Abstract Regions of Hill stability were determined using the full three-body theory for the planetary candidates that were found by the Kepler mission to lie in the Habitable Zone of the host star with radii larger than 3 Earth radii. The values obtained give a more accurate assessment of the sphere of influence of a planet than does the Hill radius using the restricted three-body expression. The values given by the two estimates for circular orbits are compared. The variation in the full three-body Hill regions were examined for a variety of possible moon masses and orbital eccentricities and inclinations. It was found that the critical moon planet separation decreased with increased moon orbital eccentricity and inclination but to a far greater extent when the planetary orbital eccentricity increased suggesting they would lie inside the Roche limit and are unlikely to have formed or exist now. The angular separation of the moon and planet and the radial velocity amplitudes of the planets likely to be observed are also affected. This is important for future observations and missions. It was also found that the giant planets in the habitable zone lie in a narrow band that can be fitted by a linear regression relation between log10(Planet luminosity) and log10 (Planet temperature) with a slope of 3.34.

中文翻译：

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宜居带开普勒巨行星周围可能系外卫星轨道的限制

摘要 对于开普勒任务发现的位于主星宜居带内半径大于地球半径 3 的候选行星，希尔稳定区域是使用完整的三体理论确定的。获得的值比使用受限三体表达式的希尔半径更准确地评估行星的影响范围。对圆轨道的两个估计值给出的值进行比较。针对各种可能的卫星质量以及轨道偏心率和倾角，检查了完整的三体山丘区域的变化。发现临界月球行星间距随着月球轨道偏心率和倾角的增加而减小，但当行星轨道偏心率增加时，其程度要大得多，这表明它们将位于罗氏极限内，现在不太可能形成或存在。月球和行星的角距以及可能观测到的行星的径向速度幅度也受到影响。这对未来的观测和任务很重要。还发现宜居带中的巨行星位于一个窄带中，可以通过斜率为3.34的log10（行星光度）和log10（行星温度）之间的线性回归关系拟合。月球和行星的角距以及可能观测到的行星的径向速度幅度也受到影响。这对未来的观测和任务很重要。还发现宜居带中的巨行星位于一个窄带中，可以通过斜率为3.34的log10（行星光度）和log10（行星温度）之间的线性回归关系拟合。月球和行星的角距以及可能观测到的行星的径向速度幅度也受到影响。这对未来的观测和任务很重要。还发现宜居带中的巨行星位于一个窄带中，可以通过斜率为3.34的log10（行星光度）和log10（行星温度）之间的线性回归关系拟合。