Final answer:
Galileo's opponents, primarily the Catholic Church, relied on Aristotelian and Ptolemaic views and the authority of ancient philosophy and theology to argue against his support of the Copernican heliocentric model. They did not provide scientific proof against his observations, which showed moons orbiting Jupiter and challenged the geocentric view.
Step-by-step explanation:
The proof provided against Galileo by his opponents, primarily the Roman Catholic Church, was influenced by the existing Aristotelian and Ptolemaic views of the universe, which posited a geocentric system where Earth was at the center of creation.
This view was deeply intertwined with Church doctrine and was politically and economically advantageous for the Church's authority. Galileo's observations and support of the Copernican heliocentric model directly challenged this established belief, leading to his house arrest and condemnation.
While Galileo used empirical evidence through his observations with the telescope, such as discovering moons orbiting Jupiter, the philosophical tradition of the time, defended by the Catholic Church, held that logical argument and divine revelation were superior to sensory experience and observation. Thus, Galileo's opponents did not provide scientific proof against him, but rather insisted on the authority of ancient philosophical and theological arguments.