The highest development of astronomy in the ancient world came with the Greeks in the period from 600 b.c. to a.d. 400. The methods employed by the Greek astronomers were quite distinct from those of earlier civilizations, such as the Babylonian. The Babylonian approach was numerological and best suited for studying the complex lunar motions that were of overwhelming interest to the Mesopotamian peoples. The Greek approach, on the contrary, was geometric and schematic, best suited for complete cosmological models. Thales, an Ionian philosopher of the 6th cent. b.c., is credited with introducing geometrical ideas into astronomy. Pythagoras, about a hundred years later, imagined the universe as a series of concentric spheres in which each of the seven "wanderers" (the sun, the moon, and the five known planets) were embedded. Euxodus developed the idea of rotating spheres by introducing extra spheres for each of the planets to account for the observed complexities of their motions. This was the beginning of the Greek aim of providing a theory that would account for all observed phenomena. Aristotle (384-322 b.c.) summarized much of the Greek work before him and remained an absolute authority until late in the Middle Ages. Although his belief that the earth does not move retarded astronomical progress, he gave the correct explanation of lunar eclipses and a sound argument for the spherical shape of the earth.

The apex of Greek astronomy was reached in the Hellenistic period by the Alexandrian school. Aristarchus (c.310-c.230 b.c.) determined the sizes and distances of the moon and sun relative to the earth and advocated a heliocentric (sun-centered) cosmology. Although there were errors in his assumptions, his approach was truly scientific; his work was the first serious attempt to make a scale model of the universe. The first accurate measurement of the actual (as opposed to relative) size of the earth was made by Eratosthenes (284-192 b.c.). His method was based on the angular difference in the sun's position at the high noon of the summer solstice in two cities whose distance apart was known.

The greatest astronomer of antiquity was Hipparchus (190-120 b.c.). He developed trigonometry and used it to determine astronomical distances from the observed angular positions of celestial bodies. He recognized that astronomy requires accurate and systematic observations extended over long time periods. He therefore made great use of old observations, comparing them to his own. Many of his observations, particularly of the planets, were intended for future astronomers. He devised a geocentric system of cycles and epicycles (a compounding of circular motions) to account for the movements of the sun and moon.

Ptolemy (a.d. 85-165) applied the scheme of epicycles to the planets as well. The resulting Ptolemaic system was a geometrical representation of the solar system that predicted the motions of the planets with considerable accuracy. Among his other achievements was an accurate measurement of the distance to the moon by a parallax technique. His 13-volume treatise, the Almagest, summarized much of ancient astronomical knowledge and, in many translations, was the definitive authority for the next 14 centuries.

After the fall of Rome, European astronomy was largely dormant, but significant work was carried out by the Muslims and the Hindus. It was by way of Arabic translations that Greek astronomy reached medieval Europe. One of the great landmarks of the revival of learning in Europe was the publication (1543) by Nicolaus Copernicus (1473-1543) of his De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres). According to the Copernican system, the earth rotates on its axis and, with all the other planets, revolves around the sun. The assertion that the earth is not the center of the universe was to have profound philosophical and religious consequences. Copernicus's principal claim for his new system was that it made calculations easier. He retained the uniform circular motion of the Ptolemaic system, but by placing the sun at the center, he was able to reduce the number of epicycles. Copernicus also determined the sidereal periods (time for one revolution around the sun) of the planets and their distance from the sun relative to the sun-earth distance (see astronomical unit).

The great astronomer Tycho Brahe (1546-1601) was principally an observer; a conservative in matters of theory, he rejected the notion that the earth moves. Under the patronage of King Frederick II, Tycho established Uraniborg, a superb observatory on the Danish island of Hveen. Over a period of 20 years (1576-97), he and his assistants compiled the most accurate and complete astronomical observations to that time. At his death his records passed to Johannes Kepler (1571-1630), who had been his last assistant. Kepler spent nearly a decade trying to fit Tycho's observations, particularly of Mars, into an improved system of heliocentric circular motion. At last, he conceived the idea that the orbit of Mars was an ellipse with the sun at one focus. This led him to the three laws of planetary motion that bear his name (see Kepler's laws).

Galileo Galilei (1564-1642) made fundamental discoveries in both astronomy and physics; he is perhaps best described as the founder of modern science. Galileo was the first to make astronomical use of the telescope. His discoveries of the four largest moons of Jupiter and the phases of Venus were persuasive evidence for the Copernican cosmology. His discoveries of craters on the moon and blemishes on the sun (sunspots) discredited the ancient belief in the perfection of the heavens. These findings were announced in The Sidereal Messenger, a small book published in 1610. Galileo's Dialogue on the Two Chief Systems of the World (1632) was an eloquent argument for the Copernican system over the Ptolemaic. However, Galileo was called before the Inquisition and forced to renounce publicly all doctrines considered contrary to Scripture.

Isaac Newton (1642-1727), possibly the greatest scientific genius of all time, succeeded in uniting the sciences of astronomy and physics. His laws of motion and theory of universal gravitation provided a physical, dynamic basis for the merely descriptive laws of Kepler. Until well into the 19th cent., all progress in astronomy was essentially an extension of Newton's work. Edmond Halley's prediction that the comet of 1682 would return in 1758 was refined by A. C. Clairault, who included the perturbing effects of Jupiter and Saturn on the orbit to calculate the nearly exact date of the return of the comet. In 1781, William Herschel accidentally discovered a new planet, eventually named Uranus. Discrepancies between the observed and theoretical orbits of Uranus indicated the existence of a still more distant planet that was affecting Uranus's motion. J. C. Adams and U. J. J. Leverrier independently calculated the position where the new planet, Neptune, was actually discovered (1846). Similar calculations for a large "Planet X" led in 1930 to the discovery of Pluto, now classed as a dwarf planet.

By the early 19th cent., the science of celestial mechanics had reached a highly developed state at the hands of Leonhard Euler, J. L. Lagrange, P. S. Laplace, and others. Powerful new mathematical techniques allowed solution of most of the remaining problems in classical gravitational theory as applied to the solar system. In 1801, Giuseppe Piazzi discovered Ceres, the first of many asteroids. When Ceres was lost to view, C. F. Gauss applied the advanced gravitational techniques to compute the position where the asteroid was subsequently rediscovered. In 1838, F. W. Bessel made the first measurement of the distance to a star; using the method of parallax with the earth's orbit as a baseline, he determined the distance of the star 61 Cygni to be 60 trillion mi (about 10 light-years), a figure later shown to be 40% too large.