There was always a very strong link between mathematics and astronomy in the ancient world. In Baghdad’s scholarly library, they collected astronomical calculations and theories from Greek literature (bought from Constantinople) that was based on earlier Babylonian work. They also brought in Sanskrit astronomy books from India. The Indian mathematical system may have come first from these astronomy books. Arabic and Persian translators absorbed them, and as they came to understand the numerical system, they wrote explanatory texts.
Ancient people focused on understanding and predicting the movement of the stars and planets so that they could mark days and hours of religious observance. Although beliefs varied, the general sense that God was looking down through the stars, and could only be known by studying them, seems universal. Astrology was part of astronomy; when it eventually came into Europe via Arabic science, it was taken to be as factual as the movements of the planets.
Greek scientists invented the astrolabe to use the stars to locate exactly where one stood on earth. Knowledge of the astrolabe persisted as the culture shifted to Byzantine dominance, and at least one work about it appeared in Syriac. Of course, these books came to Baghdad. Muslims had an additional religious belief to accommodate; they wanted to face the Kaaba in Mecca when they prayed.
The later “mariner’s astrolabe” for use at sea was not yet invented, and the general type seems to have been round, not a quarter-circle as later adopted in Europe. (I only wish I could explain these to you for real, but I don’t understand what an astrolabe does.)
The basic instrument was the round, flat mater, shaped like a shallow dish, with interchangeable plates called tympans. Each was made for a specific latitude and engraved with circles for altitude and azimuth. “Azimuth” is an Arabic word, a Muslim/Persian improvement. The top plate, the rete, was curiously cut so as to turn freely and point out significant stars. The mater’s edge had markings for hours and degrees; there was often a rotating straight-edge rule, too. A device on the back, the alidade, was used to sight stars; the back was also engraved with tables for calculation.
Baghdad’s scholarly library became the new center for astronomical research. Persian science (cf. “the Magi of the East”) had already been advanced. Now they translated Euclid and Ptolemy, updating the more ancient works with commentaries. (They thought Ptolemy was a Pharaoh.) They also resurrected a Greek idea for a celestial globe and created a spherical astrolabe.
Making the astrolabe in bronze or brass, not wood, was another significant improvement. Made of metal, it didn’t warp; it was more accurate, not to mention longer-lasting. The earliest extant metal astrolabe was found in Spain and dated to the Umayyad era when Cordoba was the capital.
Umayyad Spain was, of course, the entry point for the new wave of astronomical science to enter Europe. In cities like Barcelona, the new Arabic treatises could be translated into Latin. That’s why we sometimes note that Greek texts were preserved only through Arabic; the great Library of Alexandria held originals, but it burnt down; while later the House of Wisdom in Baghdad was destroyed by Mongols. The Latin translations of the Arabic translations are sometimes all we have left, preserved at cathedral schools and monastic libraries.