Not sure where you got the 'Muslim View on the Earth being the center of the universe' from or the other views supposedly held by Muslims. There is nothing in the Islamic faith that says the Earth is the centre of the Universe.
You can watch this award winning film with Ben Kingsley about what the Muslims were doing while Europe was supposedly languishing in the '

ark Ages':
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You might want to study something of Ibn al-Haytham, known as 'Alhazen' in the West, regarded by many as the first scientist, who was born in Basra (Iraq) around 965CE. I've included some fragments of information on how the Ptolemaic view planetary motion passed from the Greeks to the Muslims and then the Europeans.
"He[Ibn al-Haytham] made significant contributions to the principles of optics, as well as to physics, anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, psychology, visual perception, and to science in general with his early application of the scientific method..."
He wrote the ground-breaking book, 'Book of Optics', along with '

oubts Concerning Ptolemy', 'On the Configuration of the World', 'The Model of the Motions', 'Treatise on Light', 'Treatise on Place'... and known for the scientific method, experimental science, experimental physics, experimental psychology, visual perception, analytic geometry, non-Ptolemaic astronomy, celestial mechanics...
On Book of Optics: "The book had an important influence on the development of optics, as it laid the foundations for modern physical optics after drastically transforming the way in which light and vision had been understood, and on science in general with its introduction of the experimental scientific method. Ibn al-Haytham has been called the "father of modern optics", the "pioneer of the modern scientific method," and the founder of experimental physics. The Book of Optics has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in the history of physics,..."
"The Islamic astronomers adopted the Ptolemaic-Aristotelian cosmology, but eventually criticism emerged. One of the first critics was Ibn al-Haytham (Alhazen), a leading physicist of 11th-century Cairo. In his Doubts on Ptolemy he complained that the equant failed to satisfy the requirement of uniform circular motion, and he went so far as to declare the planetary models of the Almagest false..."
"At the other end of the Islamic world a fresh critique of the Ptolemaic mechanisms was undertaken in the 13th century by Nasir al-Din al-Tusi. One of the most prolific Islamic polymaths, with 150 known treatises and letters to his credit, al-Tusi also constructed a major observatory at Maragha (the present-day Maragheh in Iran). Al-Tusi found the equant particularly dissatisfactory. In his Tadhkira ("Memorandum") he replaced it by adding two more small epicycles to the model of each planet's orbit. Through this ingenious device al-Tusi was able to achieve his goal of generating the nonuniform motions of the planets by combinations of uniformly rotating circles..."
"Finally a completely concentric rearrangement of the planetary mechanisms was achieved by Ibn al-Shatir, who worked in Damascus in about 1350. By using a scheme related to that of al-Tusi, Ibn al-Shatir succeeded in eliminating not only the equant but also certain other objectionable circles from Ptolemy's constructions. He thereby cleared the way for a perfectly nested and mechanically acceptable set of celestial spheres..."
"Ibn al-Shatir's forgotten model was rediscovered in the late 1950's by E. S. Kennedy and his students at the American University of Beirut. The discovery raised an intriguing question. It was quickly recognized that the Ibn al-Shatir and Maragha inventions were the same type of mechanism used by Copernicus a few centuries later to eliminate the equant and to generate the intricate changes in the position of the earth's orbit." [This doesn't imply that Copernicus copied it or knew of it].
In conclusion:
"In eliminating the equant, and even in placing the planets in orbit around the sun, Copernicus was in part trying to formulate a mechanically functional system, one that offered not only a mathematical representation but also a physical explanation of planetary motions. In a profound sense he was simply working out the implications of an astronomy founded by Ptolemy but transformed by the Islamic astronomers. Today that heritage belongs to the entire world of science."