Final answer:
Galileo's observations suggested that the Sun and the Moon were not perfect spheres, revealing imperfections that aligned with a heliocentric solar system, contrary to the then-prevailing geocentric model.
Step-by-step explanation:
Galileo's telescopic discoveries of mountains on the Moon and spots on the Sun were controversial because they suggested that the Sun and the Moon were not perfect spheres. In contrast to the prevailing belief in their perfection, these observations indicated imperfections and similarities to Earth, challenging the celestial status quo. While the Greeks like Aristotle recognized the spherical nature of Earth and the Moon, they could not detect stellar parallax and therefore rejected the notion of Earth moving. However, Galileo's observations of the Jovian moons showed that not everything orbits Earth, hinting at a heliocentric solar system where planets like Venus exhibit phases supporting their revolution around the Sun. These findings, along with the craters and irregularities on the Moon, undermined the Ptolemaic geocentric model and supported the Copernican view of a heliocentric system.