Investigations of approximate expressions for the transit duration

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.