By the Archaic period, however, educated Greek men and women knew from observing solar eclipses and ships sailing to the horizon that the moon was a round ball. The astronomer Thales in the 600s BC also knew that the moon didn’t make its own light, but shone by reflecting light from the sun. In the 400s BC, Greek scientists like Anaxagoras knew why eclipses happened.
Greek and Roman Science, by Don Nardo (1998). Nardo has written a lot of good books about the ancient world for kids; this one is no exception.
Greek Astronomy, by Thomas Heath (1932). A collection of what ancient Greek writers had to say about astronomy, in their own words, with a long introduction. For adults.
The History & Practice of Ancient Astronomy, by James Evans (1998). Includes both the history, and directions to actually re-do the experiments that ancient Greek astronomers used to figure out their conclusions. For adults.
Greek Science After Aristotle, by G. E. R. Lloyd (1975).