Final answer:
Galileo's legacy implies a promise of continued discovery in science and astronomy, emphasizing empirical research to reveal more about the universe.
Step-by-step explanation:
The promise Galileo Galilei makes about the future, particularly in the context of astronomy and science, is not explicitly stated as his own, but it can be inferred from his actions and the legacy he left behind. Galileo is renowned for advocating the experimental method and observation as ways to inquire about nature's laws. By doing so, he turned the telescope to the sky, upending long-held philosophical beliefs and elucidating our understanding of the heavens. His support of the Copernican heliocentric system suggested that future research, guided by empirical evidence and open inquiry, could reveal astonishing truths about our universe and place within it. Galileo's work and ideas paved the way for future discoveries and stressed the importance of data-driven science, implicitly promising an ever-expanding knowledge about the cosmos.