Final answer:
The observation of the phases of Venus demonstrated that Venus orbits the Sun and goes through a full cycle of phases, providing strong evidence for the Copernican heliocentric model and contradicting the Ptolemaic geocentric system.
Step-by-step explanation:
The observation of the phases of Venus was a significant milestone in astronomy that supported the Copernican theory of heliocentrism, the idea that the planets, including Earth, revolve around the Sun. Galileo's telescopic observations showed that Venus exhibited a full cycle of phases similar to those of the Moon, which contradicted Ptolemy's geocentric model. In Ptolemy's Earth-centered universe, Venus would only show limited phases; however, Galileo observed Venus displaying the complete set, providing compelling evidence that Venus must orbit the Sun. Additionally, this evidence suggested that, like the Moon, Venus appears illuminated from different angles as it orbits around the Sun, reinforcing the heliocentric model. The discovery of Venus's phases was a critical piece of evidence that paved the way for the acceptance of the heliocentric system.