Editing Celestial spheres (section)

====Astronomical discussions====
A series of astronomers, beginning with the Muslim astronomer [[Ahmad ibn Muhammad ibn Kathīr al-Farghānī|al-Farghānī]], used the Ptolemaic model of nesting spheres to compute distances to the stars and planetary spheres. Al-Farghānī's distance to the stars was 20,110 Earth radii which, on the assumption that the radius of the Earth was {{convert|3,250|mi|km|abbr=off}}, came to {{convert|65,357,500|mi|km|abbr=off}}.<ref>Van Helden, ''Measuring the Universe'', pp. 29–31.</ref> An introduction to Ptolemy's ''Almagest'', the ''Tashil al-Majisti'', believed to be written by [[Thābit ibn Qurra]], presented minor variations of Ptolemy's distances to the celestial spheres.<ref>Van Helden, ''Measuring the Universe'', p. 31.</ref> In his ''[[Zij]]'', [[Muḥammad ibn Jābir al-Ḥarrānī al-Battānī|Al-Battānī]] presented independent calculations of the distances to the planets on the model of nesting spheres, which he thought was due to scholars writing after Ptolemy. His calculations yielded a distance of 19,000 Earth radii to the stars.<ref name="Van Helden pp. 31-2">Van Helden, ''Measuring the Universe'', pp. 31–2.</ref>

Around the turn of the millennium, the [[Astronomy in medieval Islam|Arabic astronomer]] and polymath [[Ibn al-Haytham#Astronomy|Ibn al-Haytham (Alhacen)]] presented a development of Ptolemy's [[geocentric model]]s in terms of nested spheres. Despite the similarity of this concept to that of Ptolemy's ''Planetary Hypotheses'', al-Haytham's presentation differs in sufficient detail that it has been argued that it reflects an independent development of the concept.<ref>{{cite book|first=Y. Tzvi|last=Langermann|year=1990|title=Ibn al Haytham's on the Configuration of the World|pages=11–25|location=New York|publisher=Garland Publishing}}</ref> In chapters 15–16 of his ''[[Book of Optics]]'', Ibn al-Haytham also said that the celestial spheres do not consist of [[solid]] matter.<ref>{{cite journal|first=Edward|last=Rosen|year=1985|title=The Dissolution of the Solid Celestial Spheres|journal=Journal of the History of Ideas|volume=46|issue=1|pages=13–31 [19–20, 21]|doi=10.2307/2709773|jstor=2709773}}.</ref>

Near the end of the twelfth century, the [[Al-Andalus|Spanish Muslim]] astronomer [[Nur Ed-Din Al Betrugi|al-Bitrūjī (Alpetragius)]] sought to explain the complex motions of the planets without Ptolemy's epicycles and eccentrics, using an Aristotelian framework of purely concentric spheres that moved with differing speeds from east to west. This model was much less accurate as a predictive astronomical model,<ref>{{cite book|first=Bernard R.|last=Goldstein|title=Al-Bitrūjī: On the Principles of Astronomy|location=New Haven|publisher=Yale University Press|year=1971|volume=1|pages=40–5}}</ref> but it was discussed by later European astronomers and philosophers.<ref>Goldstein, ''Al-Bitrūjī'', p. 6.</ref><ref>Grant, ''Planets, Stars, and Orbs,'' pp. 563–6.</ref>

In the thirteenth century the astronomer [[Mu'ayyad al-Din al-'Urdi|al-'Urḍi]] proposed a radical change to Ptolemy's system of nesting spheres. In his ''Kitāb al-Hayáh'', he recalculated the distance of the planets using parameters which he redetermined. Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet's diameters to the thickness of their spheres. As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.<ref name="Van Helden pp. 31-2"/>

About the same time, scholars in European [[medieval universities|universities]] began to address the implications of the rediscovered philosophy of Aristotle and astronomy of Ptolemy. Both astronomical scholars and popular writers considered the implications of the nested sphere model for the dimensions of the universe.<ref>Grant, ''Planets, Stars, and Orbs'', pp. 433–43.</ref> [[Campanus of Novara]]'s introductory astronomical text, the ''Theorica planetarum'', used the model of nesting spheres to compute the distances of the various planets from the Earth, which he gave as 22,612 Earth radii or {{convert|73387747+100/660|mi|km}}.<ref>Grant, ''Planets, Stars, and Orbs'', pp. 434–8.</ref><ref>Van Helden, ''Measuring the Universe'', pp. 33–4.</ref> In his ''[[Opus Majus]]'', [[Roger Bacon]] cited Al-Farghānī's distance to the stars of 20,110 Earth radii, or {{convert|65357700|mi|km}}, from which he computed the circumference of the universe to be {{convert|410818517+3/7|mi}}.<ref>Van Helden, ''Measuring the Universe'', p. 36.</ref> Clear evidence that this model was thought to represent physical reality is the accounts found in Bacon's ''Opus Majus'' of the time needed to walk to the Moon<ref>Van Helden, ''Measuring the Universe'', p. 35.</ref> and in the popular [[Middle English]] ''[[South English Legendary]]'', that it would take 8,000 years to reach the highest starry heaven.<ref>Lewis, ''The Discarded Image'', pp. 97–8.</ref><ref>Van Helden, ''Measuring the Universe'', p. 38.</ref> General understanding of the dimensions of the universe derived from the nested sphere model reached wider audiences through the presentations in Hebrew by [[Moses Maimonides]], in French by Gossuin of Metz, and in Italian by [[Dante Alighieri]].<ref>Van Helden, ''Measuring the Universe'', pp. 37–9.</ref>