Historic Dispute : Is Earth the center of the universe

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Historic Dispute : Is Earth the center of the universe?

Viewpoint: Yes, early scientists believed that what appeared to be movement around Earth by the Sun and other entities was, in fact, just that.

Viewpoint: No, later scientists such as Nicolaus Copernicus and Galileo correctly realized that Earth moves around the Sun, not vice versa, and thus cannot be the center of the universe.

It is easy in our human nature to believe that we are the center of the universe. A newborn infant must learn through experimentation and sensation that he is a part of the world, not the entirety. Any parent can attest that as children mature, they must be helped to understand that the universe does not revolve around them and their needs and desires. Even as adults, we often struggle to see the world from a perspective other than our own.

Likewise, it was natural for ancient peoples to assume that the universe they observed was centered upon Earth. After all, they saw the Sun rise in the east every morning, and set in the west at night. They saw the stars and planets appearing to move across the sky. These patterns were repeated in cycles, and cycles implied revolution. There was no reason to question that what appeared to be movement around Earth was, in fact, just that. By the fourth century b.c., the Greeks had developed a picture of the stars as fixed on a celestial sphere that rotated around Earth, with the Sun, Moon, and planets moving independently beneath it.

In accordance with Greek philosophy, the orbits of the heavenly bodies were assumed to be a circle, regarded as a "perfect shape." As astronomers carefully recorded the apparent movements of the stars and planets, this conceptual model needed to be adjusted to account for the observations. The planets, named from the Greek word for "wanderers," were a particular problem, because sometimes they appeared to move backward. In the second century A.D., Ptolemy developed a complex system of circles within circles, called epicycles, which accurately reproduced the observed celestial patterns.

In the sixteenth century, the Polish scholar Nicolaus Copernicus proposed that the Sun was the stationary center of the universe, with Earth, planets, and stars moving around it. However, Ptolemy's model was more accurate in predicting the celestial movements, since that was what it had been designed to do, and this provided a powerful argument against the Copernican system. Another competing model was that of the Danish astronomer Tycho Brahe. The Tychonic system held that the Sun and Moon revolved around Earth, while everything else revolved around the Sun.

When the seventeenth-century Italian scientist Galileo Galilei built his telescope, he observed that the planet Venus showed phases, and deduced that it orbited the Sun. He also found four moons orbiting the planet Jupiter, conclusively disproving the idea that everything in the universe revolved around Earth. Although these observations were consistent with either the Copernican or Tychonic model, Galileo threw his lot in with Copernicus.

Likewise, Tycho Brahe's assistant, Johannes Kepler, became an adherent of the Copernican model. After his mentor's death, and using Tycho's extensive and precise observations, Kepler developed a heliocentric system in which the orbits were elliptical rather than circular. This finally produced more accurate predictions than Ptolemy's epicycles and greatly advanced the Sun-centered (heliocentric) view.

The concept of ourselves as the center of the universe was no easier for human societies to give up than it is for individuals. Copernicus escaped censure because his theories weren't published until he was on his deathbed. Galileo, however, attracted the attention of the Inquisition, and was found guilty of heresy, forbidden to publish, and sentenced to house arrest for life. This was relatively lenient treatment for the time, perhaps meted out because of Galileo's age and poor health. In 1600, the philosopher Giordano Bruno had been burned at the stake for espousing the same ideas.

Moving the designated center of the universe from Earth to the Sun may have been the hardest step, but it was only the beginning. As astronomy progressed in the nineteenth and early twentieth centuries, we gradually became aware that our planet orbits an ordinary star tucked away in an arm of an ordinary spiral galaxy, of no particular prominence within an enormous universe. But most people don't find that discouraging. Though it turns out that we are not at the center of anything, the universe we know today has far more wonders than Ptolemy could have imagined.

—SHERRI CHASIN CALVO

Viewpoint: Yes, early scientists believed that what appeared to be movement around Earth by the Sun and other entities was, in fact, just that.

Throughout most of recorded history, man believed that Earth was the center of the universe. This belief, which we now call the geocentric theory of the universe, was so strong that the few who dared to challenge it were often persecuted or even killed for their heretical beliefs. The persecution suffered by Italian mathematician and astronomer Galileo Galilei during the early seventeenth century for expressing his views opposing the prevailing geocentric model is well known. On the other hand, few are familiar with the story of Italian philosopher Giordano Bruno. Bruno was burned as a heretic in 1600 for supporting the same position as Galileo, namely that the Sun was actually the center of the universe and Earth revolved around it while rotating on its own axis. For centuries it had been an integral part of man's belief system that Earth was the center of the universe. This belief was not easily overturned.

There were many reasons for man's conviction that a geocentric system described his universe. Mythology and religion played important roles, as did prevailing scientific theories. However, probably the oldest and most persuasive reason for believing that Earth was the center of the universe was common sense based on everyday observations.

The Geocentric Theory

For an untold number of years, man had watched the Sun "rise" in the east every morning, move across the sky through the day, and "set" in the west. This simple motion repeated itself the next day, and the next, and the next, ad infinitum. Man had no reason to suspect that this daily motion was anything other than what it seemed, or that it had ever been different, or would ever change. Some explanations for this phenomenon were based on myths. For instance, one such myth envisioned the Sun dying every day only to be reborn the next day. However, the obvious logical explanation for the Sun's movement was that Earth is a stationary object, and the Sun revolved about it every day. It is comparable to looking out a window at a scene as it passes by one's field of vision. You may be moving past the stationary scenery, or you might be stationary while the scenery moves past your window. If you experienced no sensation of movement, the obvious conclusion would be the latter. Man experienced no sensation of movement on Earth; therefore, the conclusion was that the Sun moves while Earth remains stationary. Because similar observations were made of the motion of the Moon and the planets (although their motion was a bit more complicated), it was thought that Earth must be at the center of the universe. Then the heavenly bodies revolved about Earth. There was very little reason to suspect otherwise.

The ancient Babylonians observed and studied the motions of the heavens, even developing mathematical techniques to predict the motions of the heavenly bodies. However, it was the Greeks who first developed scientific theories concerning these motions. With only a few exceptions, the ancient Greek philosophers believed Earth was the center of the universe. One Greek philosopher, Eudoxus, proposed a rather complicated system of fixed spheres to which the Sun, Moon, the five known planets (Mercury, Venus, Mars, Jupiter, Saturn), and the stars were attached. With Earth fixed at the center, these spheres revolved and carried the heavenly bodies in a circular motion around Earth. By employing some rather sophisticated mathematics, Eudoxus was able to explain reasonably well the motion of the Sun and Moon, as well as the motions of the planets. However, his system was only partially successful in predicting the motion and location of the various heavenly bodies as they revolved about Earth. One reason for the popularity of Eudoxus' model was that it was adopted by Aristotle. Aristotle was a Greek philosopher whose teachings were extremely influential until the dawn of modern science.

Greek astronomers realized that observational discrepancies existed in the geocentric theory of the universe. The most obvious difficulty was the unexplained irregularities in the motion of the planets. Astronomers noted that the planets sometimes appeared to move in a direction opposite to that of their usual movement. This motion, called retrograde motion, presented a mathematical and physical puzzle that was tackled by many Greek astronomers. They constructed ingenious models that met with varying degrees of success to explain retrograde motion. Eudoxus' model of the universe, with its collection of concentric spheres, was useful in explaining retrograde motion for some, but not all, of the planets.

The puzzle of retrograde motion, as well as certain other incongruencies in Eudoxus' system, was eventually "solved" by the use of epicycles. Essentially, an epicycle is a circle on a circle. The planet moves on a circle (called the epicycle) while this circle revolves around Earth on a larger circle (see figure 1). In this way, the planet appears to move backwards on occasion as it moves around its epicycle in the direction opposite to its motion on the larger circle. The use of epicycles helped preserve two of the primary tenets of ancient astronomy: the centrality of Earth and the belief in the perfection of uniform circular motion in the heavens.

The Ptolemaic Model

The work of the second-century Greek astronomer Ptolemy represents the apex of the geocentric theory. In his work, entitled the Almagest , Ptolemy described a complicated system that was exceptionally accurate in its description of the motion of heavenly bodies. To do so, Ptolemy had to expand on Aristotle's rather simplistic description of circular motion. Ptolemy used two devices in his model in an effort to predict more accurately planetary motion: the previously mentioned epicycle and another device called eccentric motion. Eccentric motion was one in which the planet traveled around a circle whose center was not Earth (see figure 2). Although both epicyclical and eccentric motion had been proposed by Apollonius as early as the third century b.c., it was Ptolemy who eventually used these two devices to construct a geocentric model that was successful in matching observational data. This system had the added benefit of providing an explanation for the varying length of the seasons, a feat earlier models had failed to accomplish.

The Ptolemaic model proved successful in predicting the motions of heavenly bodies and was the prevailing theory used by astronomers for centuries. However, the Ptolemaic model was not universally accepted. The eccentric motion violated the basic premise of uniform circular motion as prescribed by Aristotle. There were those, like the eleventh-century Muslim scientist Ibn al-Haytham, who tried to create models retaining the predictive powers of the Ptolemaic system without sacrificing the doctrine of uniform circular motion. Ultimately Ptolemy's model won the day, primarily due to its impressive accuracy.

Aristotelian Physics

In addition to everyday observations, another argument for the centrality of Earth evolved from the physical theories of Greek philosophers, especially Aristotle. Aristotelian physics, which was the dominant paradigm until the Scientific Revolution, assumed the existence of five elements. Four of these elements, earth, water, air, and fire, formed the world and its surrounding atmosphere. The fifth element, the ether, was perfect and unchanging and formed the celestial bodies. In Aristotle's conception of the physical world, earth, as the heaviest element, naturally tended toward the center of the universe. Of course, this center of the universe was the center of Earth itself. Water, lighter than earth, also tended toward the center, gathering on top of the heavier earth. The lighter elements, fire and air, rose and collected above earth and water. Because the tenets of Aristotelian physics became so ingrained into society's picture of the universe, the concept of the centrality of Earth went essentially unchallenged. Astronomy began with this belief as a central assumption, and it was seldom questioned.

Later, in Europe, Aristotelian physics blended with Medieval Christianity to form a conception of the physical world that would dominate scientific thought until the work of Galileo, Sir Isaac Newton, and the other founders of modern science. Ideas such as the perfection of the heavens, the immobility of Earth, and the centrality of human creation all contributed to the pervading thought that Earth must be the center of the universe. The third century b.c. Greek mathematician/astronomer Aristarchus was labeled impious for placing the Sun at the center of the universe. Centuries later, Christians called upon the Bible to support their geocentric claim. They argued that Joshua commanded the Sun to stand still during a great battle so that his army might have more daylight in which to fight (Joshua 10: 12-13). The key to this passage was that Joshua did not command Earth to stand still, but rather the Sun. For the Sun to stand still implied that it must first be moving.

Allusions to ancient philosophers and to the Bible demonstrate that part of the reason for the acceptance of the geocentric model for so many centuries was man's preoccupation with authority. Whereas the Church was the ultimate authority in religious matters, Aristotle, Ptolemy, and other Greek thinkers were often considered the ultimate authority on scientific subjects. With a few adjustments made to their teachings to allow them to coexist with Christian doctrine, the science and philosophy of the Greeks was accepted almost without question.

The Heliocentric Theory

Although the geocentric model of the universe dominated thought from ancient time through the seventeenth century, there were those who proposed the possibility of a Sun-centered, or heliocentric model. This model, with its requirement that Earth not only revolve about the Sun but also rotate on its own axis, was fraught with error, according to common opinion. First, argued the defenders of the geocentric model, if Earth moved man would have some sort of perception of that movement. If Earth were moving at the speed required to explain movements observed in the heavens, a strong wind would continually

blow in the direction opposite to the motion of Earth. In addition, if one were to throw a stone straight up into the air, a moving Earth would cause the stone to fall some distance behind its original position. Everyday observations confirmed that none of these things happened. This was evidence in support of the geocentric model. Furthermore, it was ridiculous to assume, the argument went, that the heaviest element (earth) was propelled through the universe while the lightest (ether) remained motionless. The precepts of Aristotelian physics made such motion impossible. It was infinitely more logical that the heavy Earth was stationary while the light ether possessed the movement necessary to explain observable phenomena.

An even more sophisticated argument held that if Earth were revolving about the Sun, the motion of Earth should cause an apparent change in the position of the stars. This motion is called stellar parallax (see figure 3). Stellar parallax is not observable to the naked eye, or even through the first telescopes; therefore, proponents of the geocentric model argued that Earth was not moving around the Sun. Furthermore, if stellar parallax could not be observed due to the great distances involved, the universe would have to be much larger than anyone had imagined—too large, the geocentric theorists believed, to be a viable alternative.

Even some time after sixteenth-century astronomer Copernicus proposed his heliocentric model of the universe, most Europeans clung to the geocentric model. In answer to some of the questions raised by Copernicus' model, the Danish astronomer Tycho Brahe developed a new structure for the universe that was a compromise between the heliocentric model and the geocentric model. Brahe placed Earth at the center of the universe, with the Sun and the Moon revolving about it. However, instead of also requiring the other planets to revolve around Earth, in Brahe's model the planets revolved about the Sun as it revolved about Earth (see figure 4). This system seemed to encompass the physical and theological advantages of the geocentric model, as well as the observational and mathematical advantages of the heliocentric model. Brahe's complicated and rather illogical system serves to show just how far man would go in order to preserve the idea of geocentricity.

Eventually, all of the arguments used to defend the geocentric model of the universe were abandoned. The time it took to repudiate these arguments is a testament to the physical and astronomical systems devised to explain the world by the Greeks. It would take the complete overthrow of Aristotelian physics and Ptolemaic astronomy to finally nullify the geocentric theory. Yet, even today, we speak of the Sun "rising" and "setting" as if it moved rather than Earth.

—TODD TIMMONS

Viewpoint: No, later scientists such as Nicolaus Copernicus and Galileo correctly realized that Earth moves around the Sun, not vice versa, and thus cannot be the center of the universe.

The geocentric (Earth-centered) model of the universe was almost universally accepted until the work of astronomers Nicolaus Copernicus, Galileo Galilei, and Johannes Kepler in the sixteenth and seventeenth centuries. There were, however, a few radicals who proposed alternatives to the geocentric model in ancient times. For instance, followers of the Greek philosopher Pythagoras (to whose school the Pythagorean theorem is attributed) proposed that Earth revolved around a "central fire." Although this central fire was not the Sun, Pythagoras' theory was one of the earliest expressions of the novel idea that Earth might not be the center of the universe. Later, a few other Greek philosophers followed suit. In the fourth century b.c., Heracleides sought to resolve difficulties involved in the observations of Venus and Mercury by proposing that these two planets revolved around the Sun, while the Sun in turn revolved around Earth. Heracleides also suggested that Earth rotates. A little later, Aristarchus of Samos (third century b.c.) maintained that the Sun was the center of the entire universe and that Earth revolved around it. None of these theories, however, exhibited any marked influence on mainstream scientific thought. In spite of these heliocentric (Sun-centered) theories, the geocentric model reigned supreme thanks primarily to the philosophy and physics of Aristotle and the astronomical work of Ptolemy. It was not until the work of Copernicus many centuries later that a heliocentric model was seriously considered.

The Revolutionary Ideas of Copernicus

Nicolaus Copernicus (1473-1543) developed a heliocentric model of the universe and in the process initiated the Scientific Revolution. In his model, Copernicus maintained that Earth was not the center of the universe. Instead, Copernicus believed that Earth and the other planets revolved around the Sun. Although the notion that Earth was not the center of the universe presented many problems to sixteenth-century scientists and theologians, some of the advantages of the Copernican system over the Ptolemaic were readily apparent. Copernicus' system offered a simple explanation for many of the observed phenomena that could not be easily explained within the old system. Retrograde motion was one such phenomenon. Retrograde motion is the apparent change in direction that is observed in a planet's motion as it travels across the sky. The Ptolemaic system attempted to account for retrograde motion with epicycles. An epicycle is essentially a circle on a circle. According to the Ptolemaic system the planet moves on a circle (called the epicycle) while this circle revolves around Earth on a larger circle. With the Sun at the center of the universe, however, retrograde motion is easily explained. The apparent change in direction of the planet is a direct result of its orbit around the Sun (see figure A). Notice the position of the planet (Mercury, in this case) in relation to the fixed stars. Mercury appears to move in one direction from position 1 to 2 to 3 and then change direction as it moves to position 4. This movement was much more difficult to explain in the geocentric system of Ptolemy.

Another advantage of the Copernican system was its ability to simply and effectively pinpoint the relative position of the orbits of Mercury and Venus. In the old geocentric models it was never clear in which order the orbits of Mercury and Venus occurred. When the orbits of these inner planets were analyzed in the context of Copernicus' heliocentric model, their positions were, for the first time, unambiguous. The observations confirmed that the orbit of Venus was closer to Earth than that of Mercury.

The Advances of Brahe and Kepler

Although revolutionary in his ideas concerning the motions of the heavenly bodies, Copernicus remained a product of the medieval Aristotelian natural philosophy. In some ways, Copernicus' system, as explained in his famous work of 1543, De Revolutionibus orbium coelestium (On the revolutions of the heavenly spheres), was similar to the centuries-old model developed by Ptolemy. For instance, although Copernicus placed the Sun at the center of the universe, he retained the notion that the heavenly bodies were carried around on their revolutions by solid crystalline spheres. It was not until the work of two astronomers of the next generation, Tycho Brahe (1546-1601) and Johannes Kepler (1571-1630), that this theory was challenged. Brahe observed two occurrences in the heavens that cast serious doubt on the theory of crystalline spheres. First, he observed the birth, and later disappearance, of a new star (a nova). When Brahe was able to show that this new object in the sky came into existence beyond the orbit of the Moon, he challenged the belief that the heavens were perfect and unchanging. Secondly, Brahe calculated the path of a comet (a hazy gaseous cloud with a bright nucleus) and showed that it was moving across the heavens beyond the orbit of the Moon. In other words, its orbit would take the comet "crashing" through the crystalline spheres, an obvious impossibility. Brahe concluded that there were no physical spheres containing the orbits of the planets.

Kepler's contribution to the mounting evidence pointing toward the truth of Copernicus' theory came in the form of his three laws of planetary motion. Kepler's first law states that the planets orbit the Sun following an elliptical path with the Sun at one focus of the ellipse. This revolutionary break with the tradition of circular motion allowed a simple geometrical model to explain the motions of the planets. No longer requiring awkward epicycles and eccentrics, elliptical orbits presented an elegant mathematical solution to a sticky problem. Kepler's other two laws are mathematical theories relating to the heliocentric model. His second law states that the orbits of planets sweep out equal areas in equal times, and his third law concludes that the square of the period of each orbit is proportional to the cube of the semimajor axis of the elliptical orbit—that is, one half the distance across the ellipsis at its widest point. The regularity that these three laws implied made the heliocentric model compelling to scientists who looked for order in the universe.

Interestingly, we remember Kepler's three laws of planetary motion but seldom hear of his other theories that did not stand the test of time. In Kepler's early work, Mysterium Cosmographicum (Cosmographic mystery), the astronomer defended the truth of Copernicus' heliocentric model by constructing his own model in which the orbits of the planets were separated by the five regular solids. A regular solid is one whose faces are all identical. For instance, a cube is a regular solid because its sides are all equal squares. Since only five such solids exist (cube, tetrahedron, dodecahedron, icosahedron, and octahedron), Kepler believed it was God's intention that they appear between the orbits of the six planets. Kepler argued that this was further proof of the heliocentric theory because, in the geocentric theory, the Moon was the seventh planet. If there are only five regular solids, they could not fit in between the orbits of seven planets. To Kepler, this was important evidence in favor of accepting the heliocentric model as God's divine plan.

The Discoveries of Galileo

In one of the most important series of events in the Scientific Revolution, the Italian scientist Galileo Galilei (1564-1642) turned his newly acquired telescope toward the sky and discovered many wonders that would cause man to rethink his previous conceptions of the cosmos. One of Galileo's first discoveries was that the Moon had surface features such as craters. This discovery was in direct conflict with the Aristotelian view of heavenly bodies composed of a perfect and unchanging substance. The features of the Moon indicated that it might be composed of the same sort of common material as Earth.

Galileo also discovered, with the help of his telescope, that Venus went through observable phases just as the Moon. In the Ptolemaic system, the phases of Venus (undetectable without a telescope) would be impossible. If Venus orbited Earth, inside of the Sun's orbit, it would never be seen as full. The fact that Venus appeared in phases was a strong argument that it was revolving around the Sun.

Two discoveries made by Galileo with the help of his telescope changed the way man perceived the stars themselves. Galileo noticed that the planets appeared as solid discs with a well-defined outline when viewed through the telescope. The stars, on the other hand, continued to twinkle and resisted definition even when gazed upon through the telescope. Galileo concluded that the distance to the stars must be many times greater than the distance to the planets. This meant that the size of the universe was much greater than allowed by the Ptolemaic model. In addition, Galileo was able to observe that the Milky Way was actually composed of many individual stars, suggesting that the number of stars in the sky was much greater than had been previously believed.

Finally, a crucial discovery made by Galileo was the existence of the moons of Jupiter. The old paradigm maintained that Earth was the center of all revolving bodies. This centrality formed the very essence of Aristotelian physics and Ptolemaic astronomy. The existence of bodies revolving around a center other than Earth brought into question all of the previous assumptions upon which science was based. If Earth was not the center of revolution for all heavenly bodies, then other tenets of ancient science might also be false.

In addition to the evidence for the heliocentric model discovered by Galileo with the aid of his telescope, the great Italian scientist also made an equally important contribution to the eventual acceptance of Copernicus' theory. If the heliocentric model were true, then the whole of physics, essentially unchanged since Aristotle, was in error. Galileo provided an alternate explanation for motion that did not require the philosophical conclusions concerning the primacy of Earth and its place in the center of the universe. In Aristotle's conception of motion, Earth must be at the center because it did not move. Motion, or lack of motion, was an inherent characteristic of a body, and Earth's lack of movement made it different from the continuously moving heavenly bodies. Galileo, on the other hand, argued that motion was only an external process and not an inherent characteristic of the body itself. Movement was not anymore an innate characteristic of the planets than lack of motion was innately inherent in Earth. Before the theory that Earth moved could be accepted, these important consequences regarding the nature of motion had to be explained.

Galileo also argued that a body in motion would continue in motion without the continuous influence of an outside force. In fact, it required an outside force to stop the body's motion. This is the concept that modern scientists call inertia. This conception of motion helped to answer one of the claims against Earth's diurnal, or daily, motion. Opponents of the heliocentric model claimed if Earth spun on its axis, a ball dropped from a tower would land some distance away from the base of the tower because Earth had moved beneath it. Galileo's answer was that the ball already possessed a motion in the direction of the spinning Earth and would continue with that motion as it fell, thus landing at the base of the tower.

One disturbing question that arose from Copernicus' theory was that of stellar parallax. If Earth did revolve about the Sun, the relative position of the stars should change as Earth moved. Unfortunately for Copernicans, this stellar parallax could not be observed. Today we know that stellar parallax can only be observed through telescopes much more powerful than those available to Galileo and his contemporaries. In fact, proof of stellar parallax was not supplied until the work of Friedrich Wilhelm Bessel in the nineteenth century. Bessel's work provided a final proof for the yearly motion of Earth revolving around the Sun.

It was also in the nineteenth century that a final proof of the rotation of Earth on its axis was supplied by the French physicist Jean-Bernard-Léon Foucault. Foucault suspended a large iron ball from a wire swinging freely from a height of over 200 feet. As the ball, known as "Foucault's pendulum," swung in the same vertical plane, Earth rotated beneath it. Foucault's pendulum is now a common exhibit at many modern science museums. A series of blocks standing in a circle around the pendulum are knocked over one by one as Earth rotates once in a twenty-four hour period.

Bessel's discovery of stellar parallax and Foucault's pendulum represented the final direct proofs of the two primary motions of Earth. These nineteenth-century events marked the end of a long process of discovery begun by Copernicus some four centuries earlier.

—TODD TIMMONS

Further Reading

A Brief History of Cosmology.<http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Cosmology.html>.

Copernicus, Nicolaus.<http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Copernicus.html>.

Galilei, Galileo.<http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.html>.

Greek Astronomy.<http://www-groups.dcs.stand.ac.uk/~history/HistTopics/Greek_astronomy.html>.

Kepler, Johannes.<http://www-groups.dcs.stand.ac.uk/~history/Mathematicians/Kepler.html>.

Kuhn, T. S. The Copernican Revolution. Cambridge, Mass: Harvard University Press, 1957.

Lindberg, David C. The Beginnings of Western Science. Chicago: University of Chicago Press, 1992.

Lloyd, G. E. R. Early Greek Science: Thales to Aristotle. New York: W. W. Norton, 1970.

——. Greek Science after Aristotle. New York:W.W. Norton, 1973.

Moss, Jean Dietz. Novelties in the Heavens. Chicago: University of Chicago Press, 1993.

Neugebauer, O. The Exact Sciences in Antiquity. New York: Dover, 1969.

Pannekoek, A. A History of Astronomy. NewYork: Dover, 1961.

Rossi, Paolo. The Birth of Modern Science. Oxford: Blackwell Publishers, 2001.

Westfall, Richard S. The Construction of Modern Science. Cambridge: Cambridge University Press, 1977.

KEY TERMS

CRYSTALLINE SPHERES:

The theory that the planets and stars orbit Earth attached to solid, transparent spheres.

EPICYCLE:

A circle moving on the circumference of another circle. Used by Greek astronomers to accurately model planetary motions.

GEOCENTRIC:

Earth-centered. The model of the universe generally accepted from ancient Greek times until the seventeenth century.

HELIOCENTRIC:

Sun-centered. The model of the universe popularized by the writings of Copernicus during the Scientific Revolution.

RETROGRADE MOTION:

The motion of the planets, as observed from Earth, in which the planet appears to change direction against the backdrop of the fixed stars.

STELLAR PARALLAX:

The apparent change in position of a distant star, as observed from Earth, due to Earth's change in position as it orbits the Sun.

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