Determination of the longitude difference between Baghdad and Khwarezm using a lunar eclipse (the method of Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani)

Rizoi Bakhromzod

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arXiv · 2601.15837

Determination of the longitude difference between Baghdad and Khwarezm using a lunar eclipse (the method of Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani)

Rizoi Bakhromzod

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Abstract

This paper examines how, in the tenth century, medieval Iranian scholars Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani determined the difference in geographical longitude between the cities of Baghdad and Khwarezm through simultaneous observation of a lunar eclipse. Brief academic biographies of these scholars are presented, with emphasis on their contributions to mathematics and astronomy. The study discusses the importance of determining geographical coordinates - especially longitude - in the science of the 10th-11th centuries, provides an overview of the methods of coordinate determination available at the time, and highlights the problem of synchronizing remote observations prior to the advent of electronic communication. Particular attention is devoted to a detailed analysis of the method based on observing a lunar eclipse to simultaneously measure longitude differences: the necessary conditions and organization of the experiment, the instruments employed, the mathematical calculations, and error estimates are described. The longitude difference obtained by al-Biruni and al-Buzjani is compared with modern values. The conclusion discusses the scientific significance of this method for the history of science and astronomy.

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Rizoi Bakhromzod. 2026-01-22. Determination of the longitude difference between Baghdad and Khwarezm using a lunar eclipse (the method of Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani). https://arxiv.org/abs/2601.15837

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