Understanding of the Moon's cycles was an early development of astronomy: by the 5th century BC, Babylonian astronomers had recorded the 18-year Saros cycle of lunar eclipses, and Indian astronomers had described the Moon's monthly elongation. The Chinese astronomer Shi Shen (fl. 4th century BC) gave instructions for predicting solar and lunar eclipses. Later, the physical form of the Moon and the cause of moonlight became understood. The ancient Greek philosopher Anaxagoras (d. 428 BC) reasoned that the Sun and Moon were both giant spherical rocks, and that the latter reflected the light of the former. Although the Chinese of the Han Dynasty believed the Moon to be energy equated to qi, their 'radiating influence' theory also recognized that the light of the Moon was merely a reflection of the Sun, and Jing Fang (78–37 BC) noted the sphericity of the Moon. In 499 AD, the Indian astronomer Aryabhata mentioned in his Aryabhatiya that reflected sunlight is the cause of the shining of the Moon. The astronomer and physicist Alhazen (965–1039) found that sunlight was not reflected from the Moon like a mirror, but that light was emitted from every part of the Moon's sunlit surface in all directions. Shen Kuo (1031–1095) of the Song Dynasty created an allegory equating the waxing and waning of the Moon to a round ball of reflective silver that, when doused with white powder and viewed from the side, would appear to be a crescent. In Aristotle's (384–322 BC) description of the universe, the Moon marked the boundary between the spheres of the mutable elements (earth, water, air and fire), and the imperishable stars of aether, an influential philosophy that would dominate for centuries. However, in the 2nd century BC, Seleucus of Seleucia correctly theorized that tides were due to the attraction of the Moon, a
d that their height depends on the Moon's position relative to the Sun. In the same century, Aristarchus computed the size and distance of the Moon from Earth, obtaining a value of about twenty times the Earth radius for the distance. These figures were greatly improved by Ptolemy (90–168 AD): his values of a mean distance of 59 times the Earth's radius and a diameter of 0.292 Earth diameters were close to the correct values of about 60 and 0.273 respectively. Archimedes (287–212 BC) invented a planetarium calculating motions of the Moon and the known planets. During the Middle Ages, before the invention of the telescope, the Moon was increasingly recognised as a sphere, though many believed that it was "perfectly smooth". In 1609, Galileo Galilei drew one of the first telescopic drawings of the Moon in his book Sidereus Nuncius and noted that it was not smooth but had mountains and craters. Telescopic mapping of the Moon followed: later in the 17th century, the efforts of Giovanni Battista Riccioli and Francesco Maria Grimaldi led to the system of naming of lunar features in use today. The more exact 1834-6 Mappa Selenographica of Wilhelm Beer and Johann Heinrich Madler, and their associated 1837 book Der Mond, the first trigonometrically accurate study of lunar features, included the heights of more than a thousand mountains, and introduced the study of the Moon at accuracies possible in earthly geography. Lunar craters, first noted by Galileo, were thought to be volcanic until the 1870s proposal of Richard Proctor that they were formed by collisions. This view gained support in 1892 from the experimentation of geologist Grove Karl Gilbert, and from comparative studies from 1920 to the 1940s, leading to the development of lunar stratigraphy, which by the 1950s was becoming a new and growing branch of astrogeology.