Al-Battani discovered the notions of trigonometrical ratios used today. Al-Biruni claimed the earth rotated around its own axis. Jabir Ibn Aflah made the first portable celestial sphere to measure and explain the movements of celestial objects.
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A review on Muslim Contribution to Astronomy by Salah Zaimeche
The work of the Muslim astronomers who lived between 9th and 12th centuries was both innovative and accurate. Its influence was felt for generations to come. Many of the most basic concepts of modern astronomy were either developed directly by them, or came about through their influence on later astronomers.
This concise biographical overview presents the work of eight of them.
Muslim scholars who worked on the subject of astronomy receive a good treatment in The Dictionary of Scientific Biography.(endnote 38)
There are also, of course, Suter, Brockelmann, Sezgin and Sarton for more details on each of such astronomers. Amongst these astronomers was Al-Battani (d. 929) who wrote The Sabian tables (al-Zij al-Sabi), a very influential work for centuries after him.(endnote 39)
Al-Battani's work also includes timing of the new moons, calculation of the length of the solar and sideral year, the prediction of eclipses and the phenomenon of parallax.'(endnote 40)
Al-Battani also popularised if not discovered the first notions of trigonometrical ratios used today,(endnote 41) and made serious emendations to Ptolemy.(endnote 42)
Al-Sufi (903-986) made several observations on the obliquity of the ecliptic and the motion of the sun (or the length of the solar year.)(endnote 43) He also made observations and descriptions of the stars, setting out his results constellation by constellation, discussing the stars positions, their magnitudes and their colour, and for each constellation providing two drawings from the outside of a celestial globe, and from the inside.(endnote 44) Al-Sufi also wrote on the astrolabe and its thousand or so uses.
Al-Biruni (973-1050) claimed that the earth rotated around its own axis.(endnote 45) He calculated the earth circumference, and fixed scientifically the direction of Makkah (Mecca) from any point of the globe. Al-Biruni wrote in total 150 works, including 35 treatises on pure astronomy, of which only six have survived.(endnote 46)
Ibn Yunus (d 1009) made observations for nearly thirty years (977-1003) using amongst others a large astrolabe of nearly 1.4 m in diameter, determining more than 10,000 entries of the sun's position throughout the years.(endnote 47)
Al-Farghani was one of Caliph Al-Mamun's astronomers. He wrote on the astrolabe, explaining the mathematical theory behind the instrument and correcting faulty geometrical constructions of the central disc, that were current then.(endnote 48) His most famous book Kitab fi Harakat Al-Samawiyah wa Jaamai Ilm al-Nujum on cosmography contains thirty chapters including a description of the inhabited part of the earth, its size, the distances of the heavenly bodies from the earth and their sizes, as well as other phenomena.(endnote 49)
Jabir Ibn Aflah (d. 1145) was the first to design a portable celestial sphere to measure and explain the movements of celestial objects. Jabir is specially noted for his work on spherical trigonometry. Al-Bitruji's work 'Kitab-al-Hay'ah' was translated by the Sicilian based Michael Scot, and bore considerable influence thereafter.
On how the works of various Muslim astronomers have been used, or relied upon by scholars who followed them has received attention by many of the sources already cited. There remains many matters of contention as can be expected. Indeed, if it is easy for many scholars to find the Greek origin in many Islamic works, however flimsy the evidence, the other way round, that is recognising the Muslim origin of any breakthrough of significance amongst the likes of Copernicus, Galileo, etc, is denied even when the evidence is beyond the glaring.
No better instance than Copernicus' theories based on those of Nasir al-Din al-Tusi and Ibn Shatir. Pedersen, for instance, noting the resemblance, still finds no line of transmission.(endnote 51)
This line of transmission North bluntly states it, holding that Greek and Latin materials that made use of al-Tusi's device were circulating in Italy at about the time Copernicus studied there.(endnote 52) And North does not hesitate to add that Copernicus made repeated uses of al-Tusi's and his followers' devices.(endnote 53)
On this issue see also works by Gingerich,(endnote 54) and above all the masterly delivery by George Saliba, which explains all about this matter at http://www.columbia.edu/~gas1/project/visions/case1/sci.1.html