Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of its host stars and on the dynamical properties of the planetary orbit. The trajectory of a planet in a double star system can be determined, approximating stars and planet with point masses, by solving numerically the equations of motion of the classical three-body system. In this study, we analyze a large data set of planetary orbits, made up with high precision long integration at varying: the mass of the planet, its distance from the primary star, the mass ratio for the two stars in the binary system, and the eccentricity of the star motion. To simulate the gravitational dynamics, we use a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term integration. In our data analysis, we evaluate if an orbit is stable or not and also provide the statistics of different types of instability: collisions with the primary or secondary star and planets ejected away from the binary star system. Concerning the stability, we find a significant number of orbits that are only marginally stable, according to the classification introduced by Musielak et al. (Astron. Astrophys. 434:355, 2005). For planets of negligible mass, we estimate the critical semi-major axis \(a_{c}\) as a function of the mass ratio and the eccentricity of the binary, in agreement with the results of Holman and Wiegert (Astron. J. 117:621, 1999). However we find that for very massive planets (Super-Jupiters) the critical semi-major axis decrease in some cases by a few percent, compared to cases in which the mass of the planet is negligible.

许多系外行星是在双星系统的内部或环绕双星轨道中发现的。这颗行星是否适合居住取决于其表面是否有可能保持液态水，因此取决于其宿主恒星的光度和行星轨道的动力学特性。通过数值求解经典三体系统的运动方程，可以确定双星系统中行星的轨迹，近似恒星和具有点质量的行星。在这项研究中，我们分析了大量行星轨道数据集，这些数据集由不同的高精度长积分组成：行星的质量、它与主恒星的距离、双星系统中两颗恒星的质量比，以及恒星运动的偏心率。为了模拟引力动力学，我们使用 15 阶积分方案（IAS15，可在 REBOUND 框架内使用），为长期积分提供最佳解决方案。在我们的数据分析中，我们评估轨道是否稳定，并提供不同类型不稳定的统计数据：与主星或次星的碰撞以及从双星系统中弹出的行星。关于稳定性，根据 Musielak 等人介绍的分类，我们发现大量轨道只是略微稳定。(Astron. Astrophys. 434:355, 2005)。对于质量可以忽略不计的行星，我们估计 我们评估轨道是否稳定，并提供不同类型不稳定性的统计数据：与主星或次星的碰撞以及从双星系统中弹出的行星。关于稳定性，根据 Musielak 等人介绍的分类，我们发现大量轨道只是略微稳定。(Astron. Astrophys. 434:355, 2005)。对于质量可以忽略不计的行星，我们估计 我们评估轨道是否稳定，并提供不同类型不稳定性的统计数据：与主星或次星的碰撞以及从双星系统中弹出的行星。关于稳定性，根据 Musielak 等人介绍的分类，我们发现大量轨道只是略微稳定。(Astron. Astrophys. 434:355, 2005)。对于质量可以忽略不计的行星，我们估计临界半长轴\(a_{c}\)作为质量比和二元偏心率的函数，与 Holman 和 Wiegert 的结果一致（Astron. J. 117:621, 1999）。然而，我们发现对于非常大的行星（超级木星），与行星质量可以忽略不计的情况相比，在某些情况下，临界半长轴会减少几个百分点。