Mainly concerned with moral philosophy rather than natural philosophy which he considered unworthy and inferior, Plato is teaching that there are two realities, the fundamental unchanging ideal one of forms and ideas and understanding; and the changing, material, sensory, observed one which only imperfectly reflects the ideal. Thus our senses delude us but philosophy, thinking, leads us to the truth. Theories and models are tools and should never be interpreted as models of reality
He speaks of a spherical earth surrounded by the sphere of the heavens. Because the heavens are ideal, the only shape that can apply to heavenly bodies is spherical, and the only way in which they can move is along circular paths. The motions of the seven planets along that sphere, and those of fixed stars are circular.
He also reintroduced divinity into the world. Rather than order being
imposed by the internal nature of things, as the Ionians maintained, order
is imposed on nature by a rational god, which creates and endows the cosmos
with beauty, reason, planning and mathematics (geometry). Not only was
the universe created by a rational creator, but the universe itself has
a soul, and the planets and stars are celestial gods. And it is the steadfastness
of these gods that maintains the uniformity and regularity of the universe.
Plato's student, was certainly one of the greatest geniuses humanity has produced. To Aristotle, the universe is eternal. To him, (as for Plato) it consists of an imperfect, changing earthly region, and a perfect, unchanging celestial region with the moon representing a transitional region.
The earthly region is made up of the four elements; earth, air, fire and water. Each of these elements rise or fall depending on their nature. Air being lightest rises highest and earth being heaviest will tend to settle. The heavens are filled with a fifth element: aether; and divided into fifty five concentric crystalline spheres bearing the planets and the stars. In the center of this system is the motionless spherical1*earth. The stellar sphere lies beyond the planets, and outermost is the sphere of the "prime mover". This prime mover causes the outer sphere to rotate in a continuous circular path and inturn, the motion of this outer sphere causes the others spheres to move in turn. This system predicted many of the motions of the planets but could not explain retrograde motion or changes in brightness of the planets.
In contrast to Plato, Aristotle maintained that theories and mathematical
models do represent the way the universe really is.
1*This notion that the earth is spherical was never lost from that time on, not even in the Dark and Middle ages. Certainly Columbus never feared falling off the edge of the earth as some stories would have you believe.