The idea of multiple nesting spheres—each sphere tracking a ‘wandering star’ or planet; the fixed stars; and the motions of the Sun and Moon—is kind of complicated. Astronomers built models of the geocentric universe to try to explain it. These are called armillary spheres.
They were usually made out of brass. Here’s one you can build out of cardboard.
Even though Earth isn’t the center of the universe, the model still works for locating positions of stars as we see them from Earth. Not only was Ptolemy’s data useful for knowing where the stars are and tracking them, but we can also predict where they will be tomorrow or next year. It became possible to know exactly when the Sun will rise and set years in the future. Astronomers could predict eclipses of the Sun or Moon. You can accurately tell the time based on Ptolemy’s data. It was a pain in the neck to carry an armillary sphere around, though. Something more compact was needed.
Back to the beginning of The Western Civ User’s Guide to Time & Space