Measuring the Universe: Our Historic Quest to Chart The Horizons of Space and Time

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More than 2,000 years ago, Eratosthenes, in Alexandria, used a stick, a hole in the ground, sunllght at summer solstice, and elementary geometry to measure the circumference of the Earth with surprising accuracy, long before anyone was able to circumnavigate it. Today, scientists are attempting to measure the entire universe and to determine its origin. Although the methods have changed, the quest to chart the horizons of space and time continues to be one of the great ...

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Measuring the Universe: The Historical Quest to Quantify Space

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Overview

More than 2,000 years ago, Eratosthenes, in Alexandria, used a stick, a hole in the ground, sunllght at summer solstice, and elementary geometry to measure the circumference of the Earth with surprising accuracy, long before anyone was able to circumnavigate it. Today, scientists are attempting to measure the entire universe and to determine its origin. Although the methods have changed, the quest to chart the horizons of space and time continues to be one of the great adventures of science.

Measuring the Universe is an eloquent chronicle of the men and women– from Aristarchus to Cassini, Sir Isaac Newton to Henrietta Leavitt and Stephen Hawking–who have gradually unlocked the mysteries of "how far" and in so doing have changed our ideas about the size and nature of the universe and our place in it. Kitty Ferguson reveals their methods to have been as inventive as their results were–and are–eye-opening. Advances such as Copernicus's revolutionary insights about the arrangement of the solar system, William Herschel's meticulous creation of the first three-dimensional map of the universe, and Edwin Hubble's astonishing discovery that the universe is expanding have by turns revolutionized our concept of the universe. Connecting centuries of breakthroughs with the political and cultural events surrounding them, Ferguson makes astronomy part of the sweep of history.

To measure the seemingly immeasurable, scientists have always pushed the boundaries of the imagination–today, for example, facing the paradox of an ever-expanding universe that doesn't appear to expand into anything. In Kitty Fergeson’s skillfill hands, the unimaginable becomes accessible and the splendid quest something we all can share.

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Editorial Reviews

Publishers Weekly - Publisher's Weekly
When you wish upon a star, do you ever consider that the bright one over there in the Hyades might be closer than the one in the Big Dipper that you usually wish on? Or that your wish might get there faster? Although even the closest star (Proxima Centauri) is so far away (25 1/4 trillion miles) that humanity will probably never travel to it, Ferguson (Prisons of Light: Black Holes) demonstrates why knowing its distance from us is important, and not just for reasons of wish fulfillment. For only by drawing an accurate scale map of the universe, she explains, can scientists estimate its age, one of the most hotly contested issues of our time. Ferguson begins with attempts in antiquity to establish the distance to the sun and the five planets seen by the naked eye. She discusses the findings of Copernicus, Kepler and Galileo, and how each drew on the others' work. Her simple explanations of the discoveries of stellar parallax, the Doppler effect and redshift, and of absorption spectra make important scientific concepts clear for general readers. She goes on to elucidate how astronomers determine how far away other stars are by using a type of star called Cepheid, as well as the spectacular stellar self-destructions known as supernovae as "standard candles." To conclude her engrossing survey, Ferguson covers some of the paradoxes that scientists confront, such as that some estimates of the age of the universe have determined that it is younger than some of its oldest stars, and that the amount of observable mass in the universe is only about 10% of what should be there. (July) Copyright 1999 Cahners Business Information.
Library Journal
Ferguson (The Fire in the Equations: Science, Religion, and the Search for God) is a popular science author, and deservedly so--she has a gift for explaining difficult scientific concepts in clear prose, and her engaging style conveys a real sense of the social, political, and intellectual times in which these discoveries were made. She captures the excitement and wonder of discovery and provides an understanding of what motivates scientists. This book has the feel of a historical novel--in Ferguson's hands, astronomy becomes part of the sweep of history. Starting with Eratosthenes and his calculation of the earth's circumference using the shadows cast in a well, and moving through Stephen Hawking's work on black holes, Ferguson tells the tale of our search for our place in the universe. This book is nicely illustrated with photos, tables, and diagrams, and there is also a useful glossary. Recommended for academic as well as public libraries.--James Olson, Northeastern Illinois Univ. Lib., Chicago Copyright 1999 Cahners Business Information.
Booknews
A veteran popularizer of science, Ferguson traces how people in western history have attempted to measure space from the ancient Greeks to modern physicists and astronomers. She begins with Eratosthenes' accurate measurement of the circumference of the Earth in the third century BC and progresses to the theories of Stephen Hawking and his contemporaries. Her account is for general readers. She includes a glossary that does not indicate pronunciation. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From The Critics
This book is an exciting introduction to the scientific method. It opens with an account of Ferguson'ss sense of discovery when her father proposed that they determine the height of a windmill by comparing the length of its shadow with the shadow of a meter stick. She "reveled in our wonderous secret: not the height of the windmill but the knowledge of how to find it." The book provides insights into the personalities of astronomers like Edwin Hubble, already a lawyer when he turned to astronomy, who is quoted as saying, "I would much rather be a second-rate astronomer than a first-rate lawyer." The author attributes Penzias and Wilson's discovery of the cosmic background radiation to "the stubborn curiosity of these two men and points out that, several years earlier, another Bell Laboratories engineer had observed the same radiation, but "didn't pursue it or suspect its significance." The book chronicles discoveries spanning more than two millennia concerning the size of the Earth, the size of the solar system, the size of our galaxy, and the size of the universe, focusing not on the actual numbers, but on the ingenuity required to determine those numbers.

Ferguson gives an interesting and entertaining discussion of the evolution of scientific ideas, explaining how the solution to one question, such as determining that the Earth moves around the Sun, leads naturally to the next question: Why can't motion of the stars be detected? Well-executed illustrations supplement clear descriptions of the models for motion in the solar system. Drawing on an analogy to a carousel ride, Ferguson explains the complex Ptolemaic concepts of eccentrics and epicycles in a way that should beunderstandable to middle school and high school students. However, she fails to provide either a diagram or an explanation for the correct, but certainly not obvious, statement that Tycho Brahe's model of the solar system, with the planets orbiting the sun while the Sun orbits the Earth, "is the geometric equivalent of the Copernican model."

Readers will come away from this book convinced that ingenuity has solved many of the important problems of astronomy, but other problems remain for the next generation of astronomers. The author provides an up-to-date account of efforts to determine the rate of expansion of the universe and answer the question of whether it will it expand forever or collapse back upon itself. Highly Recommended, Grades 7-12, Teaching Professional, General Audience. REVIEWER: Dr. George J. Flynn (State University of New York)

Kirkus Reviews
Science writer Ferguson (Prisons of Light: Black Holes, not reviewed) traces astronomers• efforts to gauge the size and age of the earth, moon, and stars, from the ancient Greeks to space-age cosmologists. Think big. The saga begins with a pint-size system centered on earth and ends (for now) with today's picture of the sun as a minor player on the outskirts of a mid-size galaxy, one of billions in the universe. Think ingenious. Ferguson covers everything from the canny methods Eratosthenes used to measure the circumference of the earth (plane geometry played a big part) to the numerous measuring techniques available today, including the use of Cepheid variable stars, statistical parallax, spectroscopy/luminosity methods, etc. To some extent, this book chronicles the history of technology, because only with the construction of bigger and better telescopes (and, ultimately, the ability to place telescopes in orbit to eliminate atmospheric distortion) could more accurate measurements be made. You would think with all that, there would be some consensus. Uh-uh: Think margins of error, think many unknowns. The boundaries of space remain problematic; the issues of whether the universe is closed or open, spherical or tuba-shaped are undecided. Even the "inflationary" theory•the idea that shortly after the Big Bang the universe underwent a spectacularly rapid expansion that scattered matter around in ways that could condense into blobs and clusters of galaxies with voids between•is under attack. Many weird and wonderful puzzles remain: the issue of dark matter, the "weight" of neutrinos, a conjectured fifth force that works like anti-gravity, not to mention parallel universes,wormholes, singularities, and others ideas bubbling from the fertile imaginations of Hawking, Penrose, and others. In addition to lucidly detailing the wild surmises of today's astronomers and astrophysicists, Ferguson sets past pioneers•Galileo, Cassini, Newton, et al.•in their cultural context, seeing them vis-à-vis contemporary challengers, as well as church and state. Good science history finely seasoned with politics, personality, and sociology.
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Product Details

  • ISBN-13: 9780802713513
  • Publisher: Walker & Company
  • Publication date: 7/1/1999
  • Pages: 352
  • Lexile: 1300L (what's this?)
  • Product dimensions: 6.50 (w) x 9.25 (h) x 1.25 (d)

Meet the Author

Kitty Ferguson is a science writer and the author of Prisons of Light: Black Holes; The Fire in the Equations: Science, Religion, and the Search for God; and Stephen Hawking: Quest for a Theory of Everything. She is also a professional musician. Ms. Ferguson lives in Northern New Jersey.

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Read an Excerpt




Chapter One


A Sphere
with a View


{400-100 B.C.}


"The great mind, like the small, experiments with different alternatives, works out their consequences for some distance, and thereupon guesses (much like a chess player) that one move will generate richer possibilities than the rest.... It still remains to ask how the great mind comes to guess better than another, and to make leaps that turn out to lead further and deeper than yours or mine. We do not know."
Jacob Bronowski


Eratosthenes of Cyrene, who held the distinguished title of director of the Alexandria Library from 235 to 195 B.C., also had two nicknames: "Pentathlos" and "Beta." Pentathlos was a name for athletes who entered the pentathlon, which required five skills. Eratosthenes was not an athlete. The nickname implied lie was a jack-of-all-trades. The word beta stood for the letter B or number two or second. Put those together and you get "jack-of-all-trades and master of none." Whether Eratosthenes's colleagues gave him those names out of fondness or scorn isn't known, but whatever mockery this venerable polymath may have endured, Beta is remembered while most who dubbed him that have long since been forgotten.

    Eratosthenes's accomplishments were, indeed, numerous and eclectic. He attempted to fix the dates of the major literary and political events since the conquest of Troy; he composed a treatise about theaters and theatrical apparatus and the works of the best-known comic poets of the"old comedy"; he suggested a way of solving a problem that had tantalized mathematicians for two centuries—"duplicating a cube"; and he let his voice be heard on the subject of moral philosophy and felt it essential to criticize those who were "popularizing" philosophy ... "dressing it up in the gaudy apparel of loose women." But it was none of those achievements that won him his place in the history books. What modern school-children learn about him is that he invented "the sieve of Eratosthenes"—a method for sifting through all the numbers to find which are prime numbers—and that he discovered a way to measure the circumference of the Earth with astounding accuracy.

    The idea that scholars before Columbus believed the world was flat is a fable created in modern times. Admittedly, the shape of the Earth probably wasn't of much daily practical interest to most people in the ancient world. However, already long before Eratosthenes, those few who were wondering about it at all were not seriously suggesting that the Earth was any shape but spherical. The Pythagoreans, a school of thinkers revered for their genius in mathematics and music, had decided as early as the sixth and fifth centuries B.C. that the Earth is a sphere. A century before Eratosthenes, Plato pictured a cosmos made up of spheres within spheres, nested one within the other, with a spherical Earth at the center. Only a little later than Plato, Aristotle vigorously subscribed to the idea of a spherical Earth, and his defense proved convincing not only to the ancient world but also to the Middle Ages.

    Aristotle rested his case partly on observational evidence: During an eclipse of the Moon, the shadow cast by the Earth on the Moon is always curved. Also, in Aristotle's words:


There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighborhood of Cyprus which are not seen in the northerly regions; and stars which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the Earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be so quickly apparent.


Aristotle speculated that the oceans of the extreme west and the extreme east of the known world might be "one," and he reported with some sympathy the arguments of those who had noticed that elephants appeared in regions to the extreme east and the extreme west, and who thought therefore that those regions might be "continuous."

    Aristotle's philosophy also argued for a spherical Earth. He had concluded that five elements—earth, air, water, fire, and aether—each have a natural place in the universe. The natural place for the element earth is at the center of the universe, and for that reason earth (the element) has a natural tendency to move toward that center, where it must inevitably arrange itself in a symmetrical fashion around the center point, forming a sphere. Aristotle reported that mathematicians had estimated the Earth's circumference as 400,000 stades; that is, about 39,000 miles or 63,000 kilometers (more than half again as large as the modern measurement). No record survives of the method used to arrive at that number.


The Intellectual Spoils of War


When Aristotle died in 322 B.C. at age sixty-two, the military campaigns of his most highly achieving pupil, Alexander the Great, had just ended with Alexander's death. Vastly widened mental horizons were part of Alexander's extraordinary legacy. His campaigns had carried Greek knowledge, language, and culture throughout Asia Minor and Mesopotamia as far east as present-day Afghanistan and Pakistan, all the way to the Indus River, as well as to Palestine and Egypt. The culture of Greece and its colonies and the cultures of the conquered peoples began to mix and enrich one another. This was the dawn of the Hellenistic era, as opposed to the Hellenic. That is, Greekish, as opposed to Greek.

    At the time of Alexander's and Aristotle's deaths, within a year of one another, Athens was still the undisputed center of the intellectual world. That preeminence was not to last. Alexander's generals divided his empire, and Ptolemy's portion was Egypt and Palestine. He made Alexandria, near the mouth of the Nile, his capital. This already prospering city began to grow in size and splendor, and Ptolemy and his successors, reputedly ruthless in their exploitation of the lands under their control, amassed a surplus of wealth, some of which they chose to spend on literature, the arts, mathematics, and science. Scholars are divided as to which Ptolemy should get the credit (Ptolemy's successors were also named Ptolemy), but either the first or the second, and perhaps it took both, extended the royal patronage to found a library and a museum. The word museum meant "temple to the muses," both a religious shrine and a center of learning.

    Meanwhile the old, justly famous schools across the sea in Athens, schools founded by Plato, Aristotle, Epicurus, and the Stoics, were no longer producing vibrant new ideas to quite the extent they once had, though they were still the places a young man of Eratosthenes's time would have wished to go for his education. Alexandria began to rival and eventually supplanted Athens as the focal point of the thinking world, and the Alexandria Museum and Library became the premier research institution. The library grew large, containing by one ancient estimate nearly 500,000 rolls. The salary of the director, or librarian, came from the royal coffers.

    The story (now thought to be apocryphal) is that the contents of the library at Alexandria were burned to heat the public baths for six months in the seventh century A.D. Whether the destruction occurred quickly and calamitously then or, more likely, gradually through neglect and the many political, military, and religious turns of fortune that affected the city of Alexandria, the loss was the symbol and symptom of a greater tragedy: the widespread disappearance of any perception that such intellectual achievement was of value. By the 600s, there was probably little left to burn. It took centuries for humanity in the Western world to reach again an intellectual level on a par with the civilization that had produced that lost collection. But in the third and second centuries B.C., all this was still many centuries in the future. The Alexandria Library was in its heyday.

    The scholars connected with this august institution and their forebears in the Hellenic world would have been mystified by the present-day concept of "science" as a distinct category of knowledge and pursuit of knowledge. Some modern words have evolved from terms they used to describe similar areas of interest, but the modern words don't have precisely the same meaning these had in ancient Athens and Alexandria. Some examples: peri physeos historia (inquiry having to do with nature); philosophia (love of wisdom, philosophy); theoria (speculation); and episteme (knowledge). Hellenistic scholars thought of "physics" as one of three branches of philosophy. The other branches were "logic" and "ethics."

    Another key difference between the ancient and modern ways of thinking is that Hellenic and Hellenistic scholars tended to be somewhat scornful of the notion that their effort might serve mundane, practical purposes. They preferred to think of it as contributing to wisdom, or improvement of one's character, or leading to greater appreciation of the beauty of the universe and understanding of its creator. The life of a scholar, the life of "contemplation," was considered an exquisitely happy life. Doctors, whose efforts were intended to have more everyday practical value, were apt to differentiate themselves entirely from the "philosophers," whose work was its own reward, an end in itself, not a means to an end. The Ptolemys were of course far from displeased when research could be applied to problems connected with weaponry, but their financial support and their efforts to outbid all competitors when it came to collecting the masterpieces of Greek literature and encouraging distinguished scholars to flock to Alexandria were far more strongly motivated by desire for prestige—to add to the luster and apparent power of the dynasty. It seemed not to occur to these men and women in ancient times that scholarly endeavors might hold the key to material progress.

    Theirs was also a perspective in which how to solve a problem was as interesting as actually solving it, often more so, an attitude arising partly out of necessity, for Greek and Hellenistic scholars were fascinated with questions that they lacked the technology to answer definitively. A modern analogy might be the typical "word problem" in grade school. Let's say you're presented with the question: If you ride your bicycle at an average speed of thirty miles per hour, and it takes you ten minutes to get from home to school, how far is school from home? You do not immediately start quibbling that thirty miles per hour is not an accurate measurement of the speed you normally ride, that it actually takes you twelve minutes to get to school, and that this exercise isn't going to end with anyone knowing how far from home your school really is. No. What everyone is interested in is your showing that you understand how to solve the problem. Move back a step and imagine that it is also up to you to invent the method for solving it—that no one, in fact, has ever even thought it possible to calculate the distance from your home to your school and that you can't ride there to measure it directly. You have put yourself in the shoes of Eratosthenes and others whose work this chapter describes, a situation that allows, indeed encourages, the formation of hypotheses, sometimes out of thin air ... statements such as, "We don't know that this is true, but let's assume for a moment that it is, and see where that gets us." Or even such a statement as, "We know that this is not true, but let's pretend for the moment that it is and ask `what then?'" To criticize the results of an exercise like that by saying the results are "wrong" (i.e., do not accord with twentieth-century findings) is to miss the point.

    The scholarly mind-set of his era partly explains why Eratosthenes took on what might seem to have been an impossible problem and tried to find an answer that was of no use to the ancient world: the circumference of the Earth. His success was rooted in the widened horizons and the mixture of cultures that characterized the Hellenistic world. It also had a great deal to do with the sort of man he was.


A Sunlit Well at Syene


Eratosthenes, "son of Aglaos," was born not in Egypt or Greece but in the ancient city of Cyrene, on the northern coast of Africa in what is now Libya. Citizens of Crete and Santorini had founded Cyrene some 350 years earlier, and it had become one of the most cultured cities of the Hellenistic world, though still subordinate to the Egypt of the Ptolemys. Cyrene counted some distinguished figures among its citizenry. The founder of the Cyrenaic school, Aristippos, had been a pupil of Socrates. Aristippos's daughter, Arete, followed him as head of the school, and her son, Aristippos II, succeeded her. He was nicknamed "Metrodidactos," which translates as "mother-taught."

    The date given for Eratosthenes's birth is the "126th Olympiad," referring to the Olympic games that took place every four years. In modern dating, that puts it between 276 and 273 B.C. He received most of his education in Athens at the feet of eminent scholars of the New Academy and the Lyceum. Plato and Aristotle had originally founded these schools (in Plato's day the New Academy had been simply the Academy), and though much had changed about them by the time Eratosthenes arrived, they were still the most prestigious educational institutions.

    By the middle of the century, Eratosthenes had written a few philosophical and literary works, and some of these had come to the attention of Ptolemy III Euergetes. The "brain-drain" from Athens being in the general direction of Alexandria, Eratosthenes in about 244 B.C. agreed to move there and become a fellow of the museum and tutor to the prince, Philopator. It is perhaps not to Eratosthenes's credit that his pupil, though a patron of arts and learning, gained a reputation for dissipation and crimes that rivaled Nero's and Caligula's later in Rome.

    In the course of time, Eratosthenes became a senior (alpha) fellow of the museum, and upon the death of the chief librarian he took over that post—an unparalleled vantage point from which to keep up with everything that was going on in the scholarly world.

    Unfortunately, none of Eratosthenes's many works have survived except in fragments. It's not even certain that all the fragments are genuine. Most information about him comes from reports and references of others. However, there is enough to tell that Eratosthenes's measurement of the Earth and his motive for attempting it were rooted in his eclectic and far-ranging knowledge and interests. Eratosthenes was a man of the world, in the literal sense of those words. He refused to categorize people as Greeks opposed to barbarians, adopting a new Hellenistic global point of view that had begun to replace the more parochial mind-set of Greece in earlier centuries. He collected information about the people, products, and geography of far-flung areas. He wrote about the history of geographic measurement, recalling old ideas going back to Homer about the size, shape, and geographic layout of the Earth. In fact, he did nothing less than pull together virtually all the geographic knowledge that had been accumulating up to his own time.

    Over the centuries, this material had taken a variety of forms. It came from traders, explorers, travelers—as well as mathematicians and philosophers—and it ranged from fantastic tales to more straightforward reporting, from speculation to measurements and estimates resting on what were probably recognized as shaky assumptions. Among the more reliable sources were eyewitness accounts of Alexander the Great's expeditions and the measurements and records of distances covered on those marches. There were itineraries of coastal voyages and maps and charts connected with them. There was a treatise on harbors by Timosthenes, the admiral of the Ptolemaic fleet, who also studied the winds. There was a book titled On the Ocean by the merchant sea captain Pytheas, who in about 320 B.C. sailed north along the coast of Spain and France and reached Cornwall, then continued all the way up to the Orkneys and the Shetlands to latitudes near those of the midnight sun. Pytheas took bearings throughout his voyage and recorded them in his book, which also had descriptive passages: "The barbarians showed us where the Sun keeps watch at night, for around these parts the night is exceedingly short, sometimes two and sometimes three hours, so that only a short interval passes after the Sun sets before it rises once more." Eratosthenes respected Pytheas's information, though many other scholars were contemptuous and disbelieving. Living as Eratosthenes did in Hellenistic Egypt, he may also have known of centuries-old and astoundingly accurate Egyptian geographic calculations.

    Eratosthenes's expertise on longitude and latitude surpassed any other of his day or earlier. His predecessors had divided the map into zones. He took that work several steps farther by improving on a map devised about twenty-five years before his birth by a man named Dicaearchus of Messene, who had divided the known world by using two lines or bands that intersected one another—one running east-west, the other north-south. On Eratosthenes's revised map the two lines crossed at Rhodes, a little to the east of where Dicaearchus's lines had met. The horizontal line passed near Gibraltar (then known as the Pillars of Hercules), ran the length of the Mediterranean, and then followed the Taurus chain of mountains in southern Turkey. (Toros Daglari on later maps.) The path of that line is remarkably close to the course of the thirty-seventh parallel—an impressive achievement without the benefit of the mathematical and astronomical knowledge that would go into later mapmaking. It was not yet possible to calculate latitude with very great precision and virtually impossible to determine longitude (which would prove to be a problem in Eratosthenes's measurement of the Earth). Eratosthenes's vertical line, following the Nile, doesn't line up so perfectly with Rhodes on modern maps. He drew six more vertical lines at intervals between the western and eastern boundaries of the inhabited world, and six more horizontal lines at intervals between its northern and southern boundaries. In addition, he established and measured geographic zones, dividing the world horizontally between the tropical region, the temperate region, and the polar circles.

    Eratosthenes was also well acquainted with state-of-the-art geometry, both from Euclid's brilliant summing up about twenty-five years before Eratosthenes's birth and from his association with Archimedes, an extraordinary genius and world-class eccentric. There is the familiar tale of Archimedes' solving a mathematical problem in his bath, leaping from the water, and running naked through the streets shouting "Eureka!" This avid mathematician eventually lost his life when Roman troops sacked Syracuse. Archimedes, so the story goes, was drawing a mathematical figure in the sand when a Roman soldier (who had missed hearing an order from his superiors to respect the person of this famous old man) asked him to pack up and move along. Archimedes unwisely told the soldier not to interrupt his thought process.

    The Hellenistic world revered Archimedes as an inventor (though he himself dismissed those practical achievements as unworthy) and a useful man in wartime. According to legend, he destroyed a Roman fleet by using burning mirrors. The Middle Ages respected him as an engineer and a wizard and credited him with the invention of the Staff of Archimedes, a stick with a small flat disk that could be run up and down it, so that an observer holding it up to the Sun and noting the distance from disk to eye could derive the Sun's apparent diameter. Modern history and mathematics books recall Archimedes as a brilliant mathematician and geometer who contributed significantly to the understanding of circles and spheres. Archimedes was in the habit of sharing his discoveries and his methods with Eratosthenes and even dedicated his greatest work, Method, to him. Eratosthenes must have welcomed another scholar who was almost as eclectic as he was himself.

    Eratosthenes's thoughts stretched to the horizon in all directions. Perhaps it follows that he would have longed to know not only what was beyond those horizons but how far "beyond" was. Mapping and systematizing things geographically was his bent. Would he not have been unusually curious about how large the total map was? How remarkable if it really should turn out to be, as Aristotle speculated, "a sphere of no great size"! Eratosthenes's thoughts often took a historical turn, and he was aware of previous attempts to measure the Earth or estimate that measurement. Would he not have wanted to try his own hand at it, using Euclid's and Archimedes' newer understanding of geometry?

    There is still one circumstance to be mentioned—a simple, trivial matter, yet Eratosthenes's successful measurement of the circumference of the Earth would not have taken place without it. A happenstance, perhaps, that such a small gem of information reached the ears of this man who realized what it meant and what could be done with it. It is true that the fact that this snippet of news reached him did have something to do with the broadened mental horizons of the world, with improved communications from remote areas, with Eratosthenes's own world centering on northern Africa, and with his habit of keeping his ears and eyes open and wanting to know everything and anything. He was indeed the right man in the right time and place. Perhaps there was no other so likely to run across this back-page news and recognize its worth:

    In a well located at Syene (near modern Aswan), on the day of the summer solstice, a shaft of sunlight penetrated all the way to the bottom of the well.

    Eratosthenes knew that this signified that the Sun was shining directly down at Syene, not at an angle, which meant that Syene was on the "Tropic." A stick set up at noon at Syene on the day of the summer solstice would not cast a shadow. A stick set up at Alexandria (which he thought was the same longitude as Syene) would. Accordingly, Eratosthenes set up a stick at Alexandria on the day of the summer solstice and measured the angle of its shadow when that shadow was at its shortest.

    Figure 1.1 shows the stick at Alexandria and its shadow and what "the angle of the shadow" means. If you draw a straight line from the point marked Alexandria (where the stick is casting a shadow) to the center of the Earth, and a second straight line from the point marked Syene (where the stick casts no shadow) to the center of the Earth, those lines will of course meet at the center of the Earth. The question is: What is the angle created by those two lines where they meet? The answer, as Eratosthenes knew, is that the angle at the center of the Earth and the angle of the shadow at Alexandria will be the same angle. Figure 1.2 illustrates Eratosthenes's measurement.

    Eratosthenes found that the shadow angle at Alexandria was 7 1/5 degrees, and so he knew that the angle between the "Syene/Alexandria lines" (meeting at the center of the Earth) was also 7 1/5 degrees. A circle has 360 degrees, and it is a simple process to find out how many of the Syene-Alexandria angles (7 1/5 degrees) it will take to make 360 degrees. Think of the cross section of the Earth as a pie and the two lines coming from Syene and Alexandria as cutting out a wedge of pie. How many wedges of that size can be cut from the whole pie? Divide 360 by 7 1/5, and it comes out to 50 wedges. Eratosthenes calculated that the distance between Syene and Alexandria at the surface of the Earth—at the pie-crust edge of the pie—is 5,000 stades. (There is a story that he sent a man to pace it off for him.) He multiplied 5,000 by 50 and concluded that the distance all the way around the Earth—the circumference of the Earth—is 250,000 stades. He later fine-tuned this to 252,000 stades.

    What is this odd unit of measurement, the stade? That question brings up a problem in evaluating Eratosthenes's result. Whether or not that result matches modern measurements for the circumference of the Earth depends on the length of stade he was using. If there are 157.5 meters in a stade, Eratosthenes's result comes to 24,608 miles (39,690 kilometers) for the circumference of the Earth. That is very near the modern calculation: 24,857 miles (40,009 kilometers) around the poles and 24,900 miles (40,079 kilometers) around the equator. After he found the circumference, Eratosthenes calculated the diameter of the Earth as 7,850 miles (12,631 kilometers), close to today's mean value of 7,918 miles (12,740 kilometers).

    Another way of figuring a stade was as one-eighth or one-tenth of a Roman mile, and that would make Eratosthenes's result too large by modern standards. There was one additional small difficulty. Eratosthenes assumed that Syene lay on the same line of longitude as Alexandria. Actually, it did not.

    But this is nit-picking! No apology need be made for Eratosthenes. First of all, he arguably came astonishingly near to matching the modern measurement. Second, he found a way to solve this problem by the imaginative use of geometry. His method was ingenious and correct. If the numerical result is a little fuzzy because of a lack of agreement about the length of a stade and the impossibility of determining longitude precisely, that does not detract from the brilliance of his achievement or of the intellectual leap involved in recognizing that measuring the Earth's circumference could be done and how it could be done.

    Eratosthenes's curiosity went beyond the Earth. He also considered the astronomical questions of his day. When it came to measuring the distances to the Sun and the Moon, he must have realized that he had no tool at his fingertips to equal the news about the well in Syene. Nevertheless, he gave it a try, with far less success than he had in measuring the Earth's circumference.


Aristarchus of Samos


Another Hellenistic scholar, Aristarchus of Samos, also tried to measure the distances to the Moon and Sun. Little biographical information exists about him. He lived from about 310 to 230 B.C. and was already a grown man when Eratosthenes was born. The island of Samos was under the rule of the Ptolemys during Aristarchus's lifetime, and it is possible that he worked{ in Alexandria. Archimedes was certainly aware of his contributions, and Aristarchus knew of Eratosthenes's measurement of the Earth.

    The only written work of Aristarchus that has survived is a little book called On the Dimensions and Distances of the Sun and Moon. In it he describes the way he went about trying to determine these dimensions and distances and the results he got.

    The book begins with six "hypotheses":

1. The Moon receives its light from the Sun.
2. The Moon moves as though following the shape of a sphere
and the Earth is at the central point of that sphere.
3. At the time of "half Moon," the great circle that divides the dark portion of the Moon from the bright portion is in the direction of our eye. In other words, we are viewing the shadow edge-on.
4. At the time of "half Moon," the angle at the Earth as shown in figure 1.3 is 87°.
5. The breadth of the Earth's shadow at the distance where the Moon passes through it during an eclipse of the Moon is the breadth of two Moons.
6. The portion of the sky that the Moon covers at any one time is equal to one-fifteenth of a sign of the zodiac.


    Aristarchus's fourth and sixth assumptions are both far from accurate. The actual angle at the Earth in Aristarchus's triangle would be 89° 52', not 87°, and 89° 52' is very close to 90°. The angle at the Moon in Aristarchus's triangle is 90°. (See figure 1.3.) That makes lines B and C so close to parallel that, on a drawing, the triangle would close up and be no triangle at all. The portion of one sign of the zodiac that the Moon covers is not one-fifteenth, and it isn't clear why Aristarchus, who must have known this from observation, chose that value.

    By Aristarchus's calculation, the distance to the Sun turned out to be about nineteen times the distance to the Moon, and the Sun nineteen times as large as the Moon. Modern calculations put the ratio between their distances at four hundred to one. The measurement Aristarchus was trying to make was extremely difficult with the instruments available to him. It is no simple undertaking to determine the precise centers of the Sun and the Moon or to know when the Moon is exactly a half Moon. Aristarchus chose the smallest angle that would accord with his observations, perhaps to keep the ratio believable. Throughout antiquity and the Middle Ages, estimates of the relative distances to the Sun and Moon would continue to be too small.

    Aristarchus didn't stop with estimating the ratios but found ways of converting them into actual numerical distances to the Sun and Moon and diameters for both bodies. He could see that the apparent size (meaning the size a body appears to be when viewed from the Earth) of the Moon and that of the Sun are about the same, for during a solar eclipse, the Moon just about exactly covers the Sun. In more technical language: both bodies have about the same "angular size." Angular size tells how much of the total sky a body "covers" when viewed from Earth, and is measured in terms of "degrees of arc." The Sun and the Moon cover about the same amount of sky. They both have angular sizes of about one half of a degree of arc. A fuller explanation of those terms is in figure 4.4. For now, it is important only to know that the two bodies don't actually have to be the same size in order to have the same angular size, for how large they appear when viewed from the Earth (and how much of the total sky they cover) also has a great deal to do with how distant they are. See figure 1.4a.

    Aristarchus correctly assumed that in spite of having the same angular size as the Moon, the Sun is actually much larger, and also much larger than the Earth. He knew that if the Sun was indeed much larger than the Earth, that made it safe to assume also that the shadow cast by the Earth has about the same angular size as the Sun and the Moon (one half of a degree of arc). Figure 1.4b shows what is meant by "the shadow cast by the Earth" and its angular size.

    Aristarchus arrived at his fifth hypothesis (the breadth of the Earth's shadow at the distance where the Moon passes through it during an eclipse of the Moon is the breadth of two Moons) by observing a lunar eclipse of maximum duration, which means an eclipse in which the Moon passes through the exact center of the Earth's shadow. He measured the time that elapsed between the instant that the Moon first touched the edge of the Earth's shadow and the instant that it was totally hidden. He then found that that length of time was the same as the length of time during which the Moon was totally hidden. He reasoned that the breadth of the Earth's shadow where it was crossed by the Moon must therefore be approximately twice the diameter of the Moon itself (figure 1.4c). If, as he thought, the angle formed at the point of the Earth's shadow was the same as the angular size of the Moon, that gave him only one distance at which to put the Moon where it would cover half of the area of the shadow.

    Aristarchus concluded that the Moon was one-fourth the size of the Earth, and that the distance to the Moon was about sixty times the radius of the Earth. Both of those values are close to the modern values. Using Eratosthenes's calculation of the Earth's radius, Aristarchus arrived at an actual distance to the Moon in stades. He had less success with the distance to the Sun. His earlier estimate—that the Sun's distance is about nineteen times the Moon's distance—was in error, and a second approach he tried, though it was ingenious and correct, required timing the phases of the Moon with a precision impossible in the ancient world.

    It was another of Aristarchus's ideas that secured his place much more firmly in the annals of astronomy. Hearing of it, one has a chilling sensation of stumbling into a prophetic vision. For Aristarchus suggested, seventeen centuries before Copernicus, that the Earth is not the unmoving center of everything but instead moves round the Sun, and that the universe is many times larger than anyone in his time thought—perhaps infinitely large.

    For centuries it had been widely assumed that the Earth was the center of the universe. The accepted picture of the cosmos was a series of concentric spheres—spheres imbedded one within the other—with the Earth resting motionless at the center of the system. (See figure 1.5.)

    Plato and his younger contemporary, Euxodus of Cnidus, had introduced this model, and Aristotle's model of the universe was a further development of it, though he differed from Euxodus as to the number and nature of the spheres. However, it wouldn't be correct to think that everyone, without exception, since the dawn of human thought, had agreed that the Earth was the center and didn't move. Some Pythagorean thinkers had decided in the fifth century B.C., largely for symbolic and religious reasons, that the Earth was a planet and that the center of the universe must be an invisible fire. Heraclides of Pontus, a member of Plato's Academy under Plato, proposed that the daily rising and setting of all the celestial bodies could be nicely explained if the Earth rotates on its axis once every twenty-four hours.

    But Aristarchus went farther. What we know about his theory of a Sun-centered cosmos comes secondhand yet no one disputes his authorship of the idea because there is plenty of secondary evidence. According to Archimedes:


Aristarchus of Samos brought out a book of certain hypotheses, in which it follows from what is assumed that the universe is many times greater than that now so called. He hypothesizes that the fixed stars and the Sun remain unmoved; that the Earth is borne round the Sun on the circumference of a circle ...; and that the sphere of the fixed stars, situated about [that is, centered on] the same center as the Sun, is so great that the circle in which he hypothesizes that the Earth revolves bears such a proportion to the distance of the fixed stars as the center of the sphere does to its surface.


    Aristarchus had done no less than move the center of the cosmos to the Sun. In this astounding turnabout, the Earth moves around the Sun and, rather than the sphere of the fixed stars making a revolution of the heavens once every twenty-four hours, it is the Earth that turns, rotating on its axis—as Heraclides had suggested. The stars are extremely far away. The implication is, perhaps infinitely far.

    Did Aristarchus also speculate that the other planets move around the Sun? There is no surviving evidence that he did or that he understood the enormous significance of his model: that it provides, at a sweep, the basis for explaining the planets' positions and movements far more simply than a model with the Earth as center. In fact, there isn't even any evidence to indicate whether Aristarchus really was personally disposed to thinking the Earth moved around the Sun or whether he made the suggestion merely for the sake of argument, as in "let's just suppose for the moment that this is how things work." Why did this revolutionary suggestion come at this time and place in history? The simple answer may be that this was an intellectual environment that encouraged one to make suggestions and put forward hypotheses, even hypotheses based on assumptions that were known to be incorrect—in no way claiming they were true—as the starting point for an interesting line of inquiry.

    It's also important to ask why this idea died aborning. Seleucus of Seleucia, a Chaldean or Babylonian astronomer (Seleucia was on the Tigris River) in the second century B.C., took Aristarchus's suggestion seriously—not merely as a hypothesis. Seleucus believed Aristarchus was right. However, it appears no one else did, although antiquity was by no means a dark age when it came to astronomy. There seems to have been almost no public reaction at all. Aristarchus's suggestion must have been too far removed from common knowledge and common sense to draw much popular attention. The historian Plutarch reports one comment from the Stoic Cleanthes (the Stoics were reputedly weak in natural science, even "antiscientific") that Aristarchus of Samos ought to be indicted on a charge of impiety for putting the "Hearth of the Universe" in motion. There is no record of anyone trying to take Cleanthes's advice. Some philosophers scolded Aristarchus for trespassing on an area of knowledge that was their sole domain. There were also complaints accusing him of undermining the art of divination.

    As for astronomers, what mattered most to them was that there was no observational evidence whatsoever to support the vast distances to the stars that Aristarchus's scheme required, while there was observational and physical evidence that made his Sun-centered arrangement seem highly unlikely:


1. If the Earth moves around the Sun, observers on the Earth should see some variation in the positions of the stars when viewing from different points along the Earth's orbit. No such variation had been observed (nor could it be with the technology available at the time). Aristarchus saw that this objection wouldn't be valid if the stars are far enough away. He suggested that they are very far away indeed, perhaps even at infinite distance. (The fact that the positions of the stars do change as the Earth orbits—that there is "stellar parallax motion"—wasn't confirmed by observation until the mid-nineteenth century.)
2. If the Earth rotates on its axis, in fact, if it moves at all, this should have some noticeable effect on the way objects move through the air. Scholars realized that if the Earth rotates on its axis once every twenty-four hours, the speed at which any point on its surface is moving is very great indeed. So how could clouds, or things thrown through the air, overcome this motion? How could anything ever move east? Solid bodies moving through the air should in some way show the influence of the Earth's rotation, even if the surrounding air rotates with the Earth on the Earth's axis.
3. It's plain to see that heavy objects travel toward the center of the Earth. If this law applies to heavy objects everywhere, the center of the Earth must be the center of gravity for all things in the universe that are heavy. Furthermore, once a heavy object reaches the place toward which its natural movement sends it, it comes to rest. Applying this idea to the Earth leads inevitably to the conclusion that the Earth must be at rest in the center of the universe and that it cannot be moved except by some force strong enough to overcome its natural tendency. This argument was based on Aristotle's concept of "natural" places and "natural" movements. It is easier to see its validity if you realize that Aristotle thought of everything beyond the Moon being made up of something called aether, which was neither "heavy nor light."
4. The Sun-centered model did nothing to solve a problem astronomers had been trying to solve: the inequality of the seasons measured by the solstices and the equinoxes.


    If Aristarchus tried to answer the second, third, or fourth of these objections, those answers have not been recorded.

    It would be inaccurate, and unfair to Aristarchus's contemporaries, to say that his Sun-centered model was suppressed because of their ignorance and closed-mindedness. The fact is, his model was an inspired guess that modern technology and theory show has far more validity than he or his contemporaries could possibly have known. But there actually was nothing coming from observation at the time to recommend it over the accepted view of the universe—the Earth-centered view that had been around for hundreds of years and that would be brought to a high degree of sophistication three centuries later by Claudius Ptolemy. Earth-centered astronomy solved the problems of astronomy, as they were perceived at the time, better than Aristarchus's Sun-centered model. Aristarchus's idea was a seed sown far too early, in a season in which it could not possibly germinate and take root.


Hipparchus of Nicaea


The greatest astronomer of the ancient world, indeed one of the most skilled and important of all time, was Hipparchus of Nicaea, who was born in the northern part of Turkey in the second century B.C. Thanks to Alexander's conquests, Hipparchus had at his disposal a priceless collection of Babylonian astronomical records, including eclipse records spanning many hundreds of years. He put this inheritance to splendid use, meticulously comparing the positions and patterns of stars and planets over the past centuries with those he observed himself. Like Aristarchus and Eratosthenes, Hipparchus tried to find a way to calculate the distances and dimensions of the Sun and Moon. Using a new line of reasoning, he focused on the fact that there was no discernible change in the Sun's position against the background of stars when an observer moved from one point to another on the surface of the Earth. Hipparchus assumed that solar parallax, as such a change in position is called, was just below the threshold of visibility. His results were not close to modern calculations.

    However, Hipparchus's other efforts were far more successful. In comparing his own observations with those made about 160 years earlier, he discovered a change in the relative positions of the equinoxes and the fixed stars. That is, if you look at the stars on the evening of the spring equinox, and then again on the evening of a spring equinox some years later, the stars will not be in the same position. In fact, they won't be in the same position again for 26,000 years! This phenomenon is known as the "precession of the equinoxes." Though Hipparchus couldn't discover its cause, he gave an impressively accurate estimate of the rate of this change.

    Of all Hipparchus's writings, only one youthful, minor work survives. Information about his accomplishments comes only from the references of others, mainly Ptolemy, but that information is sufficient evidence that Hipparchus was an extremely fine astronomer and that he vastly improved observational techniques, laying a foundation for all future astronomy. Where did this man stand in the competition between Aristarchus's model of the universe and the traditional one? Definitely pro-traditional. Hipparchus was among those who did not accept Aristarchus's Sun-centered cosmos, and he influenced others to reject it. Hipparchus felt obliged to abide by the evidence of observation—observational astronomy was, after all, one of his fortes—and, clearly, observation didn't support Aristarchus and couldn't confirm the enormous distances required by the Sun-centered model. Hipparchus's own work contributed significantly to Ptolemy's later Earth-centered model of the cosmos. Some scholars even insist that Ptolemy's astronomy was by and large a reediting of Hipparchus's, that Hipparchus was the genius and Ptolemy the textbook writer.

    It seems fitting to close this discussion, and take leave of the ancient world, with a quote from the Roman Pliny the Elder:


Hipparchus did a bold thing, that would be rash even for a god, namely to number the stars for his successors and to check off the constellations by name. For this he invented instruments by which to indicate their several positions and magnitudes so that it could easily be discovered not only whether stars perish and are born, but also whether any of them change their positions or are moved and also whether they increase or decrease in magnitude. He left the heavens as a legacy to all humankind, if anyone be found who could claim that inheritance.


"If anyone be found ..."?

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Table of Contents

Acknowledgments
Prologue: Tilting with Windmills {1951} 1
Ch. 1 A Sphere with a View {400-100 B.C.} 7
Ch. 2 Heavenly Revolutions {100-1600 A.D.} 34
Ch. 3 Dressing Up the Naked Eye {1564-1642} 69
Ch. 4 An Orbit with a View {1630-1900} 109
Ch. 5 Upscale Architecture {1750-1958} 156
Ch. 6 Coming Apart in All Directions {1929-92} 192
Ch. 7 Deciphering Ancient Light {1946-99} 222
Ch. 8 The Quest for Omega {1930-99} 266
Ch. 9 Lost Horizons 300
Epilogue: Magnificent Enigma 310
Notes 317
Glossary 323
Index 333
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