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.

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.

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.

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.

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, Clean-thes the Stoic, went so far as to declare that Aristar-chus 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.

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,

Star Words

Geocentric means earth-centered, and the geocentric model of the universe is one in which the earth is believed to be at the center of the universe. Heliocentric means sun-centered and accurately describes our solar system, in which the planets and other bodies orbit the sun.

Star Words

Geocentric means earth-centered, and the geocentric model of the universe is one in which the earth is believed to be at the center of the universe. Heliocentric means sun-centered and accurately describes our solar system, in which the planets and other bodies orbit the sun.

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.

Close Encounter

Aristarchus also tried to estimate the size of the sun and moon and their distance from the earth. His geometry was off, so the values he derived proved inaccurate. However, he did fix a reasonably accurate value for the solar year (see Chapter 3 for a definition and discussion of the term) and is honored by a lunar crater named for him. The peak in the center of the Aristarchus crater is the brightest feature on the face of the Moon.

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 V5o of 360 degrees, Eratosthenes figured that the two cities were separated by V5o 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.

Did you ever wonder why "clockwise" is the way it is and not the other way? On a sunny Saturday morning, put a stick vertically in the ground, as Eratosthenes did so many years ago. Now, as the sun comes up, mark where the shadow of the stick points at 1 hour intervals—10 a.m., 11 a.m., 12 p.m., 1 p.m., 2 p.m. You should notice a few interesting things. Stand to the south of your stick and look at it. Where is the mark for 12 p.m. (noon)? Is it at about the same place as noon on your wall clock? How about the marks for 1 p.m. and 2 p.m.? The sun's daily motion across the southern sky determines the "clockwise" motion of the shadow. The shadow of the gnomon was the "hour hand" on one of the oldest clocks—the sundial—and you can see the echo of this ancient timekeeping technique in the orientation of the numbers, and the "clockwise" sweep of the hands on your wristwatch.

Did you ever wonder why "clockwise" is the way it is and not the other way? On a sunny Saturday morning, put a stick vertically in the ground, as Eratosthenes did so many years ago. Now, as the sun comes up, mark where the shadow of the stick points at 1 hour intervals—10 a.m., 11 a.m., 12 p.m., 1 p.m., 2 p.m. You should notice a few interesting things. Stand to the south of your stick and look at it. Where is the mark for 12 p.m. (noon)? Is it at about the same place as noon on your wall clock? How about the marks for 1 p.m. and 2 p.m.? The sun's daily motion across the southern sky determines the "clockwise" motion of the shadow. The shadow of the gnomon was the "hour hand" on one of the oldest clocks—the sundial—and you can see the echo of this ancient timekeeping technique in the orientation of the numbers, and the "clockwise" sweep of the hands on your wristwatch.

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.

Eratosthenes drew a fanciful map of the world whose circumference he had estimated so precisely. (Image from arttoday.com)

The Least You Need to Know

V The Babylonians were the first known astronomers, making observations as early as 3000 b.c.e.

V The Chinese used astronomical observation to aid in predicting such events as eclipses and to create and reinforce the sense of divine order in the universe.

V Egyptian astronomy was in large part intended to help the dead find their way in the afterlife.

V From our perspective, the Greeks are the most important of the ancient astronomers because they used their careful observations to analyze, measure, and explain physical reality.

V With his keen eye for observation and his genius for using observation to draw conclusions beyond what could be directly observed, the Greek philosopher Eratosthenes may be considered the first astronomer in the modern sense of the word.

Chapter 3

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