  Transiting planet lightcurves have historically been used predominantly for
measuring the depth and hence ratio of the planet-star radii, p. Equations have
been previously presented by Seager & Mallen-Ornelas (2003) for the analysis of
the total and trough transit lightcurve times to derive the ratio of semi-major
axis to stellar radius, a/R*, in the case of circular orbits. Here, a new
analytic model is proposed which operates for the more general case of an
eccentric orbit. We aim to investigate three major effects our model predicts:
i) the degeneracy in transit lightcurve solutions for eccentricity, e>0 ii) the
asymmetry of the lightcurve and the resulting shift in the mid-transit time,
Tmid iii) the effect of eccentricity on the ingress and egress slopes. It is
shown that a system with changing eccentricity and inclination may produce a
long period transit time variation (LTTV). Furthermore, we use our model in a
reanalysis of HD 209458 b archived data by Richardson et al. (2006), where we
include the confirmed non-zero eccentricity and derive a 24 micron planetary
radius of R_P = 1.275 +- 0.082 R_J (where R_J = 1 Jovian radius), which is 1%
larger than is we assume a circular orbit.
