How did Islamic observatories at Maragheh and Samarkand advance astronomy?

Islamic observatories at Maragheh and Samarkand were pivotal in advancing astronomy by fostering critical engagement with Ptolemaic theory and achieving unprecedented observational precision.12

The Maragheh Observatory

Established around 1260, the Maragheh observatory became a center for creative mathematical modeling. Astronomers there, such as Nasir al-Din al-Tusi, sought to resolve philosophical inconsistencies in Ptolemy’s work, specifically regarding the use of the equant point and non-uniform circular motions. Al-Tusi developed the "al-Tusi couple," a mechanism using two circular motions to produce linear oscillation, which allowed for more physically plausible planetary models. His student, al-Shirazi, further refined these models by using minor epicycles to eliminate the need for the equant point.12

The Samarkand Observatory

The observatory at Samarkand, founded by Ulugh Beg around 1420, was the most productive in the Islamic world. It advanced astronomy through:23
* Precision Instrumentation: Equipped with a large quadrant, astronomers created a highly accurate star catalog.2
* Mathematical Mastery: Scholars like al-Kashi achieved remarkable computational precision, such as calculating the sine of 1° to 10 sexagesimal places, which was essential for the accuracy of Ulugh Beg’s Astronomical Tables.3
* Correction of Ptolemy: Through systematic observation, Ulugh Beg and his team identified and corrected several errors in the computations of Ptolemy.4