eccentricities are common, <e>~0.3. Future
surveys for extrasolar planets using the transit technique will also have
sensitivity to detect these longer period planets. Orbital eccentricity affects
the detection of extrasolar planets using the transit technique in two opposing
ways: an enhancement in the probability for the planet to transit near
pericenter and a reduction in the detectability of the transit due to a shorter
transit duration. For an eccentricity distribution matching the currently known
extrasolar planets with P>10 day, the probability for the planet to transit is
~1.25 times higher than the equivalent circular orbit and the average transit
duration is ~0.88 times shorter than the equivalent circular orbit. These two
opposing effects nearly cancel for an idealized field transit survey with
independent photometric measurements that are dominated by Poisson noise. The
net effect is a modest ~4% increase in the transiting planet yield compared to
assuming all planets have circular orbits. When intrinsic variability of the
star or correlated photometric measurements are the dominant source of noise,
the transit detectability is independent of the transit duration. In this case
the transit yield is ~25% higher than that predicted under the assumption of
circular orbits. Since the Kepler search for Earth-sized planets in the
habitable zone of a Solar-type star is limited by intrinsic variability, the
Kepler mission is expected to have a ~25% higher planet yield than that
predicted for circular orbits if the Earth-sized planets have an orbital
eccentricity distribution similar to the currently known Jupiter-mass planets.
