Babylonians were very good sky observers but their ability to build models of the universe was limited. The Greeks were always asking why things happened the way they did, a question that would never have occurred to Babylonians.
An early model predicted lunar phases and eclipses. This model had to change the basic assumptions about the structure of the universe:
Eclipses are just shadows cast from one body onto another. At New Moon the moon is between the Earth and the Sun and it is possible for the shadow of the Moon to be cast onto the Earth, producing a solar eclipse. At Full Moon the Earth is between the Sun and the Moon and the shadow of the Earth can fall onto the Moon, producing a lunar eclipse. This simple model relies on two changes in the basic assumptions:
Phases of the Moon are seen to be simply geometry - as the Moon goes around the Earth, how much of the sunlit portion do we see from the Earth.
Once phases and eclipse are understood, the Greeks can take the next logical step. If the shadow of the Earth produces the lunar eclipse, we can judge the shape of the Earth. The Babylonians recorded many lunar eclipses, but all were sections of a circle. The only shape that can only cast a circular shadow is the sphere.
If we now know the shape of the Earth, can we measure the size of the Earth. Erastosthenes, the curator of the Greek library in Alexandria, came across a note from the far southern city of Syene that said, "At noon on the summer solstice, we can see the bottom of a deep well." The Sun has to be at the zenith at this time. But where is the Sun in the sky at Alexandria at the same moment. Erastosthenes measured that the Sun was 7.5 degrees South of the zenith. With these data we can estimate the size of the Earth. The angular difference of the Sun in the two cities is about 1/50th the circumference of a circle. Thus the distance between the two cities must be 1/50th the circumference of the Earth.
Using other measurements of the Moon at critical times in its orbit, the Greeks were able to obtain the relative distance and sizes of the Earth, Moon, and Sun. They saw that the Sun was enormous compared to the Earth and the Moon, but that the Earth was larger than the Moon. Useful in this analysis was the fact that the angular sizes of the Moon and the Sun are almost exactly the same.
These advances lead to the first comprehensive models of the universe. A major player in one of the models was Aristotle. He presented evidence that the Earth was the stationary, center of the Universe. His model is called "Geocentric."
Aristotle divided the universe into two realms. In the Terrestrial Realm motion could be predicted only when the composition of the object was known. Elements had natural tendencies of motion. Earth and water tended to sink, while air and fire tended to rise. Objects that followed their natural tendencies (natural motion) required no forces. Opposing the natural tendency (violent motion) required force. There was an overall tendency in the Terrestrial Realm to seek rest. Likewise in the Terrestrial Realm everything was corruptible (changing).
Rules are different in the Celestial Realm. Here objects glowed but not by fire. It was called Aether and had the property of glowing without consuming. Motion of the celestial objects was constant and circular. Also celestial objects were incorruptible. Objects like meteors or comets must belong to the Terrestrial Realm in the upper Earth's atmosphere. The Geocentric model of Aristotle could not account for retrograde motion.
Aristarchus of Samos preferred the "Heliocentric" model with the Sun at the center and the planets orbiting it. The lack of stellar parallax must now be because the stars are too far away to have percepable shifts. Thus the Heliocentric model must be huge, an idea that ancient astronomers were not prepared to accept. The model that comes down through history is the Geocentric Model.
About 140 AD Claudius Ptolemy introduced a major revision of the geocentric model in order to account for retrograde motion, the apparent occasional backwards motion of the planets through the sky. He started by noting that the Sun and Moon showed a variation in their apparent size as they moved around us. To account for this Ptolemy offset the Earth from the center of the orbit of the Sun and Moon. Thus at some places in the orbit the Sun or Moon would be closer to us and appear bigger in the sky.
The planets all showed retrograde motion, however. Ptolemy devised a system of circles on circles (epicycles on deferents) to account for this motion. So tightly held was the belief in circular motion that this system persisted into the 17th century.
After the fall of Rome the knowledge of the ancient world moves into the new world of Islam. These astronomers were not model builders, but they were very good sky observers, who expanded the Greek models. In Europe illiteracy was almost universal, communications were poor, and the Alexandrian library was destroyed.
The Geocentric model is later tied to the teachings of the Christian religion through the work of Thomas Aquinas.