Today's view of the Universe is far different from that held a few thousand or even a few hundred years ago. Our view continues to change, sometimes at an almost frantic pace, particularly over the last twenty years or so. The Universe as science defines it refers not only to the celestial phenomena with which we are acquainted now, but also to whatever new ones may yet be discovered. The ancient Greeks referred to the Universe as the cosmos, which implied to them more than just physical existence: their concept was that of a physical system that has order, harmony, and beauty among its parts and in the dynamic and coherent arrangement of those parts.
Astronomy, more so than any other science, has captured today's popular imagination. For most people astronomy is a science synonymous with the future. And yet, astronomy may well be the oldest of the sciences and even the "mother" of all science. Our pursuit of knowledge about the physical world has been strongly shaped by our fascination with the changing panorama in the heavens. Intellectual thought has been inspired by both the beauty and the immensity of the astronomical world. Astronomy has not only stimulated other sciences, such as physics and mathematics, but has also inspired creative efforts in art, music, and literature. Let us begin our exploration of the cosmos by seeking the origin or origins of science itself.
1.1. Historical Origins of Science
1.1.1. Origins of Scientific Thought
History shows us that one of man's preoccupations has been the nature of his physical existence; what is it made of, how did it come into being, and how will it end, if ever. Since apparently no other experience, outside of human physiological functions, is any more universal to the peoples of the Earth than that of the heavens, we can trace the roots of this concern about our physical existence back thousands or even tens of thousands of years when our ancestors first began contemplating the heavens. Cave paintings, cliff carvings, stone and wood monuments, and pottery fragments found worldwide all testify to the importance that the heavens played in early thought. For example, we have evidence that stone-age man in Europe was apparently keeping track of cycles of lunar phases on pieces of bone some 30,000 years ago.
To many ancient peoples the heavens were more than a source of wonder; they held power over earthly existence, in that celestial gods were believed to be able to control human destiny. Astrology became the key that revealed divine plans for the course of human events. Although possessing no scientific basis and having clearly diverged from astronomy by the seventeenth century, early astrology did make one contribution to astronomy: it spurred the persistent and orderly recording of regularities in the movement of the Sun, Moon, and planets relative to the background stars. And because of this, well before the dawn of recorded history some 6000 years ago, these regularities were highly developed knowledge. Some of the earliest astronomical texts, which record the movement of the planets, are found on Babylonian cuneiform tablets dating from almost 2000 B.C. (Planet comes from the Greek language, and it means "wanderer," in contrast with the fixed stars.)
Concern for astronomical knowledge was not been confined to the peoples of the Mediterranean. For sometime in the third millennium B.C., before the building of the pyramids in Egypt, early Britons began the construction of Stonehenge (Figure 1.1). It has long been known that the orientation and structure of Stonehenge has astronomical significance; its principle axis marks the direction of sunrise at the time of the summer solstice. Hundreds of stone monuments in Scotland, England, and France have been shown to display a sophistication in astronomy far beyond that expected of the early inhabitants of these areas. Many of these same comments can be made about the astronomical significance of many New World structures, such as Carocol in Mexico shown in Figure 1.1.
Most ancient peoples devised an explanation for what we can loosely call the origin, structure, and evolution of the Universe, the subject matter of modern cosmology. Out of a great dark void or chaos the world was created by divine intervention. This is the story of the beginning in many ancient cosmologies. In these cosmologies we find a common thread: an inclination for people to envision their known world as the center of the Universe. This egocentric perspective later blossomed into a geocentric one; that is, the whole Earth was at the center. Ancient cosmologies were only idealized sketches against which the activities of nature took place, but few, if any, aspects of natural phenomena were actually incorporated into them. Not until many centuries later were explanations of the details of nature considered to be a necessary part of science and in particular cosmology.
In this discussion, the important question is whether or not these concerns of various early peoples are primitive beginnings on the road that ultimately leads to modern science. In spite of the apparent existence of this rudimentary scientific thinking by various peoples worldwide, scholars are unable to see how all of their diverse activities eventually merged to produce the science we recognize and practice today. For we know that much of the purpose behind the acquisition of astronomical knowledge was to produce calendars for agricultural purposes. Such purposes are really an outgrowth of the survival instinct. What we must do is to differentiate between survival activities which are on the road leading to modern technology and those activities that are an inquiry into the nature of the world. Over simplifying, we can say that, since the earliest of times, there has existed in human beings a theological-philosophical strain concerned more with the nature of our existence than simply survival as a species. And, it is possibly not unreasonable to say that science is an outgrowth of such theological-philosophical motivations. However, historical evidence still does not provide a link between such concerns and modern science. Lacking evidence to the contrary, current scholarship suggests that Greek philosophy alone is the predecessor of modern science. To most scholars it seems an inescapable conclusion that the Greeks were the originators of that method of thinking known as science.
According to Aristotle (384-322 B.C.), the dawn of systematic scientific thinking began in the sixth century B.C. in the Hellenic cities of Ionia in western Asia Minor. The times were those following the Homeric period (900-700 B.C.) when the eastern end of the Mediterranean was in great upheaval because of the invasion and destruction of the highly developed civilizations of Knossus, Mycenae, Pylas, and others. This era can be compared to that following the re-emergence that took place in Europe centuries later after the collapse of the Roman Empire. The Ionian cities were prosperous and involved in wide-ranging commerce. Unfortunately little remains of their written texts from that period. What we have are commentaries by later writers, such as Aristotle, of the philosophical activities that began in Ionia. Even though we have only fragments of their work or hearsay reports concerning these pre-Socratic philosophers, enough of Greek philosophy of the fifth and sixth centuries B.C. has been passed on so that various themes can be traced.
The first Ionian philosopher of whom anything is known was Thales (632-546 B.C.) of Miletus. He said that water is the fundamental substance and all things are derived from it. Exactly what he meant by this we do not know, as no written record by him remains. Aristotle is our authority on Thales and he seems uncertain himself as to Thales' meaning. We are left to guess and to surmise that what he was proposing was the concept of an a unity that permeates nature. What did Thales observe that lead him to propose such a startling idea? Was it an observation of the cycle of water falling as rain, collecting in rivers to run to the sea, there to evaporate forming clouds to fall again as rain? Or did he observe the intimate connection between biological processes in living matter and water? We shall probably never know for sure. But lacking evidence to the contrary, scholars are persuaded that the thoughts of Thales are as good as any in which to place the origin of science.
More is known of Anaximander (about 590 B.C.), a somewhat younger Milesian. In his writings, we find a fundamental theme found in later Greek thought. He imagines the cause of things not in a mystical or mythical way. Unlike Thales hypothesis that a fundamental substance like water is the source of unity in the physical world, Anaximander postulates that a featureless matrix, called "the Unlimited" or "the Infinite," is the source of physical existence by a separation of opposites. Exactly what he means by this we are not sure. Although his world system is not rooted in mechanism as we might argue today, neither is it rooted in mysticism as his predecessors contended. Its roots are in law: All natural processes, he wrote, are governed by an overriding principle of cosmic justice, or Necessity. By denying man's preferred status in nature, he asserts that things happen because they must, which was the first step on the road to scientific rationalism.
At this point we need to leave Greek natural philosophy to consider those astronomical concepts and observations that were the foundation for the two competing Greek geometrical theories of the nature of the world, the geocentric and the heliocentric concepts.
1.2.1. Constellations
In the clear skies of the Tigris, Euphrates, and Nile valleys, where the earliest civilizations flourished more than 5000 years ago, watchers of the heavens singled out and named various groupings of stars, called constellations, primarily for calendrical and navigational purposes. To aid their memory, they imagined that they saw in these groupings the likenesses of mythological beings, animals, and monsters and named the constellations accordingly. The names and shapes of constellations are part of our heritage from ancient Greece, who in turn inherited them from these older civilizations. Greek astronomers identified and named 48 constellations. Forty more were added, most of them in southern skies, by European mapmakers and astronomers in the seventeenth and eighteenth centuries.
Standing in midlatitudes of either hemisphere a practiced observer can see about four-fifths of the constellations during the course of the year. Star maps containing the constellations for each of the four seasons can be found inside the front and back covers to help you. Of the 88 constellations, about half lie in the Milky Way or near its borders. As you learn the constellations, hearing the name of one will bring to mind an area of the sky, just as earthbound place names identify a particular geographical area.
The "catch figure," or asterism, often associated with a constellation should not be assumed to be the outline of the constellation's namesake. An example is the asterism of the Big Dipper, which is the recognizable figure for the constellation Ursa Major, the Great Bear. (Some asterisms and constellation figures are shown in Figure 1.6). In today's astronomy, the constellations define specific areas of the sky with north-south and east-west boundaries. All celestial objects lie within the borders of one of the 88 constellations. Stars that identify a constellation form an apparent grouping as seen from Earth and are not necessarily in proximity to each other in space.
To ancient peoples, the sky appeared to be the inside of a immense dome covering the Earth and extending as far as they could see. Little wonder that they conceived of the Earth as a small sphere (some saw the Earth as being more like a flat plate) at the center of a huge sphere, with the stars located just inside or on the large sphere. This two-sphere concept is still used by astronomers for organizing the sky. The imaginary outer sphere is known as the celestial sphere (Figure 1.3).
Watching the sky, early peoples could see that stars rise above the eastern horizon--the circle that divides the visible celestial hemisphere from the invisible one--cross the sky during the night, and later set below the western horizon. This daily (or diurnal) behavior was attributed by most peoples, including the Greeks, to the rotation of the celestial sphere from east to west. Today we know that the apparent rising and setting of stars is actually caused by the Earth's rotation in the opposite sense, that is, from west to east.
Ancient peoples also observed that during their diurnal motion the stars move around two points on the celestial sphere, the north and south celestial poles (NCP and SCP). To them these were the ends of the axis about which the celestial sphere rotated. To us they are the points of intersection of the Earth's axis of rotation with the celestial sphere. (The significance of Polaris, the North Star, is that it lies within 1o of the north celestial pole and is a relatively bright marker of the NCP's position).
For any observer, the point directly overhead is called the zenith. And the imaginary arc on the celestial sphere running from the north point of the horizon through the north celestial pole and zenith to the south point of the horizon is called the celestial meridian. This line is the dividing line between rising and setting, since the highest point above the horizon that any star reaches in its daily motion occurs when the star crosses the celestial meridian. For this reason, the celestial meridian is a basic reference in timekeeping.
Which stars are or are not visible depends on the observer's geographic latitude. An observer in northern latitudes notices that not all stars rise above and set below the horizon daily. Stars near the NCP are always above the horizon, while stars near the SCP are always below the horizon. As ancient peoples traveled to different latitudes, they noticed that the stars that were visible to them changed. For example, as travelers moved northward, they could see stars near the northern horizon that previously had not been visible, and stars previously visible near the southern horizon were now below it. Such an effect along with some others was used as evidence that the Earth is spherical and not flat.
Over the course of the year, the Sun does not rise due east and set due west; only twice during the year will it actually do this. During the rest of the year and depending on the observer's latitude, the Sun shifts its rising and setting position relative to the east and west points. This annual migration of the Sun through an observer's sky is shown in Figure 1.4 for typical northern latitudes.
At the time of the summer solstice, the first day of summer in the Northern Hemisphere which occurs on or about June 21, the Sun rises as far north of the east point and sets as far north of the west point as at any time during the year. Over the three months of summer, the Sun moves back south toward the east and west points when it rises and sets. During summer, the hours of daylight are longest and the Sun is highest in the sky. At the time of the autumnal equinox, the first day of autumn, which occurs on or about September 22, the Sun rises due east and sets due west. On this day, all places on Earth experience 12 hours of daylight and 12 hours of darkness. During the three months following the autumnal equinox, the Sun continues its southward migration in the sky, so that by the time of the winter solstice, the first day of winter, which occurs on or about December 22, the rising and setting points are as far south as at any time during the year. At the time of the winter solstice, the angular distance of the rising and setting points of the Sun south of the east and west points is equal to the angular distance of the rising and setting points north of the east and west points at the time of the summer solstice. The length of daylight is now the shortest, and the Sun is lowest in the sky. Over the six month period from winter solstice through the time of the vernal equinox, the first day of spring, which occurs on or about March 21, to the summer solstice, the Sun rises and sets farther north each day. At the time of the vernal equinox, the Sun rises due east and sets due west, when there are again 12 hours of daylight and 12 hours of darkness.
1.3. Cyclic Phenomena of the Heavens
Historically, the common cyclic phenomena of the sky, such as the Sun's daily rising and setting, played an important role in the development of the geocentric and heliocentric concepts. Many of these phenomena were not discovered in any literal sense, but had been observed and known long before anyone wrote about them. What is new and has changed over time is an explanation in either the geocentric or heliocentric conceptual scheme of why, for example, the Sun rises and sets. Rather than trace their historical development, let us consider only our present understanding of these cyclic phenomena. This discussion should make the discussion in Chapter 2 of the geocentric and heliocentric concepts easier to comprehend.
The different seasons are caused by the tilt of the Earth's axis of rotation relative to its orbital plane and by the Earth's revolution once a year about the Sun. As seen from Earth, the Sun appears to move eastward about 1o each day relative to the stars (Figure 1.5). Because of this, stars rise about 4 minutes earlier each night than they did the previous night. Consequently, by the end of a month, stars are rising approximately 2 hours earlier than they did in the previous month. At the end of a year, the nightly change adds up to 24 hours, and the annual cycle of the heavens begins again.
Over time most ancient peoples were able to identify the Sun's yearly path through the constellations, a path called the ecliptic. Earth's geographic equator projected onto the celestial sphere produces an imaginary line called the celestial equator. The celestial equator intersects the ecliptic at two points, the vernal equinox and the autumnal equinox. The Moon and planets move almost entirely along a narrow band of sky, the zodiac, which is 16o wide and is centered on the ecliptic. The zodiac is divided into 12 constellation divisions, or signs, through which the Sun passes in successive months (Figure 1.6).
The Earth's axis of rotation is tilted 23.5o to its orbital plane, which is consequently the angle between the ecliptic and the celestial equator. In the Northern Hemisphere we incline away from the Sun in December and toward it in June (Figure 1.5). Consequently, the amount of sunlight falling on the surface of either hemisphere varies depending on whether the hemisphere is inclined toward or away from the Sun, as shown in Figure 1.5.
In the Northern Hemisphere spring begins in March at the time of the vernal equinox, when the Sun crosses the celestial equator from south to north. Summer starts in June at the time of the summer solstice, when the Sun reaches its maximum distance of 23.5o north of the celestial equator. The next season, autumn, begins in September at the time of the autumnal equinox, when the Sun crosses the celestial equator from north to south. Finally, winter commences in December, when the Sun reaches its maximum angular distance of 23.5o south of the celestial equator at the time of the winter solstice. In the Southern Hemisphere, the seasons are reversed; for example, Christmas occurs there during the warm summer months.
The daily rising and setting of the Sun, the year of the Sun's seasons, and the monthly period for the phases of the Moon were important cyclic events for ancient peoples. All these repetitive cycles were important to them in establishing a concept of time.
Our understanding of the reasons for the Moon's phases predates even Aristotle, who was aware that the Moon "shines" by reflecting sunlight. The parallel rays of the distant Sun always illuminate one-half the Moon's surface as well as one hemisphere of the Earth; when the Moon is visible, we are seeing rays of sunlight reflected off the Moon's surface.
When the Moon is between the Earth and the Sun--the time of a new moon--its dark side faces us (Figure 1.8), and we do not see it at all. Because the Moon moves eastward relative to both the Sun and stars, within a few days a thin crescent appears low in the western sky after sunset and sets shortly after the Sun. In the next few days, a growing crescent appears higher in the sky after sunset and therefore sets later on successive nights. One week after new moon, the Moon is at first quarter and will be on the celestial meridian at sunset; it will set about 6 hours after the Sun. In the following week, the Moon, now more than half a crescent, becomes full as it continues its easterly movement around the Earth. Two weeks after new moon is the time of full moon, when the Moon lies on the opposite side of the Earth from the Sun. We see it rise at approximately 6 P.M. and set about 6 A.M. One week later the Moon is at last quarter where it rises about midnight and sets around noon. Finally, we see the declining crescent-shaped Moon rise shortly before sunup as it is about to overtake the Sun one month after the previous new moon.
If we observe the Moon's movement against the stars, we find that it moves a little over a 0.5o per hour, or about 13o per day. Thus the Moon takes around 27.3 days to complete its orbit of 360o; this period is called the sidereal month (Figure 1.9). However, because the Earth is also moving around the Sun, the time between two successive cycles of lunar phases is longer than the sidereal month. Although the Moon has completed its revolution around the Earth at the end of 27.3 days, it takes about 2 more days to bring the Moon back to the Earth-Sun line so that it again appears as a new moon. Thus the period of lunar phases, the synodic month, is 29.5 days.
Although the Moon is some 400 times smaller than the Sun, it is also some 400 times closer to us, meaning that both the Sun and Moon have the same angular size, about 0.5o, as seen from the Earth. This produces one of the most impressive and yet important scientific coincidences in nature: When the Moon comes directly between the Earth and the Sun (Figure 1.10), the Moon's shadow or part of it falls on the Earth's surface. As seen from that point the Moon covers the Sun, blocking out the Sun's light. This is known as a solar eclipse.
A solar eclipse is possible only when the Moon is near a new phase. Since the plane of the Moon's orbit is inclined to the Earth's orbital plane by about 5o, the Moon must additionally be at or near one of the two points in its orbit where that orbit intersects the Earth's orbital plane. This lineup occurs at least twice each year and at most, but rarely, five times a year.
The totally dark portion of the shadow the Moon casts during a solar eclipse is called the umbra; the penumbra is the partial shadow or semidark portion. If one stands in the umbral shadow, one sees the Sun completely covered by the Moon, and this is called a total solar eclipse. If one stands in the penumbral shadow, one sees a partially covered Sun, and this is called a partial solar eclipse. The penumbral shadow covers a much larger area on the Earth's surface than does the umbral shadow, making a partial solar eclipse visible over a wider region than a total solar eclipse.
The average length of the Moon's conical shadow is not quite equal to the Moon's mean distance from the Earth. An annular solar eclipse takes place when the Moon, in addition to the conditions under which a partial or total solar eclipse occurs, is also farthest from the Earth. At this point its umbral shadow is too short to reach the Earth, so that one sees the slightly smaller, darkened disk of the Moon surrounded by a brilliant ring of still-exposed Sun.
Under the most favorable conditions in the Earth's equatorial regions, the Moon's umbral shadow is some 270 km wide, while the penumbral shadow is close to 6000 km wide. At this time, the totality of the eclipse lasts longest along the path of the eastward-moving shadow, the maximum length being about 7.5 minutes. Total eclipses for the 20-year period from 1980 to the year 2000 are listed in Table 1.1..
Usually, if an eclipse of the Sun occurs, an eclipse of the Moon precedes or follows it by 2 weeks. The Earth, Moon, and Sun are then sufficiently in line for the full Moon to move totally or partially into the Earth's shadow producing a lunar eclipse. Since the Earth's diameter is nearly four times that of the Moon, the conical-shaped shadow cast by the Earth is about four times wider at the base and four times longer than the Moon's shadow. Lunar eclipses may be partial or total, everyone on the dark side of the Earth seeing the lunar eclipse at the same time.
A year may bring as many as three lunar eclipses--or none at all. More often we have two eclipses of the Sun and two of the Moon in each calendar year. Centuries of observing eclipses taught the Babylonians that eclipses recur at regular intervals. After 18 years and 10 or 11 days, the circumstances of an eclipse are repeated approximately. By 200 B.C., Babylonian astronomers could predict with surprising accuracy future lunar eclipses. Their prediction method came about by noting numerical relations, what we today would call an numerical algorithm, in tabulated observations, rather than devising a geometrical relationship for the Sun, Moon, and the Earth as the Greeks later did.
Ancient astronomers devised names to identify particular positions of the planets relative to the Earth and Sun on the celestial sphere. This early system forms the basis for current definitions of planetary configurations (Figure 1.11). Between the Earth and Sun revolve Mercury and Venus; because of their smaller orbits they are called the inferior planets. As seen from the Earth and measured relative to the Earth-Sun line, Mercury and Venus appear to move counterclockwise around the Sun while swinging from one side of the Sun to the other, as shown in Figure 6.3. The angular distance (in degrees) any planet appears east or west of the Sun is called its elongation.
From a position closest to the Earth called inferior conjunction, when it is in line with the Sun, either of the inferior planets appears to move rapidly westward from the Sun, which causes its phase to change from new to crescent. When the inferior planet reaches its greatest angular distance west of the Sun, known as maximum western elongation, it is conspicuous in our skies as a "morning star" and its phase is quarter. Thereafter, the planet appears to reverse its course and move eastward back toward the Sun until its elongation is a minimum, a configuration known as superior conjunction. At this point, the planet is on the opposite side of the Sun from the Earth, and its phase is full. Leaving superior conjunction, an inferior planet continues to move eastward on its way toward its greatest angular distance east of the Sun, known as maximum eastern elongation. Here it is seen in the heavens as an "evening star" and its phase is also quarter. Next, the inferior planet moves back toward the Sun and inferior conjunction, completing its cycle of planetary configurations and moonlike phases.
Planets with orbits outside Earth's are called superior planets. To the ancients, the superior planets were the three naked-eye planets Mars, Jupiter, and Saturn. When a superior planet is nearest to us and also brightest, its configuration is known as opposition--opposite the Sun in the sky and visible throughout the night. Although the superior planet moves eastward relative to the stars, it lags behind the swifter Earth's motion and so appears to drift westward from the Earth-Sun line until it is 90o east of the Sun, at which point it is in eastern quadrature. Here it rises at noon and is an "evening star." Although north and south are absolute directions in space defined by the Earth's axis of rotation, east and west are a sense of rotation defined by the Earth's rotation from west to east. Continuing to drift eastward relative to the Earth-Sun line, the superior planet's elongation decreases; it is thus approaching the Sun. It arrives at a configuration known as conjunction, where the superior planet is on the opposite side of the Sun from Earth and will rise and set with the Sun. From here the superior planet passes through western quadrature, 90o west of the Sun. At this point the superior planet rises at midnight and is a "morning star." Finally, the superior planet returns to opposition, its cycle of configurations complete. As seen from the Earth, superior planets do not exhibit a cycle of moonlike phases as do the inferior planets.
The length of time for one orbit of a planet around the Sun is known as its sidereal period. It is the time taken to complete a 360o circuit around the sky relative to the stars. Unfortunately, there is no marker along a planet's orbit to indicate when it has completed a 360o revolution. From the Earth we actually observe what is called the synodic period--the time it takes a planet to return to a particular configuration with respect to the Earth-Sun line (such as from opposition to opposition). The synodic and sidereal periods differ because the Earth is advancing in its own orbit as a given planet revolves around the Sun. A simple mathematical relation, known since the time of the Greeks, allows us to calculate the sidereal period after measuring the synodic period.
Since Earth's orbital period is shorter than that of a superior planet, the Earth overtakes a superior planet and passes it. This occurs while the planet's configuration changes from western quadrature through opposition to eastern quadrature. During this period of passing, the planet appears to temporarily interrupt its normal eastward motion relative to the stars and move westward (Figure 1.12). This countermotion is known as retrograde motion, in which the superior planet executes a closed or open loop and then continues its usual path eastward relative to the stars. Relative to the Earth-Sun line, however, it is moving toward an area of the sky east of the Sun. The reason for retrograde motion is illustrated geometrically in Figure 1.13.
Now having surveyed the common Earth-Sky relationships and the regularity of the heavens, and remembering that the Greeks and other peoples of that period were well aware of these regularities, we can discuss the historical development of astronomy, leading up to the modern conception of the dynamics of planetary motion.
1.4. Greek Cosmology
1.4.1. Size and Shape of the Earth
Although there is a tendency to dwell on those ancients who may have envisioned the Earth as flat, knowledge that the Earth and Moon are spherical was widespread in the Greek world by the fifth century B.C. Aristotle argued that the circular shadow projected by the Earth when it eclipsed the Moon was clear evidence of the Earth's spherical nature. This argument had been known for a long time.
As Hellenistic culture spread throughout the eastern Mediterranean world, a new establishment for science was centered in Alexandria after about 300 B.C. The Museum and its associated Library in Alexandria was one of the most famous centers of learning in the ancient world. The Museum was a center for scientific and mathematical research. One of its geographers, Eratosthenes (273-193 B.C.), knowing that the Earth was a sphere, and from the earlier work of Aristarchus (320?-?250 B.C.), that the Sun was at least 20 times farther away than the Moon (the correct value is nearer 400), reasoned that rays of sunlight ought to be parallel when they reach the Earth, enabling him to measure the Earth's circumference by the argument shown in Figure 1.14.
Eratosthenes chose observing stations at Alexandria and Syene to the south, where the Aswan Dam is now located on the Nile River. For the time of the experiment he chose local noon on the day of the summer solstice, which comes at the same moment at both sites because they are very nearly on the same meridian of longitude. He probably selected that day, since the Sun was as far north as it would be during the year, meaning that it would pass very near the zenith at local noon at Syene.
At noon an observer in Syene observed that the Sun was directly overhead, while an observer in Alexandria found the Sun to be 7o south of the zenith. Measurers had paced off the distance between the two cities as about 4900 stadia (1 stadium = 0.16 kilometer). Because a straight line cuts two parallel lines at equal angles, the angle at the center of the Earth is equal to the zenith angle, 7o. Working a simple proportion, Eratosthenes found the Earth's circumference as follows: C/4900 stadia = 360o/7o, or C = 252,000 stadia, or about 40,320 kilometers (km). In principle, Eratosthenes' experiment was correct. Although his measuring technique was inaccurate by modern standards, his results were surprisingly close to today's mean value of 40,030 km.
As early as 2000 B.C. the Babylonians had begun recording the movements of planets, and a thousand years later the Greeks had inherited much of that knowledge. The Greeks, who to a great extent are responsible for developing geometry and trigonometry, sought a geometrical explanation of planetary motions rather than the simply numerical relationships found by the Babylonians. For them to see the Earth, which was not in their minds a planet, as the center of a world system was not unreasonable, even though they were aware of the difficult concept of a spherical Earth. A geocentric (Earth-centered) cosmology certainly seems more intuitively obvious than does, say, a heliocentric (Sun-centered) one. For centuries, various Greek schools of philosophy proposed, debated over, and elaborated on several geocentric theories.
Any conceptual scheme had to explain the observed motions of the Sun, Moon, and five naked-eye planets, all of which seemed to wander among the stars. Never changing their course, the Sun and Moon move eastward on the celestial sphere in a somewhat steady fashion relative to the stars. The inferior planets, however, move eastward through the background stars of the zodiac for a time and then undergo retrograde motion, moving westward. The superior planets generally follow an eastward path relative to the background stars with only a brief period of retrograde motion westward. All the planets further confound an understanding of their motion by moving swiftly some times and slowly at other times while displaying noticeable variations in brightness.
Greek philosophers, with their aesthetic taste for symmetry, reasoned that nature arrayed her celestial bodies on the perfect geometric figure, the sphere, and moved them in the perfectly symmetric plane figure, the circle. Beginning with Plato and possibly earlier, generations of astronomers thought that planetary movements must be accounted for by combinations of uniform circular motions with the Earth at the center. With this geocentric concept, they tried a variety of conceptual models to account for the observed motions. The ultimate product of geocentric cosmology was the Ptolemaic system.
The heliocentric concept, which followed the geocentric one, did not originate with Copernicus. He became aware that in the third century B.C. the Greek natural philosopher Aristarchus had proposed the Sun as the center of planetary motion. In his treatise, On the Sizes and Distances of the Sun and Moon, Aristarchus estimated that the Sun is 20 or so times farther from the Earth than the Moon (the actual value is about 400), and since both have approximately the same angular size, the Sun must be 20 times larger than the Moon or, he reasoned, about 7 times the Earth's diameter (the actual value is almost 109 times). From these estimates he apparently thought it natural to put the largest and only self-luminous body in the Solar System, the Sun, at the center of the system. Additionally, Aristarchus attributed the daily movement of the heavens to the rotation of the Earth on its axis. Annual changes in the sky and the planet`s motions could be explained if they and the Earth then revolved about the Sun. Even prior to Aristarchus, the Greeks were aware that the Moon, and possibly the planets, "shine" by reflecting sunlight, a notion they probably came to by observing lunar eclipses. It is also possible that Aristarchus recognized that the stars were self-luminous and conceivably like the Sun only farther away, but this is speculation.
Aristarchus's contemporaries objected to the heliocentric concept for several reasons: If the Earth does move, why don't we feel its motion, which must be exceedingly fast? Moreover, if the Earth moves, why don't we see every unattached object on the Earth's surface sailing swiftly past us in the opposite direction? However, what seems to have been the strongest argument against the heliocentric concept was the failure to see a shift (which would be due to the Earth's orbital motion) in the apparent position of nearby stars relative to more distant stars, a phenomenon known as parallax. We know today that nearby stars do appear to change place, but they are so far away from us that the apparent angular displacement, or parallactic shift, is extremely small, even for the closest stars, and can be measured only with a large telescope.
The fact that the parallactic phenomenon could be adduced as a criticism suggests that the Greeks possibly were aware that the stars are not all at the same distance from the Earth--a point they may have arrived at by arguing that all the stars have about the same brightness and that therefore the fainter ones are the more distant ones. However, even though they may have suspected that the stars are not all at the same distance from us, they apparently did not realize that even the nearest stars are too incredibly distant to reveal parallactic shifts to the naked eye.
Within a couple of centuries after Aristarchus, the heliocentric cosmology had lost out to the geocentric until its revival by Copernicus. Several generations of astronomers at the Museum in Alexandria set for themselves the goal of removing discrepancies between the geocentric concept and observed planetary motions. They felt that their revised geocentric concept must retain the circular motions and uniform rates appearing in such theories as Aristotle's geocentric system. They fashioned their geocentric model on the basis of several earlier natural philosophers, especially Heraclides (388?-?315 B.C.), Apollonius (261?-?190 B.C.), Hipparchus (190?-120 B.C.), and a later one of their own, Ptolemy (A.D. 100?-?170). The resulting system had a number of combinations of circles and off-center motions. To be an acceptable conceptual scheme, the geocentric theory had to represent more accurately the many small cyclic changes and large general motions of the world system. In this they succeeded, and the final version, which dominated philosophical thought for 13 centuries until the time of Copernicus, was published around A.D. 150 in the Syntaxis of Astronomy, an astronomical encyclopedia compiled by the last of the great Alexandrian astronomers Claudius Ptolemy.
Ptolemy's geocentric system, taken in part from the earlier work of Heraclides and Apollonius, presented each planet as moving uniformly around a small circle called an epicycle (Figure 1.15). The center of the epicycle in turn revolved uniformly around the circumference of a large circle called a deferent. By means of proper combinations of sizes and rates of motion for the epicycle and deferent, planetary motions could be mostly direct and occasionally retrograde. Also, since a planet on an epicycle is sometimes nearer and sometimes farther from the Earth, this accounted for the observed variations in planetary brightness. To represent the irregular rates of motion of the planets, Ptolemy continued to employ the device attributed to Hipparchus of having the deferent off center from the Earth (to produce an eccentric deferent), so that a planet would appear to go fastest when it was closest to the Earth.
Having constructed orbits for the Sun, Moon and planets out of a combination of epicycles and eccentric deferents, Ptolemy found that the heavenly bodies were moving at an even more irregular rate than could be accounted for by these devices. His solution to this problem was to suppose that the planets' motions were uniform not as viewed from either the Earth or even the center of the eccentric deferent, but from a point on the other side of the center of the deferent from the Earth; this point was called the equant as in Figure 1.15.
Why was science invented by the Greeks and not the Babylonians, the Egyptians, or any other peoples? Evidence to answer such a question has long since vanished, if it ever existed, and we can but speculate. We do know, however, that the Greeks, although bound by common cultural ties, were not organized into a single, rigid, monolithic state as were many other peoples at that time. Greece was a loose confederation of self-governing city-states. Besides science the Greeks gave the world both democracy and a language capable of expressing subtle distinctions in concepts. Thus the Greeks perceived not only a physical world operating under laws, but they conceived of a rule of law governing social order and incorporated that vision in to their very language. Whether one or the other of these three contributions--language, democracy, or science--lead to the others, or all three are by-products of some interaction or conditioning by their peculiar environment we can not say. But these three elements of what Jacob Bronowski (1908-1974), mathematician and science commentator, has called the ascent of man go hand-in-hand and tell us much about the mental and emotional outlook of the ancient Greeks.
Ptolemy's cosmological model (Figure 1.16 ) lasted until Copernicus challenged it in the sixteenth century when he declared that the Earth is a planet and the Sun is the rightful occupant of the center of the Universe. Even then, however, Ptolemy's system did not totally disappear until the time of Newton in the late seventeenth century. But the belief that the Earth, the Sun, the Moon, and the planets must occupy the center of the Universe, since man is apparently the center of creation, did not completely disappear until the beginning of our own century, almost 350 years after Copernicus's death.