Properties of analytic transit light-curve models

In this paper, a set of analytic formulae is presented with which the partial derivatives of the flux obscuration function can be evaluated - for planetary transits and eclipsing binaries - under the assumption of quadratic limb darkening. The knowledge of these partial derivatives is crucial for many of the data modelling algorithms and estimates of the light-curve variations directly from the changes in the orbital elements. These derivatives can also be utilized to speed up some of the fitting methods. A gain of similar to 8 in computing time can be achieved in the implementation of the Levenberg-Marquardt algorithm, relative to using numerical derivatives.