The orbital elements of each planet are the eccentricity and the direction of the apsidal line of its orbit defined by the ecliptic longitude of either of its apses, i.e., the two points on its orbit where the planet is either furthest from or closest to the Earth, which are called the planet’s apogee and perigee. In the geocentric view of the solar system, the eccentricity of Venus is a bit less than half of the solar one, and its apogee is located behind that of the Sun. Ptolemy correctly found that the apogee of Venus is behind that of the Sun, but determined the eccentricity of Venus to be exactly half the solar one. In the Indian Midnight System of Āryabhaṭa (b. ad 476), the eccentricity of Venus is assumed to be half the solar one, and also the longitudes of their apogees are assumed to be the same. This hypothesis became prevalent in early medieval Middle Eastern astronomy (ad 800–1000), where its adoption resulted in large errors of more than 10° in the values for the longitude of the apogee of Venus adopted by Yaḥyā b. Abī Manṣūr (d. ad 830), al-Battānī (d. ad 929), and Ibn Yūnus (d. ad 1007). In Western Islamic astronomy, it was used in combination with Ibn al-Zarqālluh’s (d. ad 1100) solar model with variable eccentricity, which only by coincidence resulted in accurate values for the eccentricity of Venus. In late Islamic Middle Eastern astronomy (from ad 1000 onwards), Āryabhaṭa’s hypothesis gradually lost its dominance. Ibn al-A‘lam (d. ad 985) seems to have been the first Islamic astronomer who rejected it. Late Eastern Islamic astronomers from the middle of the thirteenth century onwards arrived at the correct understanding that the eccentricity of Venus should be somewhat less than half of the solar one. Its most accurate medieval value was measured in the Samarqand observatory in the fifteenth century. Also, the values for the longitude of the apogee of Venus show a significant improvement in late Middle Eastern Islamic works, reaching an accuracy better than a degree in Khāzinī’s Mu‘tabar zīj, Ibn al-Fahhād’s ‘Alā’ī zīj, the Īlkhānī zīj, and Ulugh Beg’s Sulṭānī zīj.

中文翻译：

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中世纪伊斯兰天文学中金星的轨道要素：传统与观测精度之间的相互作用

每颗行星的轨道要素是其轨道的偏心率和由其任何一个近星点的黄道经度定义的近点线的方向，即其轨道上行星离地球最远或最近的两点，这被称为行星的远地点和近地点。在太阳系的地心视图中，金星的​​偏心率比太阳偏心小一半，而且它的远地点在太阳之后。托勒密正确地发现金星的远地点在太阳的远地点之后，但确定金星的离心率恰好是太阳的一半。在 Āryabhaṭa 的印度午夜系统（生于公元 476 年）中，金星的​​偏心率被假定为太阳偏心率的一半，并且它们的远地点经度也被假定为相同。这个假设在中世纪早期的中东天文学（公元 800-1000 年）中变得普遍，在那里它的采用导致了 Yaḥyā b 采用的金星远地点经度值的超过 10° 的大误差。Abī Manṣūr（公元 830 年）、al-Battānī（公元 929 年）和 Ibn Yūnus（公元 1007 年）。在西方伊斯兰天文学中，它与 Ibn al-Zarqālluh（公元 1100 年）的具有可变离心率的太阳模型结合使用，这只是巧合导致了金星离心率的准确值。在伊斯兰中东天文学后期（从公元 1000 年开始），Āryabhaṭa 的假设逐渐失去了主导地位。Ibn al-A'lam (d. ad 985) 似乎是第一个拒绝它的伊斯兰天文学家。从 13 世纪中叶开始，晚期东方伊斯兰天文学家得出了正确的理解，即金星的偏心率应该略小于太阳偏心率的一半。其最准确的中世纪数值是在 15 世纪的撒马尔罕天文台测量的。此外，金星远地点的经度值在中东伊斯兰晚期作品中显示出显着改进，其准确度高于 Khāzinī 的 Mu'tabar zīj、Ibn al-Fahhād 的 'Alā'ī zīj、Īlkhānī zīj和 Ulugh Beg 的 Sulṭānī zīj。