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Ptolemaic astronomy, a geocentric model of the universe, was critiqued by Nasir al-Din Tusi in his work. Tusi argued that the Ptolemaic model was mathematically complex and physically implausible. He proposed an alternative model, the Tusi couple, which provided a simpler and more accurate explanation of planetary motion. Tusi's work contributed to the development of modern astronomy and laid the foundation for future scientific advancements.