凌日系外行星某些观测量的经典和相对论长期时间变化
Classical and relativistic long-term time variations of some observables for transiting exoplanets
摘要：
我们解析地计算出了沿椭圆轨道运行的凌日系外行星的两体类点牛顿加速度的经典和广义相对论动力学扰动引起的一些直接可观测量Y的长期时间变化，即在一个轨道旋转上平均的时间变化。更具体地说，观测量$Y$，我们处理的凌日持续时间，径向速度和时间间隔之间的主要和次要的日食。考虑的动力学效应是恒星和行星的离心扁率、它们的潮汐隆起相互作用、遥远的第三体X和广义相对论（史瓦西和兰斯-蒂林）。我们考虑到的影响，由于所有的开普勒轨道元素的扰动参与一致和统一的方式。首先，我们明确地计算它们的瞬时时间变化，由于考虑的动力学效应，并将它们插入到Y的瞬时变化的一般表达式中;然后，我们取一个轨道旋转的整体平均值，即所获得的瞬时速率$\dot Y(t)$专门用于所考虑的扰动。相反，有些混合表达式可以经常在文献中找到：在它们中，通常，近星点的长期岁差只是直接插入瞬时公式。给出了一个典型的恒星-行星的情况下，所获得的结果的数值评估，并在10年的时间跨度与预期的观测精度进行比较。我们的结果，在原则上，也适用于其他天文场景。它们可以允许，例如，设计各种引力理论的测试，用我们太阳系中的自然和人造物体。（节录）
英文摘要：
We analytically work out the long-term, i.e. averaged over one orbital revolution, time variations of some direct observable quantities Y induced by classical and general relativistic dynamical perturbations of the two-body pointlike Newtonian acceleration in the case of transiting exoplanets moving along elliptic orbits. More specifically, the observables $Y$ with which we deal are the transit duration, the radial velocity and the time interval between primary and secondary eclipses. The dynamical effects considered are the centrifugal oblateness of both the star and the planet, their tidal bulges mutually raised on each other, a distant third body X, and general relativity (both Schwarzschild and Lense-Thirring). We take into account the effects due to the perturbations of all the Keplerian orbital elements involved in a consistent and uniform way. First, we explicitly compute their instantaneous time variations due to the dynamical effects considered and plug them in the general expression for the instantaneous change of Y; then, we take the overall average over one orbital revolution of the so-obtained instantaneous rate $\dot Y(t)$ specialized to the perturbations considered. Instead, somewhat hybrid expressions can be often found in literature: in them, the secular precession of, typically, the periastron only is straightforwardly inserted into instantaneous formulas. Numerical evaluations of the obtained results are given for a typical star-planet scenario and compared with the expected observational accuracies over a time span 10 yr long. Our results are, in principle, valid also for other astronomical scenarios. They may allow, e.g., for designing various tests of gravitational theories with natural and artificial bodies in our solar system. (Abridged)
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