The need for a rough working rule to connect the rival solar and lunar reckonings of time appears to have been a compelling motive behind the development of a recognizably scientific astronomy by the Babylonian priestly schools of the last three centuries before Christ. Upon a sketchy foundation of observations they constructed elaborate numerical tables (ephemerides) predicting the phenomena of the sun, moon, and planets with due allowance for the principal inequalities of their motions. They idealized the paths of these objects into the circle which the Greeks later called the zodiac, divided into 12 equal "signs". They also established an approximate common multiple of the month and the year, a 19-year period since called (after its supposed Greek inventor, Meton) the "Metonic cycle", by which the Church calendar is still governed. (See also Calendar; Zodiac)

The Babylonians conceived of the earth as a disc of land surrounded by a moat of sea and surmounted by a solid firmament; below were the abode of the dead and the great deep. Babylonian astronomy stemmed partly from the practice of drawing, from the configurations of the heavenly bodies, omens as to the fortunes of the nations (judicial astrology) or of individuals (horoscopic astrology). This superstition, invading the Roman Empire, dominated the life and thought of Christendom until the rise of modern science; it is not yet wholly extinct.

The ancient Egyptians conceived the cosmos more crudely as a box-shaped receptacle with the sun-god traveling in a boat along a celestial river. They introduced the 365-day Egyptian year which was later adopted as a convenient unit by Greek and medieval astronomers.

The tradition of scientific astronomy which has come down to us through more than two thousand years originated in a synthesis of the observations and procedures of the Babylonian ephemerists with the natural philosophy and geometrical technique of the Greeks. Starting from prevailing mythological ideas, the Greeks advanced to a naturalistic conception of the cosmos, referring celestial phenomena either to the properties of some universal element or to a set of regulative principles to which nature was held to conform. Pythagoras (sixth century b.c.) and his school conceived the earth as a sphere, and taught that the paths of the heavenly bodies could all be resolved into uniform circular motions about the earth.

These doctrines, reduced to mathematical precision by Eudoxus of Cnidos (fourth century b.c.), were developed by Aristotle (c. 384-322 b.c.) into a cosmological system which survived almost unchallenged down to the 16th century. He conceived of a finite, spherical universe, centered upon the stationary earth. At the moon's distance, the sphere was divided into a central core constituted by the four elements (earth, water, air, fire), and an ethereal realm of heavenly bodies. To account for the planetary motions, he supposed each planet to be attached to the equator of a uniformly rotating sphere, the poles of which were embedded in a second exterior sphere concentric with the first but turning about an independent axis with a period of its own. This sphere was similarly related to a third, and so on to the number required to give the planet a compound motion such as it exhibited when viewed from the earth at the common center of all the spheres. Aristotle assigned four spheres each to Saturn and Jupiter and five spheres to each of the other planets (including the sun and moon). As all these spheres were conceived to form a single system, it was necessary to interpolate between each pair of planets a set of "reacting" spheres to prevent all the motions except the diurnal one (common to the heavenly bodies) from being handed down from the outer to the inner planets. The total number of spheres therefore amounted to 55. The four elements were supposed to undergo continual transformation one into another, so that we lived in a region of change and decay; but Aristotle held the heavenly bodies and their carrying-spheres to be composed of an incorruptible "ether" and therefore to be incapable of any change of substance.

In opposition to this view, Heracleides of Pontus (fourth century b.c.) attributed to the earth a daily axial rotation, and he taught that Venus and Mercury circulated round the sun. Aristarchus of Samos (third century b.c.) broadly anticipated the modern heliocentric (sun-centered) planetary scheme. Aristarchus also formulated a geometrically correct method for determining the relative distances of the sun and moon; his results, however, were incorrect because of the primitive instruments with which he worked. His younger contemporary, Eratosthenes of Cyrene, successfully applied what has become a classic procedure for estimating the circumference of the earth. Knowing that Syene in Upper Egypt is under the Tropic of Cancer, and that the gnomon of a sundial cast no shadow at the summer solstice, he assumed that Syene and Alexandria had the same longitude, and ascertained that the distance between the two was 5,000 stadia. The zenith distance for Alexandria was determined to be 1/50 of the circumference of the meridian, and Eratosthenes assumed that the earth was spherical, which fixed the circumference of the earth at 250,000 stadia. In his measurement he erred from modern estimates by only one percent.

A geocentric (earth-centered) planetary system, established in the Hellenistic age through the labors of Hipparchus of Rhodes (second century b.c.), was completed and expounded by Ptolemy of Alexandria (second century a.d.) in his Almagest (or Syntaxis). This astronomical classic, which remained authoritative for at least 1,400 years, contains the oldest surviving star catalog; it records the discovery by Hipparchus of the precession of the equinoxes; it describes the instruments available to the ancients for the measurement of celestial angles; and it explains the epicyclic representation of lunar and planetary motions which was accepted until the 17th century.

According to this system, a planet was represented as uniformly describing a circle (the epicycle) about a center which meanwhile described a larger circle (the deferent) about the earth (see Fig. 1). By this means a realistic representation could be given of the characteristic variations in the planet's rate of travel through the constellations and in its distance from the earth (as suggested by changes in its brightness). The representation could be refined by introducing additional epicycles one upon another, or by referring the uniform motion in a circle not to its center but to some other point, the equant. The representations of the planetary motions and their reduction to numerical tables represented the principle contributions of Ptolemy to astronomy.

Following the decay of ancient culture, Greek science was deviously transmitted to medieval Christendom by way of the Islamic civilization. The Arabs absorbed the remains of the Hellenistic tradition in the lands they overran in the seventh century; and Baghdad became a center for the translation (direct or through Syriac versions) of scientific classics, including Ptolemy's Almagest, into Arabic. From there the tradition moved westward to Cairo and to the Muslim universities of Spain. Observations by the great Muslim astronomer Al-Battani (died 929) indicated the progressive motion of the solar apogee.

The Arabs concentrated upon the redetermination of astronomical constants and the construction of planetary tables; but their principal achievement was to maintain the tradition and preserve the classic texts of ancient astronomy during the time of intellectual stagnation in the Christian West.

In the twelfth century Latin translations of Arabic versions of Aristotle and Ptolemy served to introduce Western Christendom to a system of natural philosophy and a numerical theory of planetary motions which retained their authority throughout the Middle Ages. In the fifteenth century these classics became available in the original Greek; and in Nürnberg (Nuremberg) Johann Müller (1436-1476), called Regiomontanus, revived the construction and use of astronomical instruments.