Final answer:
The observation not supporting the Sun-centered model is 'He measured the parallax of a comet', as Galileo's documented observations were of Jupiter's moons, the Moon's geography, and the phases of Venus, all of which supported the heliocentric theory.
Step-by-step explanation:
The observation made by Galileo that does not support the Sun-centered model is B) He measured the parallax of a comet. Galileo's telescopic discoveries include observations such as A) observing objects orbiting Jupiter, which showed that not all celestial bodies revolve around the Earth. This was evidence against the geocentric model and in favor of the heliocentric model. Moreover, D) observing mountains on the Moon suggested that celestial bodies, including the Earth, could be similar rather than the Earth being unique and the center of the universe. However, the crucial observation that supported the Sun-centered, or heliocentric, view was C) observing the phases of Venus, which showed that Venus must orbit the Sun, revealing different parts of its daylight side at different times. These phases could not be explained by the earlier Ptolemy's geocentric model