Galileo believed that the planets and Earth revolved around the sun (which is correct). The church believed in the ancient Greek belief that the sun/planets revolve around the Earth. When Galileo's theory was presented and proven factual, the church thought "If we're wrong about this, people might start to question our beliefs and break our hold on power."
The Church sought to silence Galileo because he supported the heliocentric model, which challenged their geocentric beliefs. They feared losing authority as Galileo's findings posed a threat to their teachings and power. Ultimately, Galileo was tried for heresy and placed under house arrest for the rest of his life.
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