Ibn al-Zarqālluh’s discovery of the annual equation of the Moon

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
S. Mohammad Mozaffari
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Abstract

Ibn al-Zarqālluh (al-Andalus, d. 1100) introduced a new inequality in the longitudinal motion of the Moon into Ptolemy’s lunar model with the amplitude of 24′, which periodically changes in terms of a sine function with the distance in longitude between the mean Moon and the solar apogee as the variable. It can be shown that the discovery had its roots in his examination of the discrepancies between the times of the lunar eclipses he obtained from the data of his eclipse observations over a 37-year period in the latter part of the eleventh century and the predictions made on the basis of the lunar theories in the Mumta\(\textit{\d{h}}\)an zīj (Baghdad, ca. 830) and al-Battānī’s zīj (Raqqa, d. 929), which were available to him at the time. What Ibn al-Zarqālluh found is, in fact, a special case of the annual equation of the Moon, which is applicable in the oppositions and, thus, in the lunar eclipses. The inequality was discovered independently by Tycho Brahe (d. 1601) and Johannes Kepler (d. 1630). As Ibn Yūnus (d. 1009) reports in his \(\textit{\d{H}}\)ākimī zīj, Ibn al-Zarqālluh’s medieval Middle Eastern predecessors, the Persian astronomers Māhānī (d. ca. 880) and Nayrīzī (d. 922) as well as ‘Alī b. Amājūr (fl. ca. 920), were already acquainted with the problem of the eclipse timing errors, but it had remained unresolved until Ibn Yūnus provided a provisional, and incorrect, solution by reducing the size of the lunar epicycle. As we argue, the diverse ways to tackle the same problem stem from two different methodologies in astronomical reasoning in the traditions developed separately in the Eastern and Western regions of the medieval Islamic domain.

Abstract Image

Abstract Image

伊本-扎尔卡鲁赫发现月球的年度方程
Ibn al-Zarqālluh(al-Andalus,卒于 1100 年)在托勒密的月球模型中引入了一个新的月球纵向运动不等式,其振幅为 24′,该振幅以月亮平均值与太阳远地点之间的经度距离为变量,通过正弦函数周期性地变化。可以证明,这一发现源于他对 11 世纪后半期 37 年月食观测数据中得出的月食时间与根据《Mumta(textit{d{h}\)an zīj》(巴格达,约 830 年)和《al-Battāan zīj》(巴格达,约 830 年)中的月球理论做出的预测之间差异的研究。830 年)和 al-Battānī'szīj(拉卡,卒于 929 年)中的月球理论为基础。Ibn al-Zarqālluh 发现的实际上是月球年方程的一个特例,它适用于对冲,因此也适用于月食。这个不等式分别由第谷-布拉赫(卒于 1601 年)和约翰内斯-开普勒(卒于 1630 年)发现。正如伊本-尤努斯(Ibn Yūnus,卒于 1009 年)在他的 \(textit\{d{H}})ākimī zīj 中所述,伊本-扎尔卡鲁赫的中世纪中东前辈,波斯天文学家马哈尼(Māhānī,卒于约 880 年)和纳伊尔齐(Nayrīzī,卒于 922 年)以及'Ali b. Amājūr (卒于约 880 年)都发现了月食的不等式。Amājūr (约卒于 920 年),都已了解月食时间误差的问题,但直到伊本-尤努斯 (Ibn Yūnus)提供了一个临时的、不正确的解决方案,即缩小月球周径,这个问题才得以解决。正如我们所论证的那样,解决同一问题的不同方法源于中世纪伊斯兰教东西部地区分别形成的传统中两种不同的天文推理方法。
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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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