The Babylonians accumulated records of astronomical observations for many centuries. The records enabled them to see repeated patterns in the motions of the celestial objects. They used the patterns to predict the positions of the Moon and planets.
Mechanical explanations of astronomical phenomena were first used by the astronomers of Miletus. Their ideas about the stars eventually developed into the concept of the celestial sphere.
The idea that the celestial bodies were spheres and that they moved on perfectly circular paths originated with Pythagoras and his students.
Eudoxus devised a model in which the motion of a planet was produced by the rotation of several spheres. The opposite rotations of two spheres produced a figure-eight motion of a planet. The eastward rotation of a third sphere distorted the figure eight and produced a motion resembling the observed retrograde motions of the planets.
Aristotle argued that all the celestial bodies were spheres and moved on circular paths. He believed that the Earth was motionless in the center of the universe.
The small angle equation describes the relationship of the angular diameter of an object to its linear diameter and its distance. If any two of these variables are known, the third can be found.
Aristarchus showed that it is possible to use geometry to find the distance of the Moon and the relative distances of the Moon and Sun. By doing so he showed that the universe is enormous compared with the size of the Earth. Aristarchus proposed that the Sun, not the Earth, is the center of the universe, but this idea was not accepted by most other Greek astronomers.
Eratosthenes found the difference in the altitude of the noonday Sun at Syene and Alexandria. He realized that this is the same as the difference in latitude of the two cities. This difference allowed him to find the ratio of the circumference of the Earth to the distance between Syene and Alexandria.
The celestial coordinates of stars change with time because of precession, the slow circular shifting of the celestial poles with respect to the stars. Hipparchus discovered precession when he compared his measurements of stellar positions with those of earlier Greek astronomers.
Greek astronomy culminated with the geocentric system of Ptolemy. In Ptolemy's model the retrograde motion of a planet was produced by the combination of two circular motions. A planet moved in a circle on an epicycle, which itself moved on a deferent. The system could predict accurately the positions of the planets and was in use for nearly 1500 years.
