  In this work, we investigate the accuracy of various approximate expressions
for the transit duration of a detached binary against the exact solution, found
through solving a quartic equation. Additionally, a new concise approximation
is derived, which offers more accurate results than those currently in the
literature. Numerical simulations are performed to test the accuracy of the
various expressions. We find that our proposed expression show yields a >200%
improvement in accuracy relative to the most previously employed expression. We
derive a new set of equations for retrieving the lightcurve parameters and
consider the effect of falsely using circular expressions for eccentric orbits,
with particularly important consequences for transit surveys. The new
expression also allows us to propose a new lightcurve fitting parameter set,
which minimizes the mutual correlations and thus improves computational
efficiency. The equation is also readily differentiated to provide analytic
expressions for the transit duration variation (TDV) due to secular variations
in the system parameters, for example due to apsidal precession induced by
perturbing planets.

Earth and Planetary Astrophysics