Ptolemy's geocentric Theory

Ptolemy proposed his Geocentric theory in the 2nd century A.D. What he did was just an elaboration of already existing idea that earth was in the center of universe, proposed by Aristotle, in to a complete cosmological model.

According to his theory, the earth stood at the center, surrounded by some eight spheres, the Moon, the Sun, the stars, and the five other planets known till the time: Mercury, Venus, Mars, Jupiter, and Saturn.

The first sphere supposedly carried Moon followed by Mercury, Venus, Sun, Mars, Jupiter, Saturn, and some fixed stars--eighth sphere--in the remaining seven spheres. The outer most sphere that is supposed to carry the so-called fixed stars, rotate across the sky; the stars thus remain fixed with respect to earth--according to him.

What about the region beyond the eighth sphere ?

He didn't explained that, as there is no way one can observe beyond stars--no telescope and no Galileo.

Does this theory provided a reasonably accurate system for predicting the positions of heavenly bodies in the sky ?

Yes, it was, but got one serious flaw: to predict the positions correctly, Ptolemy had to make an assumption that the moon followed a path that sometimes brought it twice as close to the earth as at other times. And that meant that the moon ought sometimes to appear twice as big as at other times!