Newton was the first to provide a mathematical framework to describe the oblateness of the Earth, a framework later expended by Maclaurin, Jacobi, and Poincaré and applied to other astronomical objects. In the Solar System, the Jacobi triaxial ellipsoid has successfully described the shape of Haumea and Chariklo, while Ceres appears to be an oblate spheroid of the Maclaurin type. Beyond the Solar System, new exoplanets are being discovered almost daily showing vastly different characteristics (e.g. mass, temperature, eccentricity, radius, orbital period). Recently, Kepler-427b was shown to be a moderately oblate spheroid, and it is possible to imagine that certain exoplanets could be triaxial ellipsoids. Considering the wealth of data now available from the current and past missions whose aim is to hunt for new extra-solar systems, it has become vital to broaden the range of parameters to be estimated for a single exoplanet. In this paper, we present a new algorithm to model variations in transit light curves induced by ellipsoidal exoplanets, which will be ultimately released to the community as a MATLAB-based package. Most variations happen during the ingress and egress phase of the transit. Combining several transits can lead to the detection of oblateness by measuring the precession of the obliquity angle of the exoplanet over time. For the first time, we also model reflected light curves for ellipsoidal exoplanets.

牛顿是第一个提供描述地球扁率的数学框架的人，后来麦克劳林，雅各比和庞加莱扩展了该框架，并将其应用于其他天文物体。在太阳系中，雅可比三轴椭球成功地描述了Haumea和Chariklo的形状，而谷神星似乎是Maclaurin型的扁球体。除太阳系外，几乎每天都会发现新的系外行星，它们表现出截然不同的特征（例如质量，温度，离心率，半径，轨道周期）。最近，开普勒-427b被证明是中等扁球体，可以想象某些系外行星可能是三轴椭球体。考虑到目前和过去的任务旨在寻找新的太阳系外系统的大量数据，扩大单个系外行星估计参数的范围已变得至关重要。在本文中，我们提出了一种新的算法来建模由椭圆形系外行星引起的瞬态光曲线的变化，该算法最终将作为基于MATLAB的软件包发布到社区。大多数变化发生在过境的进出阶段。通过测量随着时间变化的系外行星倾斜角的进动，可以将几次过境组合起来可以检测到倾斜度。首次，我们还为椭圆形系外行星建立了反射光曲线模型。最终将作为基于MATLAB的软件包发布给社区。大多数变化发生在过境的进出阶段。通过测量随着时间变化的系外行星倾斜角的进动，可以将几次过境组合起来可以检测到倾斜度。首次，我们还为椭圆形系外行星建立了反射光曲线模型。最终将作为基于MATLAB的软件包发布给社区。大多数变化发生在过境的进出阶段。通过测量随着时间变化的系外行星倾斜角的进动，可以将几次过境组合起来可以检测到倾斜度。首次，我们还为椭圆形系外行星建立了反射光曲线模型。