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In 1610 reports reached Prague that Galileo had discovered new planets, and Kepler felt compelled to find out for himself what had actually been seen. Reading Starry Messenger and later observing through a borrowed telescope, he became one of Galileo’s earliest and most important defenders. Kepler not only confirmed the existence of Jupiter’s moons but also argued publicly for the reliability of telescopic observations, and went further by explaining, for the first time, how the telescope worked in theory through his optical treatise Dioptrice. Alongside this defence of new instruments, the episode follows Kepler’s search for harmony in the structure of the cosmos, culminating in the discovery of his third law of planetary motion. It then traces his long and difficult effort to complete the Rudolphine Tables, based on Tycho Brahe’s observations. Published in 1627, the tables proved vastly more accurate than anything before them and made possible the successful prediction of planetary transits. Though Kepler did not live to see their full impact, the tables ensured that his astronomy could no longer be ignored. Support the show (https://buymeacoffee.com/completehist...) Support the show: buymeacoffee.com/completehistoryofscience Contact: thecompletehistoryofscience@gmail.com BlueSky: https://bsky.app/profile/gethinrichar... Music Credit: Folk Round Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License