Final answer:
Galileo's observations of Venus' full range of phases were inconsistent with the Ptolemaic model, which proposed an Earth-centric solar system, and supported the Copernican heliocentric model.
Step-by-step explanation:
Galileo's telescopic observations of the phases of Venus provided evidence that supported the Copernican theory of a heliocentric solar system and refuted the Ptolemaic model. In the Ptolemaic model, Venus and other planets were thought to orbit Earth, but this model predicted different phases for Venus than those Galileo observed.
Through his observations, Galileo noticed that Venus exhibits a full range of phases, similar to the Moon, which could only happen if Venus orbits the Sun, as stated in the Copernican model.
In the Ptolemaic system, Venus should not show the full sequence of phases because it was believed to circle Earth. However, Galileo's observations revealed that Venus does go through the full cycle of phases, like a full moon, crescent, and gibbous, which challenged the geocentric view and indicated that Venus must revolve around the Sun. These findings were instrumental in the eventual acceptance of the heliocentric model over the geocentric model.