托勒密和乌鲁贝格的星表：机读版本以及与现代依巴谷星表的比较
The star catalogues of Ptolemaios and Ulugh Beg: Machine-readable versions and comparison with the modern Hipparcos Catalogue
摘要：
在古代晚期和整个中世纪，恒星在天球上的位置是从托勒密的星表中获得的。1437年，一份基于新测量的星表出现了，其中包括Ulugh Beg的位置和10世纪天文学家al-Sufi的星等。我们根据图默（1998）和诺贝尔（1917）的版本提供了这两个星表的机器可读版本，并通过与现代依巴谷星表的比较来确定其精度。星表中的星等与现代视觉星等有很好的相关性;托勒密的“微弱”指示被发现对应于他的星等5和6。对经度/纬度中的误差分布的高斯拟合给出了范围内的宽度sigma ~ 27 arcmin / 23 arcmin| Delta lambda，Delta beta| Ptolemaios <50弧分，Ulugh Beg的sigma约为22弧分/18弧分。符合范围|Delta lambda，Delta beta| <100弧分的宽度大10- 15%，表明误差分布比高斯分布更宽。位置误差超过150弧分的恒星比例，托勒密约为2%，乌卢贝格约为0.1%;未识别恒星的数量，托勒密约为1颗，乌卢贝格约为3颗。这些数字证明了这两个星表（由图默和诺贝尔编辑）的优秀质量。
英文摘要：
In late antiquity and throughout the middle ages, the positions of stars on the celestial sphere were obtained from the star catalogue of Ptolemaios. A catalogue based on new measurements appeared in 1437, with positions by Ulugh Beg, and magnitudes from the 10th-century astronomer al-Sufi. We provide machine-readable versions of these two star catalogues, based on the editions by Toomer (1998) and Knobel (1917), and determine their accuracies by comparison with the modern Hipparcos Catalogue. The magnitudes in the catalogues correlate well with modern visual magnitudes; the indication `faint' by Ptolemaios is found to correspond to his magnitudes 5 and 6. Gaussian fits to the error distributions in longitude / latitude give widths sigma ~ 27 arcmin / 23 arcmin in the range |Delta lambda, Delta beta|<50 arcmin for Ptolemaios and sigma ~ 22 arcmin /18 arcmin in Ulugh Beg. Fits to the range |Delta lambda, Delta beta|<100 arcmin gives 10-15 per cent larger widths, showing that the error distributions are broader than gaussians. The fraction of stars with positions wrong by more than 150 arcmin is about 2 per cent for Ptolemaios and 0.1 per cent in Ulugh Beg; the numbers of unidentified stars are 1 in Ptolemaios and 3 in Ulugh Beg. These numbers testify to the excellent quality of both star catalogues (as edited by Toomer and Knobel).
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