Eratosthenes Sizes Up the Earth

Anaxagoras’s explanation of eclipses was a bold exercise in the use of science to understand a phenomenon well beyond everyday experience. One other such exercise came from Eratosthenes of Cyrene (ca. 276–ca. 194 B.C.E.). A careful observer, Eratosthenes noted that at the town of Syene (present-day Aswan, Egypt), southeast of Alexandria, the rays of the sun are precisely vertical at noon during the summer solstice. That is, a vertical stick in the ground would cast no shadow. He further noted that, at Alexandria, at exactly the same date and time, sunlight falls at an angle of 7.5 degrees from the vertical.

As we’ll see in the next chapter, small differences and apparently inconsequential discrepancies often have profound implications in astronomy. Eratosthenes instinctively understood the importance of details. Assuming—correctly—that the sun is very far from the earth, he reasoned that its rays are essentially parallel when they strike the earth. Eratosthenes believed (as did Aristotle, whom we’ll meet in the next chapter) that the earth was a sphere. He further reasoned that the angle of the shadow cast in Alexandria (7.5 degrees) was equal to the difference in latitude (see Chapter 1, “Naked Sky, Naked Eye: Finding Your Way in the Dark”) between the two cities. How did he figure that? Think of it this way: Imagine poking a stick vertically into the earth at the equator and at the North Pole, and imagine the sun is directly over the stick at the equator. The stick at the equator will have no shadow, and the stick at the North Pole will cast a shadow at an angle of 90 degrees from the stick.

Now, move the stick from the North Pole to a latitude of 45 degrees. The shadow will now fall at an angle of 45 degrees from the stick. As the stick that was at the North Pole gets closer and closer to the equator (where the other stick is), the angle of its shadow will get smaller and smaller until it is beside the other stick at the equator, casting no shadow. Noting that a complete circle has 360 degrees, and 7.5 degrees is approximately 1/50 of 360 degrees, Eratosthenes figured that the two cities were separated by 1/50 of the earth’s circumference, and that the circumference of the earth must simply be fifty times the distance between Alexandria and Syene.

The distance from Syene to Alexandria, as measured in Eratosthenes’s time, was 5,000 stadia. He apparently paid someone (perhaps a hungry grad student) to pace out the distance between the two cities. So he calculated that the circumference of the earth was 250,000 stadia. Assuming that the stadion is equivalent to 521.4 feet, Eratosthenes calculation of the earth’s circumference comes out to about 23,990 miles and the diameter to about 7,580 miles. These figures are within 4 percent of what we know today as the earth’s circumference—24,887.64 miles—and its diameter, 7,926 miles. And he figured that out with only a few sticks—and one long hike. Eratosthenes made other important contributions to early astronomy. He accurately measured the tilt of the earth’s axis with respect to the plane of the solar system, and compiled an accurate and impressive star catalog and a calendar that included leap years.

We may consider Eratosthenes the first astronomer in the modern sense of the word. He used careful observations and mathematics to venture beyond a simple interpretation of what his senses told him. This combination of observation and interpretation is the essence of what astronomers (and all scientists) do. It is a cruel irony that Eratosthenes lost his eyesight in old age. Deprived of his ability to observe, he committed suicide by starvation.

Anaxagoras Explains Eclipses

Anaxagoras (ca. 500–ca. 428 B.C.E.) believed that the earth was flat, but speculated that the sun was a large, red-hot body and that the moon was much like the earth, complete with mountains and ravines. Most important, Anaxagoras theorized that solar eclipses were caused by the passage of the moon between the sun and the earth. His was the first explanation of an eclipse that didn’t involve the supernatural and certainly didn’t summon up any dragons.

Aristarchus Sets the Sun in the Middle and Us in Motion

Living in a technology-driven society, we’ve become accustomed to thinking of linear progress in science, a movement from point A, which takes us to point B, then to point C, and so on. We don’t think that steps backward can ever occur. If this were the way knowledge actually was built, the model of a geocentric (or earth-centered) universe would have died during the second century B.C.E.

Far in advance of his peers, Aristarchus of Samos (ca. 310–230 B.C.E.) proposed that the earth is not at the center of the universe or the solar system, but that it orbits the sun while also rotating.

This theory sounds completely reasonable to our modern ears, but it did not sit well with the Greek philosophical establishment, nor with common sense. Why, one might ask, if the earth is orbiting the sun, and spinning on its axis do we not all go flying into space as we would if the earth were a large merry-go-round? Without a theory of gravity (which keeps everything stuck to the surface of the earth as it spins), there was no good answer to this valid question.

One philosopher, Cleanthes the Stoic, went so far as to declare that Aristarchus should be punished for impiety. Maybe if he had been punished, becoming a martyr to his idea, the heliocentric (sun-centered) solar system would have caught on much sooner than it did. But it didn’t. The geocentric model of Aristotle and others held sway for millennia.

Pythagoras Calls Earth a Globe

Anaximander and Anaximenes may no longer be household names, but a lot of us remember Pythagoras (ca. 580–ca. 500 B.C.E.) from high school geometry. We all heard about the man who is credited with the Pythagorean theorem (“The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse,” or A2 + B2 = C2). He also taught that the earth was a globe—not a cylinder and certainly not flat—and that it was fixed within a sphere that held the stars. The planets and the sun moved against this starry background.

Anaximenes Says Stars Burn

Anaximenes of Miletus (active around 545 B.C.E.) theorized that what he called aer (air or vapor) was the most basic form of matter and was also the substance that formed the life spirit of animals, the soul of humankind, and the divine essence of the gods. He also believed that, when rarified, aer turned to fire, and he held that the sun, moon, and stars were collections of rarified aer, masses of fire, which, he believed, were set into a great crystal hemisphere.

Anaximander Puts Earth in Space

The word philosopher means “lover of wisdom,” which accurately describes the passion of the Greek philosophers. These were not idle thinkers eating grapes in secluded gardens. These were men who observed the world around them and wondered how the elements that made up the earth worked together and how human beings fit into the resulting grand scheme. For some eight centuries, Greek philosophers confronted some of the most fundamental questions in the natural sciences. What is the smallest division of matter? What are we and the world made of? How big are the earth and the universe? Beginning with Thales, the first of the important Greek philosophers (born about 624 B.C.E.), and culminating with Ptolemy (who died about C.E. 180 and whom we’ll meet in the next chapter), a series of Greek philosophers thought most intensely about the sky and the wonders it presented. Thales’ junior colleague and student, Anaximander (610–546/545 B.C.E.), is often called the founder of astronomy. He might even more accurately be called the father of a particular branch of astronomy, cosmology, which deals with the structure and origin of the universe. Anaximander theorized that the world and everything in it were derived from an imperceptible substance he called the apeiron (unlimited), which was separated into various contrasting qualities and eventually differentiated into all matter, including the earth. Importantly, Anaximander rejected what was then the prevailing notion that the earth was suspended from or supported by something in the heavens. He held that the earth floated freely in space at the center of the universe. Without reason to move anywhere, the earth, shaped like a short cylinder (we’d call it a soup can today), floated motionless. As for the stars, they were fiery jets, and the sun a chariot wheel whose rim was hollow and filled with fire.

Grecian Formula

We could go on with speculation about the astronomy of the Far East, Near East, and New World (and those interested should read E. C. Krupp’s Echoes of the Ancient Skies: The Astronomy of Lost Civilizations, New York, 1983), but it would be just that: fascinating speculation. For these early astronomers left few written records, and those they did leave either note only their observations or link such observations to religion and mythology. These earliest records do not show any effort to use astronomical observation to explain the physical realities of the world and the cosmos. For these first attempts, we must turn to the Greeks.

The Stonehenge

The ancient peoples of the Far East and the Middle East had no monopoly on the stars. The endlessly fascinating Stonehenge, built in stages between about 2800 B.C.E. and 1550 B.C.E. on the Salisbury Plain in Wiltshire, England, seems almost certainly to have been designed as a kind of astronomical observatory or, as some scholars have argued, a computer of astronomical phenomena. Various features of Stonehenge are aligned on the positions of the sun and moon where each rise and set on particular days known as solstices (the days of longest and briefest daylight, which begin the summer and winter, respectively). Thus it is widely agreed that Stonehenge was at least in part used for the keeping of a calendar.
Elsewhere in England and on the continent other circular stone monuments, akin to Stonehenge, are to be found. These have also been studied for the relation they bear to astronomical phenomena.
The New World, too, has its celestially oriented ancient structures. Around C.E. 900, at Cahokia, in southern Illinois, a Native American people known to us as the Mound Builders erected more than a hundred earthen mounds, the layout of which seem to mirror a concept of a cosmic plan. Farther south, the Maya of Mexico built magnificent stepped pyramids, like the one at Chichén Itzá in the Yucatan, clearly oriented toward the sunset at the winter solstice, as if to mark the annual “death” of the sun.
The Maya (and later, the Aztecs) used celestial observation to formulate a calendar as accurate as that which the Chinese had developed. A host of North American, Mesoamerican, and South American Indian monuments reveal careful orientation toward specific astronomical events. For example, the great kiva (a subterranean ceremonial chamber perhaps dating from C.E. 700 to 1050) at Chaco Canyon, New Mexico, built by the Anasazi, ancestors of the Zuni, Hopi, and Navajo, is oriented to mark the sunrise on the day of the summer solstice. Mayan and Aztec structures found throughout Mexico, such as the Hall of Columns at Alta Vista, dating to about C.E. 700, seem to be oriented to mark sunrise on the days of the equinoxes (the days of equal night and day, which mark the beginning of spring and fall). Monte Albán, built by the Zapotec of ancient Oaxaca, Mexico, as early as the eighth century B.C.E., seems to be oriented to the sun at zenith and to the rising of the star we call Capella.

The Universe-in-a-Box

The pyramids were not observatories, although it is tempting to think of them as such. The astronomical alignments they demonstrate were symbolic or magical rather than practical. Indeed, except for their very accurate calendar, the Egyptians seem to have made little of what we would call scientific use of their many astronomical observations. The ancient Egyptians drew images of constellations (an Egyptian star map was discovered by one of Napoleon’s generals in 1798 when the French army campaigned in Egypt) and made accurate measurements of stellar positions. However, they also reached the fantastic conclusion that the universe was a rectangular box, running north and south, its ceiling flat, supported by four pillars at the cardinal points—due north, south, east, and west. Joining the pillars together was a mountain chain, along which the celestial river Ur-nes ran, carrying boats bearing the Sun, the Moon, and other heavenly deities. In fact, many early cultures developed an accurate astronomical calendar side by side with a fanciful mythology.

Celestial Pyramids

To think of the Egyptians is to think of the pyramids, the great tombs of the pharaohs. Prayers carved into the walls of pyramid chambers make reference to the stars and to the pharaoh’s ascent into the sky among them. Texts inscribed on the monuments at Saqqara, Egypt, tell of the pharaoh joining the circumpolar stars, which neither rise nor set, and therefore live eternally. These texts also tell of the pharaoh’s journey to the constellation Orion—identified by the Egyptians with Osiris, the eternally resurrected god.
Replete as the pyramids are with such astronomical texts, it is little wonder that many archaeologists and others have speculated about the astronomical significance of the pyramid structures themselves. Certainly the Great Pyramid, by far the largest of the 80 or so known pyramids along the Nile’s west bank, is celestially aligned. Internal shafts or ducts point to the star Thuban, which in ancient Egyptian times was the North Star. Other shafts point to Orion’s Belt at certain times of the year, as if to indicate the afterlife destiny of the pharaoh, toward the deathless North Star (which does not rise or set) on the one hand, and toward the constellation associated with the eternally reborn god Osiris on the other.

The Venus Tablet

Some time between 1792 and 1750 B.C.E., during the reign of Hammurabi, the Babylonian king who gave the world its first code of laws, the so-called Venus Tablet was inscribed, devoted to interpreting the behavior of that planet. Babylonian astronomers believed that the movements and positions of planets with respect to the constellations could influence the fate of kings and nations. This interest in the positions of planets as a portent of the future was one early motivation for careful study of the heavens.
It is easy to imagine why, of all the planets, Venus captured the attention of the Babylonians. If you see a bright, steadily shining object in the west at or before sunset, or in the eastern sky at or before sunrise, it is almost certainly Venus—the brightest celestial object after the Sun and the Moon. Like the Moon, Venus has distinct phases, seen here.

Egyptian Astronomy

While the Chinese, the Babylonians, and the Chaldeans used astronomical observations to help them rule and regulate the living, the ancient Egyptians used the observations and measurements they made to help the dead find their place in the afterlife. Actually, Egyptian astronomers worked for both the living and the dead. They created a calendar to help predict the annual flooding of the Nile—essential information for a people whose entire agriculture was subject to the whims of that river. To create their calendar, Egyptian sky watchers concentrated in particular on the rising of the star Sirius (which they called Sothis). Working from these data (measuring the time from one rising of Sirius to the next), Egyptian astronomers were able to determine that a year was 365.25 days long.

Time, Space, Harmony

More than 4,000 years later, the fate of Hsi and Ho is still regrettable, but not nearly as important as the fact that we know about their fate at all. The Chinese made records of their astronomical observations and, indeed, along with the Babylonians were some of the earliest people to do so. Some oracle bones (animal bones used to foretell the future) from the Bronze Age Shang dynasty (about 1800 B.C.E.) bear the early Chinese ideogram character for “pillar.” Scholars believe that this ideogram is associated with a gnomon, a pillar or tower erected for the purpose of measuring the sun’s shadow in order to determine, among other things, the dates of the solstices.
Writings from the Zhou dynasty, in the seventh century B.C.E., reveal that a special tower was built to measure the sun’s shadow. During the Han era (C.E. 25–220), the town of Yang-chhêng was judged to be the center of the world, probably because the principal gnomon was installed there (or the gnomon may have been installed there because it was considered the center of the world). By C.E. 725, many smaller gnomons— what might be called field stations—were set up along a single line of longitude extending some 2,200 miles from the principal gnomon at Yang-chhêng. With this system, the Chinese could calculate calendars with considerable precision. In subsequent eras, even more elaborate gnomon towers—observatories, really—were built, including that of the astronomer Guo shou jing at Gao cheng zhen in Henan province, in C.E. 1276.
Why this passion to measure the heavens and the passage of time? Living in harmony with nature has always been important in Chinese philosophies, and, in terms of practical politics, exact knowledge of the heavens aided rulers in establishing and maintaining their absolute authority.

The Plain Old Astronomy

One of the great attractions of astronomy is that it so new and yet so old. Astronomy asks many questions that push the envelope of human knowledge. What exactly are black holes? How did the universe begin and how will it end? How old is the universe? At the same time, it is the most ancient of sciences. The Babylonians, who lived in southeastern Mesopotamia between the Tigris and Euphrates rivers (present-day southern Iraq from Baghdad to the Persian Gulf), are the first people we know of who actively studied the stars and planets. As early as 3000 B.C.E., they seem to have identified constellations and, sometime later, developed a calendar tied to the recurrence of certain astronomical events (they didn’t have NCAA basketball tournaments back then to let them know it was springtime).
Astronomy was only one of the Babylonian areas of knowledge basic to civilization. From ancient Babylonia came the first system of writing, cuneiform; the earliest known body of law, the Code of Hammurabi; the potter’s wheel; the sailboat; the seed plow; and even the form of government known as the city-state. And whenever people sought to bring order and understanding to their world, astronomy was part of the effort.
If you are reading this blog, it’s a safe bet that you’re interested in astronomy. You’re not alone today, and you haven’t been alone for at least 5,000 years and probably a lot longer.

Why the Emperor Executed Hsi and Ho

Like human beings everywhere throughout history, the Chinese in ancient times were a self-centered people. In fact, the Chinese word for their own country means “Middle Kingdom.” Their belief was that the objects in the heavens had been put there for the benefit of humankind in general and for the emperor in particular. Perhaps for this reason, they felt particularly threatened when, occasionally, something seemed to take a bite right out of the sun, then nibble away, gradually and ominously darkening the sky and the earth below.
The Chinese reasoned that a great dragon was attacking the sun, trying to consume it, and that since it was a beast, it might be susceptible to fear. So, in the midst of an eclipse, people would gather to shout, strike gongs, and generally make as much noise as possible—the more noise the better, since the beast was very big and was certainly very far away. Eventually the noise appeared to always scare off the dragon.
Because it was important to assemble as many people to make as much noise as possible, it was of inestimable value to get advance warning of an eclipse. With infinite patience, generations of Chinese astronomers observed solar eclipses and discovered something they called the Saros, a cycle in which sun, moon, and earth are aligned in a particular way every 18 years, 11.3 days—more or less.
Armed with a knowledge of the Saros, the Chinese were able to predict eclipses—usually.
We know of this because in 2136 B.C.E. there was an unpredicted eclipse, which caught the noisemakers unawares. It was only by great good fortune that the sun wasn’t consumed entirely. The Imperial Court astronomers Hsi and Ho weren’t so fortunate. They were executed for having fallen down on the job. (The royal astronomer position may have been particularly difficult to fill after the “departure” of Hsi and Ho.)