论文标题
回到基础知识：使用轨道运动的泰勒系列扩展加速系外行星过境建模
Going back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion
论文作者
论文摘要
大量的系外行星过境模型评估时间花费在计算行星及其宿主星之间的投影距离。对于圆形轨道来说，这是一个相对较快的操作，但对于偏心轨道而言，这是较慢的。但是，由于地球的位置及其时间衍生物在轨道阶段的任何特定点都是恒定的，因此可以通过将地球的$ x $ x $ x $ x $ x $ y $位置扩展到中型交易中的泰勒系列中，在过境的附近迅速而准确地计算出预计的距离。 Calculating the projected distance for an elliptical orbit using the four first time derivatives of the position vector (velocity, acceleration, jerk, and snap) is $\sim100$ times faster than calculating it using the Newton's method, and also significantly faster than calculating $z$ for a circular orbit because the approach does not use numerically expensive trigonometric functions.预计距离计算中的速度增长会导致2-25倍的运输模型评估速度，具体取决于运输模型的复杂性和轨道偏心率。使用数值差异计算四个位置衍生物的计算将$ \ sim1 \，μ$ s带有现代笔记本电脑，只需要一次对给定的轨道进行一次，并且对于物理上合理的轨道参数参数空间的主要部分，近似值将近似值引入1〜ppm的最大误差。
A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one. However, because the planet's position and its time derivatives are constant for any specific point in orbital phase, the projected distance can be calculated rapidly and accurately in the vicinity of the transit by expanding the planet's $x$ and $y$ positions in the sky plane into a Taylor series at mid-transit. Calculating the projected distance for an elliptical orbit using the four first time derivatives of the position vector (velocity, acceleration, jerk, and snap) is $\sim100$ times faster than calculating it using the Newton's method, and also significantly faster than calculating $z$ for a circular orbit because the approach does not use numerically expensive trigonometric functions. The speed gain in the projected distance calculation leads to 2-25 times faster transit model evaluation speed, depending on the transit model complexity and orbital eccentricity. Calculation of the four position derivatives using numerical differentiation takes $\sim1\,μ$s with a modern laptop and needs to be done only once for a given orbit, and the maximum error the approximation introduces to a transit light curve is below 1~ppm for the major part of the physically plausible orbital parameter space.
