The use of the rising and setting of stars to mark seasons is described in literature from the sixth century and some Mesopotamian data were known in Greece certainly by the fifth century. In the fourth century Greek astronomy begins to focus on producing geometrical models of planetary movements based on uniform circular motion. The first known geometrical model of planetary motion is associated with Eudoxus (late fourth century), who also played a central role in the axiomatization of mathematics. Though his model was geometrically sophisticated, it deviated from observed facts in many respects, thus revealing an important aspect of early Greek astronomy; that it was concerned with producing geometrical models of planetary motion rather than with describing the physical cosmos.
The mathematical models were made more complex by the introductions of epicycles (a circle whose center moves on the circumference of another circle) and eccentric models (placing the earth off the center). Such techniques were used by Aristarchus of Samos (c. 280 B.C.E.), famous for proposing a heliocentric model of the world as well as the standard geocentric one, and were developed by Hipparchus of Nicea (fl. late second century) who began to use models to predict astronomical events.
Only little is known about the achievements of these writers as their work was eclipsed by Claudius Ptolemy's (c. 100–170 C.E.) great oeuvre on astronomy, the Syntaxis (often known under its Arabic title Almagest). Here, Ptolemy derives models for the planets, Sun, and Moon from first principles, using geometrical methods and observed data. In much of his work, Ptolemy mixed a geometrical approach with observation and an interest in physical mechanisms, carefully combining the rhetorical powers of mathematical precision with the status of Aristotelian physics. Ptolemy also wrote an important work on astrology, the Tetrabiblos, and in general astrological traditions flourished in the ancient Greek world.