Both classical and relativistic weak-field and slow-motion perturbations to planetary orbits can be treated as perturbative corrections to the Keplerian model. In particular, tidal forces and General Relativity (GR) induce small precession rates of the apsidal line. Accurate measurements of these effects in transiting exoplanets could be used to test GR and to gain information about the planetary interiors. Unfortunately, models for transiting planets have a high degree of degeneracy in the orbital parameters that, combined to the uncertainties of photometric transit observations, results in large errors on the determinations of the argument of periastron and precludes a direct evaluation of the apsidal line precession. Moreover, tidal and GR precession time-scales are many order of magnitudes larger than orbital periods, so that on the observational time-spans required to cumulate a precession signal enough strong to be detected, even small systematic errors in transit ephemerides add up to cancel out the tiny variations due to precession. Here we present a more feasible solution to detect tidal and GR precession rates through the observation of variations of the time interval (Δτ) between primary and secondary transits of hot Jupiters and propose the most promising target for such detection, WASP-14 b. For this planet we expect a cumulated $\Delta \tau \, \approx$ −250 s, due to tidal and relativistic precession, since its first photometric observations.

中文翻译：

---

探测过境热木星中的广义相对论轨道进动

对行星轨道的经典和相对论弱场和慢运动扰动都可以视为对开普勒模型的扰动校正。特别是，潮汐力和广义相对论 (GR) 会导致近端线的进动率很小。对凌日系外行星中这些影响的准确测量可用于测试 GR 并获得有关行星内部的信息。不幸的是，凌日行星的模型在轨道参数上具有高度的简并性，再加上光度凌日观测的不确定性，导致近星体参数的确定存在很大误差，并且排除了对近点线进动的直接评估。此外，潮汐和 GR 进动时间尺度比轨道周期大许多数量级，因此，在累积足够强以被检测到的进动信号所需的观测时间跨度上，即使是凌日星历中的小系统误差加起来也会抵消进动引起的微小变化。在这里，我们提出了一种更可行的解决方案，通过观察热木星初级和次级凌日之间的时间间隔（Δτ）的变化来检测潮汐和 GR 进动率，并提出了最有希望的检测目标，WASP-14 b。对于这颗行星，由于潮汐和相对论进动，自其第一次光度观测以来，我们预计会出现累积的 $\Delta \tau \，\约 -250 秒。在这里，我们提出了一种更可行的解决方案，通过观察热木星初级和次级凌日之间的时间间隔（Δτ）的变化来检测潮汐和 GR 进动率，并提出了最有希望的检测目标，WASP-14 b。对于这颗行星，由于潮汐和相对论进动，自其第一次光度观测以来，我们预计会出现累积的 $\Delta \tau \，\约 -250 秒。在这里，我们提出了一种更可行的解决方案，通过观察热木星初级和次级凌日之间的时间间隔（Δτ）的变化来检测潮汐和 GR 进动率，并提出了最有希望的检测目标，WASP-14 b。对于这颗行星，由于潮汐和相对论进动，自其第一次光度观测以来，我们预计会出现累积的 $\Delta \tau \，\约 -250 秒。