One of the greatest astronomers of Islam, al-Battānī (Albatenius, Albategni, or Albategnius of the Latin West, d. ca. 929 C.E.), declares that astronomy is the most noble of the sciences, elevated in dignity, and second only to the science of religious law (Sayılı, 1960, p. 15). This praise of the discipline is not merely a practitioner's claim; it also embodies a historical truth.

Indeed, astronomy is the only natural science that escaped the censure of the medieval Muslim opponents of secular sciences (ʿulūm al-awāʿil) and found a home in mosques, receiving the blessing of mainstream religious circles, and it is virtually the only Islamic hard science that lasted well into the modern period, continuing vigorously and fruitfully long after the Mongol sack of Baghdad, when much of Islamic scientific activity began to decline. Moreover, because of its traditional link with astrology and its utility in matters such as calendar reform, the determination of the direction of prayer (qiblah), and the calculation of the times of daily prayers, Islamic astronomy enjoyed the enthusiastic and undiminished patronage of rulers and nobles throughout its history. In the internal perspective of the science, astronomy is owed credit for the birth of trigonometry and other important developments in mathematics, particularly in quantitative techniques and geometry, since all these mathematical disciplines were originally subservient to the needs of astronomers. Finally, it should be noted that astronomy was a truly international enterprise of Islam, a collaborative effort involving people all over the Islamic world, including experts from China and India. It is evident, then, that al-Battānī 's claim is hardly exaggerated.

Origins to Ptolemaicization

The origins of Islamic astronomy are intricately eclectic. The earliest Arabic treatises on this subject, sets of astronomical tables known as the zīj, were written in the first half of the eighth century C.E. in Sind and Qandahār. These treatises were based on Sanskrit sources, but they have been found to incorporate some Pahlavi material as well. Such derivations from Indian and Iranian works, which constitute the first phase of Islamic astronomy, introduced many concepts of Greek mathematical astronomy to the Arabic world—concepts that were largely non-Ptolemaic, having already reached India and Iran through circuitous routes and having been modified by local traditions. A further infusion of Indian and Iranian material marks the second phase of Islamic astronomy, but this was also the time when the works of the famous Greek astronomer Ptolemy (d. 161 C.E.) and the Pahlavi Zīk-i Shahryārān (Arabic, Zīj al-Shāh) were translated into Arabic. This activity took place during the reigns of ʿAbbāsid caliphs al-Manṣūr (r. 754–775 C.E.) and Hārūn al-Rashīd (r. 786–809), a period that also saw the emergence of a sustained Sindhind Arabic tradition growing out of the translation of a Sanskrit astronomical text, presumably that entitled Mahāsiddhānta.

During the early ʿAbbāsid period, three astronomical systems were thus pursued concurrently: the Indian (Sindhind); the Iranian (Zīj al-Shāh); and the Ptolemaic. These systems were in conflict at many points, and the Islamic astronomical activity of this period is characterized by constant efforts to reconcile them. Astronomers soon concluded that the Ptolemaic system was superior to all others known to them. Thus, with al-Battānī marking the turning point, by the beginning of the tenth century Islamic astronomy had undergone a complete Ptolemaicization: newer and better Arabic translations of Ptolemy's Almagest made by the Nestorian Christian Isḥāq ibn Ḥunayn (d. 910/11 C.E.) and the “pagan” Thābit ibn Qurrah (d. 901 C.E.) were available; Ptolemy 's Planetary Hypotheses had also been rendered into Arabic by Thābit; and the Sindhind and Shāh traditions were finally relegated to history. The story of Islamic astronomy from this point is characterized by what historian of science Thomas Kuhn would describe as “puzzle-solving” within a Ptolemaic paradigm.

Muslim astronomy in Spain was very important, in both the production of instruments and in compilations of celestial tables: Ibn al-Raqqām (d. 1315) improved gnomonics and sundials; the Andalusian polymath Abu al-Ṣalt Umayyah ibn Abu al-Ṣalt (d. ca. 1134) was probably responsible for the diffusion of the astrolabe in the Mashriq; and the most famous Arab Spanish astronomer Ibn al-Zarqālī or Azarquiel (d. 1100) seems to have been the first to design a universal astrolabe. The Toledan Tables (zīj) were compiled about 1069 by a group of Toledan astronomers, led by Abū al-Qasim Saʿid and including Ibn al-Zarqālī. The Toledan Tables were also very influential in Western Europe until the scientific revolution because they supported the so-called theory of trepidation (i.e., that the obliquity of the ecliptic and the velocity of procession are not constant). Obviously, the zīj were also very useful for astrological predictions, and prominent astrologers like al-Maghribī (d. 1283) introduced some innovations in them, especially to correct calendars.

Theoretical Innovation

Let us now, following the lead of contemporary historians, set up the theoretical problem to which these different systems offered different solutions. Consider two rotating wheels. A larger wheel (the deferent, al-ḥāmil) has a stationary center E and a point S on its rim. Let S, namely the point rotating on the circumference of the deferent, be the center of a smaller wheel (the epicycle, al-tadwīr). Let P be a point on the rim of the smaller rotating wheel. Then, if P 's rate of rotation is properly adjusted, it will appear to an observer at E, the center of the deferent, as periodically advancing and receding as the wheels turn. If in this arrangement S represents the sun, E the earth, and P a planet, then this ancient geocentric model of wheels upon wheels provides a valid if simplified explanation of the looped paths of the planets as seen from the earth.

In practice, however, this mechanism needed adjustments to bring it into accord with the observed planetary motions. Indeed, Ptolemy managed to make a drastic improvement in the correspondence between theory and observation by introducing into the arrangement a geometric device known as the equant (muʿaddal al-masīr). Ptolemy shifted the earth a small distance from the center of the deferent E to, say, E_g—thereby making the deferent eccentric with respect to the Earth. Furthermore, from E he displaced the center of the uniform motion of S to a rigorously calculated point O. Thus the motion of S was uniform with respect neither to E nor to E_g, but with respect to an imaginary point O, and this O was Ptolemy's fateful equant.

Ibn al-Haytham (known as Alhazen in Latin, d. 1039), the scientific giant of Islam, wrote an attack on Ptolemy 's planetary theory: if Ptolemy 's system was not merely an abstract geometrical model but represented the real configuration of the heavens—as Ptolemy had claimed it did—then it violated the accepted classical principle of uniform velocity for all celestial bodies, a principle that the Greek astronomer had himself espoused. Indeed, in his Planetary Hypotheses Ptolemy had conceived of the observed motions of the planets as produced by the combined motions of corporeal spherical shells in which the planets were embedded. The idea of an eccentric celestial shell was unacceptable to Ibn al-Haytham, as it was to many astronomers who shared his views.

The subsequent history of Islamic mathematical astronomy is a chronicle of attempts to modify the Ptolemaic system so that it would accord more accurately with observations while at the same time preserving the principle of uniform circular motion.

In Muslim Spain, scientists and philosophers like Ibn Bājjah (d. 1139), Ibn Ṭufayl (d. 1185), and the famous Averroёs (Ibn Rushd, d. 1198) criticized Ptolemaic theory, charging it with not truly representing the physical structure of the universe. Ibn Isḥāq al-Biṭrūjī (d. 1204; a disciple of Ibn Ṭufayl) used notions taken from Neo-Platonic rather then Aristotelian dynamics (like the impetus theory) to better explain the transmission of the daily rotation from the Prime Mover to the planetary spheres. Finally, the Andalusian al-Zarqālī (d. 1087) seems to have been the first astronomer to dispute the notion of an astronomy based on circles—introducing a new astronomy of noncircular curves.

It was more than two centuries after Ibn al-Haytham that Naṣīr al-Dīn al-Ṭūsī, the head of the celebrated Marāgheh observatory built by Hülegü Khan in 1259, inaugurated outstandingly successful efforts along these lines. Al-Ṭūsī appears to have been the first to recognize that if one circle C₁ with a diameter D rolls inside another circle C₂ with a diameter 2D, then any point on the circumference of C₁ describes the diameter of C₂. In modern terminology this device can be considered to be a linkage of two equal and constant-length vectors with constant angular velocity (one moving twice as fast as the other); this is the famous “Ṭūṣī couple.” By means of this device the observed phenomena were explained by Marāgheh astronomers solely in terms of a combination of uniform circular motions. The apex of these Marāgheh techniques is embodied in the work of Quṭb al-Dīn al-Shīrāzī (d. 1311), who, eliminating the Ptolemaic equant, constructed a highly accurate geometrical model for Mercury, by far the most errant planet visible to the naked eye. In the middle of the fourteenth century the astronomer Ibn al-Shāṭir, a muwaqqit (timekeeper) at a mosque in Damascus, further refined the al-Ṭūsī innovations and managed to develop for the Moon and Mercury new models that were far more accurate than those of Ptolemy.

Historians have pointed out that the mathematical devices created by the Marāgheh scientists and the planetary models constructed by the muwaqqit reappear two centuries later in the work of Copernicus. In particular, Copernicus 's models of the Moon and Mercury have been found to be identical with those of Ibn al-Shāṭir; moreover, both astronomers employ the Ṭūsī couple, and both eliminate the equant in essentially the same manner. Here the possibility of historical transmission has not been ruled out.

Observational Astronomy

Characteristic of the Islamic astronomical tradition is the separation of theoretical exercises from observational activity. Observational astronomy thus followed its own course, guided by the Ptolemaic concept of testing (miḥnah or iʿtibār), which requires constantly renewed corrections of the observational data collected by preceding generations. Thus from the early ʿAbbāsid period, astronomical observation was pursued intensively in Islam, with numerous observatories built over the centuries throughout the Islamic world from Baghdad to Sāmarrāʿ and Damascus, and from Egypt to Persia and Central Asia. Lunar and solar eclipses, meridian transits of the sun, transits of fixed stars, planetary positions, and conjunctions—these were all part of the observational repertoire of Islamic astronomy.

Among the observatories the one at Marāgheh stands out. Indeed, it is regarded as the first observatory in the full sense of the word. It employed a staff of about twenty astronomers, including one from China; it was supported by a library and a workshop for storing, constructing, and repairing astronomical instruments. These instruments included a mural quadrant and an armillary astrolabe, as well as solstitial and equinoctial armillaries; also included was a new instrument constructed by the Damascene al-ʿUrḍī, which had two quadrants for simultaneous measurement of the horizon coordinates of two stars. Historians have noticed striking similarities between al-ʿUrḍī 's observational devices and those of the Danish astronomer Tycho Brahe (d. 1601), even though the results of the latter are unprecedentedly precise.

Long after the Copernican Revolution, Islamic observational astronomy continued in the geocentric Ptolemaic tradition. In the 1570s a major observatory was built in Istanbul. Then, in imitation of the Samarkand observatory founded by Ulugh bek in 1420, the Indian Maharaja of Amber (1693–1743) built as many as five different observatories—at Jayapura, Ujjain, Delhi, Mathura, and Varanasi (Benares)—with the purpose of harmonizing Indian astronomy with the Islamic Ptolemaic tradition. The later Islamic observatories were not altogether fruitless exercises, because they contributed many observational techniques instruments and organizational features to European astronomy. Even though Islamic astronomy did not take the daring philosophical step of breaking out of the geocentric Ptolemaic system, it has to its credit numerous great achievements: it gave to the world of science the astronomical observatory; it created trigonometry; at Marāghah it developed new instruments and powerful mathematical techniques; and it constantly improved and corrected astronomical parameters. By consensus of historians, Islamic astronomers were the best of their age.