Early Greeks thought of the Earth as the goddess Gaia, the mother of everything. Like a mother, the Earth gave food to people. By the time of Homer’s Odyssey, Greek sailors knew the outline of the Mediterranean and the Black Sea quite well, and they knew something about the Red Sea, the Persian Gulf, and the Arabian Peninsula.
Two hundred years later in the Classical period, while some people still believed the earth was flat, educated Greeks like Thales knew that the earth was a round ball. Herodotus, in the 400s BC, knew that some people thought the ocean went all the way around Eurasia and Africa, though he wasn’t sure this was right. Herodotus had heard stories that some people had sailed all the way around Africa, too. He knows that it’s very cold in the north, and snows a lot. He knew the rivers of Eastern Europe and Ukraine: the Danube, the Dniester, the Bug, the Dnieper, the Inhul, the Molochna, and the Don, and further east: the Tigris and Euphrates, the Oxus, the Jaxartes, and the Indus.
Aristarchus, about 300 BC in the Hellenistic period, used his observations of the eclipse of the moon to prove that the earth went around the sun instead of the sun going around the earth. Aristarchus also calculated that the sun must be much bigger than the earth and the moon, and that the stars must be very, very far away. Most other astronomers were skeptical of Aristarchus’ ideas, even though they all turned out to be right. To the Greeks, who always placed man at the center of everything, it was hard to change that idea.
The Librarian Who Measured the Earth, by Kathryn Lasky (1994). An account of the life and work of Eratosthenes, who figured out the circumference of the earth. Explains how he did it. Easy reading.
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).