On level ground a shadow's length depends on the Sun's elevation angle: the lower the Sun, the longer the shadow. When the Sun is directly overhead, no shadows are cast. Astronomical noon is when the Sun is highest in the sky, and one way to find it is to find when shadows are shortest. Because the sun's height changes shadow length, a vertical gnomon was used to observe the Sun's altitude. The Sun is directly overhead at noon on the equator twice a year, at the two equinoxes, but outside the tropics the Sun is never directly overhead, so shadows are never absent at noon there. Earth completes one rotation about every 23.9 hours, which is why the Sun appears to cross the sky each day and shadows swing and change length.
Eratosthenes was invited to Alexandria by a Ptolemy king to join the Museum and Library, and he became its chief librarian. According to the ancient writer Cleomedes, he compared two cities, and at noon on the summer solstice the Sun shone straight down a well in Syene, but in Alexandria a vertical rod still cast a shadow, whose angle he measured as about 7.2 degrees. The distance from Alexandria to Syene was reported as about 5,000 stadia, measured by professional bematists, and Eratosthenes multiplied by 50 to get roughly 250,000 stadia for Earth's circumference. His result works out to about 40,000 km, and one scholar's reading gives 40,338 km, which is close to Earth's modern circumference of about 40,075 km at the equator. His method was sound, but two false assumptions about Syene's position fortuitously cancelled out.
A sundial is a tool that uses the Sun to tell the time of day, and it works because the Sun seems to move across the sky, so its shadow lands in different places as the day goes on. The earliest sundials known from the archaeological record are shadow clocks. The gnomon came to Greece from Babylon, and Anaximander is credited with introducing this Babylonian instrument to the Ancient Greeks. It was widely used in ancient China from the second millennium BC onward, and the earliest recorded use of pinhole gnomons comes from the Chinese Zhoubi Suanjing. The ancient Chinese used shadow measurements for creating calendars.
Earth casts a shadow too, and you can sometimes see it. Near sunrise and sunset, Earth's shadow shows as a dark bluish band just above the horizon, topped by a pinkish band called the Belt of Venus. Before sunrise the shadow appears to recede, and after sunset it appears to rise. Earth is much bigger than the Moon, so its umbra reaches farther: roughly 1.4 million km, beyond the Moon's orbit. In a total lunar eclipse the Moon appears orange or red, because sunlight bent through Earth's atmosphere still reaches it, and this is the same effect that turns sunrises and sunsets reddish.
Words to know
- circumference: distance around
- bematists: trained distance measurers
- gnomon: shadow caster
- fortuitously: by lucky chance
