Galileo's use of a telescope revolutionized the study of astronomy and marked a significant advancement during the Scientific Revolution. By utilizing his improved version of the telescope, Galileo was able to make groundbreaking observations, such as the moons of Jupiter, the phases of Venus, and the detailed surface of the Moon. These discoveries challenged existing views of the cosmos and supported the heliocentric theory proposed by Copernicus, thus shifting the scientific paradigm of the time.