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The Tests of Time:
Readings in the Development of Physical Theory
Edited by Lisa M. Dolling, Arthur F. Gianelli, & Glenn N. Statile

Book Description | Reviews

COPYRIGHT NOTICE: Published by Princeton University Press and copyrighted, © 2003, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. Follow links for Class Use and other Permissions. For more information, send e-mail to permissions@press.princeton.edu

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INTRODUCTION

Although Heliocentric Theory is well known, describing it without the use of unwarranted or unjustified assumptions is not easy. Simply put, the theory suggests that the earth has two motions, a rotation on an axis and an orbital motion about the sun. Further, it maintains that the sun is central to, although not exactly in the center of, the orbits of all those heavenly bodies known as the planets, of which the earth is one. The physical reference frame used to determine the motions of this "solar" system is the frame of the fixed stars, bodies that do not appear to change their positions relative to one another. In this theory the dual motions attributed to the earth are considered to be in some sense real.

The Geocentric View of Eudoxus

Although not really interested in astronomy, the philosopher Plato had a great influence on the course of its early history. Because he perceived the heavens to be more perfect than the earth, Plato urged astronomers to describe celestial motions in terms of the most perfect of geometrical shapes, the circle. In fact, for Plato, the most perfect motion would be uniform circular motion, motion in a circle at a constant rate of speed.

One of Plato's pupils, Eudoxus of Cnidus (409 B.C.-356 B.C.), was the first astronomer to follow Plato's recommendation. Blending careful observation with sophisticated mathematical constructs, Eudoxus sought to describe the motions of the heavens in terms of a series of concentric spherical shells, with the earth geometrically at the center of those shells. His model consisted of twenty-seven spheres, three each for the sun and the moon and four for each of the five known planets; Mercury, Venus, Mars, Jupiter, and Saturn. The final sphere carried all the "fixed" stars and presumably contained the whole universe. Each sphere turned on an axis at a uniform rate of speed and was attached to adjacent spheres at its axis. Since the axes of the spheres were in different planes and since the spheres could transmit their motions to one another through the axes, Eudoxus was able to "account" for the rather complicated motions that had been observed--for example, the retrograde motions of Mars, Jupiter, and Saturn. In this process the earth was not only considered to be in the center of these shells but also totally immobile and the reference point of all perceived motions.

The Aristotelian Cosmology

As mentioned, Eudoxus was somewhat successful in explaining observations of the heavens. Another of Plato's students, the philosopher Aristotle, found that the theory of Eudoxus fit nicely with his overall philosophy of nature, and he transformed it into a physical theory. Aristotle saw nature as dynamic, powerful, and teleological. Each object in nature tended toward a certain set of ends or goals, and nature as a whole tended toward a goal that was the result of the motion of the individual objects. What this meant was that each of the four inanimate elements--earth, water, air, and fire--had a natural place or equilibrium position in the universe, a place where it belonged. If nature were left alone Aristotle felt each element would move "naturally" to its proper place and nature as a whole would achieve an ideal structure.

Using this understanding of natural place and natural motion, Aristotle built a picture of the universe as a whole. Since for him there was no such thing as empty space, every object had to be surrounded by some medium. By observation it could be seen that heavy objects move naturally toward the surface of the earth and light objects move away from the earth's surface; for example, a rock falls in air, and air bubbles rise to the surface of water. More precisely, these motions appeared to be along lines perpendicular to the surface of the earth.

Now the ancient Greeks had become convinced through observations of lunar eclipses and measurements of shadows cast by sticks in the ground at various locations that the earth as a body was a sphere. Thus, the downward motions of heavy objects were directed toward the center of the earth, while the upward motions of light objects were directed away from the center of the earth. Further, since the earth as a body was made of the heaviest element--earth--its natural place would be in the center of the natural world. The center of the earth was literally, then, the center of the universe and the reference point for all motions.

The other three elements, water, air, and fire, arranged themselves accordingly in the vicinity of the spherical earth and below the moon. In this sublunar region of the universe, natural objects could undergo radical (substantial) changes. But such changes did not appear to take place in the heavens. In fact, the only change that did take place in the heavens was change of place--the heavens seemed to move in circles about the earth. Because substantial changes did not take place in the heavens and because their motion was circular, Aristotle decided that the heavens were more perfect than the sublunar region and were made of a fifth element called the ether. Since the heavens were more perfect it was fitting that they would have the most perfect motion, namely, uniform circular motion.

The marriage between Aristotle's philosophy of nature and the model of the universe of Eudoxus can now be seen. The shells of Eudoxus became hollow transparent spheres that carried the sun, moon, and five planets around the earth. Aristotle used fifty-five crystalline shells in all. Rather, Aristotle needed these additions because his model was, in effect, an interconnected quasi-mechanical system. He used a set of counteracting spheres in order to offset the one-way effects of the outer spherical shell motions upon the movements of inner shells and the planetary bodies they carried. The outermost sphere in this system, called the celestial sphere, carried all the stars and enclosed a finite universe.

In the eternal universe of Aristotle, the earth was perfectly at rest. If it ever had any translational motion, it would have eventually come to rest in the center, its natural place. Further, it could not be spinning on an axis because circular motion was only appropriate for the more perfect heavens, not for the imperfect entities of the sublunar region. The sun, the moon, and the planets all maintained the same distance from the earth at all times. Because the stars were all attached to the celestial sphere they maintained the same distance from the earth and the same relationship to one another at all times.

Early Theories of a Moving Earth

Despite the fact that a stationary earth theory is consistent with ordinary experience, there were some contemporaries of Aristotle who were willing to speculate that the earth might in reality be moving. Heraclides of Pontus (388 B.C.-315 B.C.) suggested that the daily motion of the stars could be accounted for equally well by the rotation of the earth on an axis. He maintained that the rotation of the earth would be far less violent, an Aristotelian technical term for unnatural motion, than any rotation of the much larger celestial sphere carrying the stars. Heraclides also thought that the motions of the so-called lesser planets, Mercury and Venus, could be better explained if they revolved around the sun rather than the earth.

The first complete heliocentric theory came from Aristarchus of Samos (310 B.C.-250 B.C.), who is known as the Copernicus of antiquity. In addition to its rotational motion, Aristarchus suggested that the earth itself was also a planet that moved in a circular orbit about the sun. In fact, he placed the sun at the center of the celestial sphere, which in turn he thought to be at rest.

The heliocentric theory devised by Aristarchus attempted to deal with two continuing problems whose solution had still not been adequately resolved by the existing geocentric theory. These problems were

  1. Retrograde motion of the planets. Some planets in their eastward movement through the stars can be perceived to slow down, come to a standstill, reverse direction, and eventually begin to move again in their original direction.
  2. Variations in planetary brightness during the year.

Critical problems, however, also beset the heliocentric theory of Aristarchus. One such problem was the failure to observe variation in stellar brightness. If the earth actually orbited the sun, then the stars should appear to vary in brightness, since they would no longer be equidistant from the earth. Further, if the earth moved among the fixed stars, the angular separation of stars should vary. However, this phenomenon, called stellar parallax, was not observed. To explain the absence of stellar parallax within the framework of heliocentrism would require the hypothesis that the earth's orbit be insignificantly small relative to the distances of the stars. This was a move the ancients were unwilling to make, especially because the heliocentric theory was at odds with our common experience of motion. If the heliocentric theory is correct, the earth and its inhabitants would have to be spinning like a top and hurtling through space at incredible rates of speed. Yet there is no experience of these motions. A reasonable person in ancient Greece, looking at all the evidence, would have to side with geocentrism.

The Geocentrism of Claudius Ptolemy

The geocentric theory achieved its greatest expression in the publication of Claudius Ptolemy's Almagest. This book, which was written in Alexandria, Egypt, in about A.D. 150, is the greatest surviving astronomical work bequeathed to us from antiquity. Ptolemy, however, did not simply inherit Aristotle's version of the geocentric theory. In the interim, other important contributions were made with regard to geocentric theory and method. Two individuals worthy of note in preparing the way for Ptolemaic astronomy were Apollonius of Perga, who lived in the latter half of the third century B.C., and Hipparchus of Nicea (second century B.C.), whom many scholars of astronomy rank as the greatest astronomer of antiquity.

Apollonius is credited with being the Greek mathematician who made the greatest contribution to the study of the conic sections; namely, the figures of the ellipse, parabola, and hyperbola. He is also credited with having invented the mathematical constructs called epicycles and deferents that became important parts of the Ptolemaic and post-Ptolemaic descriptive framework of geocentric, as well as Copernican heliocentric, cosmology. Without getting into the philosophical debate about actual ontological commitments, one can safely say that Apollonius not only contributed important aspects of the mathematical apparatus of ensuing geocentric theory, but did so in such a way as to bracket the issue of the physical existence of spherical shells.

Hipparchus made extraordinary contributions to astronomical methodology as well as to theoretical astronomy. He is credited with having invented or at least developed trigonometry into an important tool for numerically calculating the relationships that exist between and among the geometrical figures used to represent celestial motions. He also made extensive use of the Apollonian epicycles and deferents, and of eccentric circles, setting the stage for Ptolemy. His great contributions to lunar and solar astronomy enabled him to contribute to our understanding of the precession of the equinoxes, a phenomenon in which the sun, in its journey around the celestial plane known as the ecliptic, returns to a particular point on the ecliptic in advance of where it is expected to be relative to the background of the stars.

The completion of the mathematization of astronomy fell to Ptolemy in the second century A.D. For Ptolemy, astronomy was a mathematical exercise designed to "save the phenomena," to account for the observations of the activities of the heavenly bodies by use of mathematical hypotheses concerning their motions. This he accomplished with great success in the Almagest, in which Ptolemy rejected the heliocentrism of Aristarchus because stellar parallax was not observable and because the stars did not vary in brightness. He affirmed the Aristotelian arguments that the earth is completely at rest and in the center of the universe. Computationally it was possible for the earth to occupy other positions in the universe, but Ptolemy concluded that if the earth was not in the center of the universe, then the "order of things" would be "fundamentally upset." Although he agreed with Aristotle and Plato that the heavens move spherically, he eliminated all the hollow transparent spheres, but not the celestial sphere. He considered the sun, moon, and five planets to be independent bodies, while he kept the stars attached to the celestial sphere that enclosed the universe.

To account for solar, lunar, and planetary motions Ptolemy used the following mathematical devices:

  1. Eccentric Circles.
    No celestial bodies move with simple uniform circular motions. Both the sun and the moon appear to speed up and slow down, while the planets at times appear to move in opposing directions. Eccentric circles are circular paths of motion that are meant to be observed from some internal point displaced from the circle's center. This allows for better approximations of celestial motions, as celestial objects, such as the sun, appear to move faster and slower, toward perigee and apogee, while supposedly orbiting uniformly around the circumference of the circle.
  2. Epicycle/Deferent System.
    This system is far more powerful than that of eccentrics, although Apolloinus had already shown them to be geometrically equivalent, with the latter being a special case of the former. In this system a celestial body revolves uniformly around a smaller circle called an epicycle, the center of which itself revolves uniformly around a larger circle called a deferent. The observer is then situated at the center of the deferent circle. Ptolemy considered the epicycle/deferent system to be more powerful than eccentric circles since they possess a greater degree of freedom for representing observed motions. Epicycles were found to explain variations in brightness much better than eccentrics. Epicyclic movement consisted of a kind of looping motion that enabled Ptolemy to explain the retrograde motions of the outer planets.
  3. Equant Point.
    Ptolemy introduced the device known as the equant, a point displaced from the center of a deferent circle. The earth is positioned equidistant from this center, but on the opposite side from the equant. With the help of the equant, Ptolemy was able to work out the motions of the planets. Copernicus would later eliminate the equant from his astronomical repertoire of mathematical techniques because he thought it to be in violation of the Platonic ideal to preserve uniform circular motion. Relative to the equant Ptolemy could conserve uniform angular motion, in that a revolving body would sweep out equal areas around the equant in equal times. As a result, however, observation from the perspective of the earth would no longer be uniform. It can accurately be said that the equant point, in allowing for greater mathematical manipulation of epicyclic movement, contributed to Ptolemy's view that the epicycle/ deferent system was superior to the eccentric.

Using these mathematical devices, Ptolemy was able to produce the first comprehensive and systematic quantitative account of celestial motions. Ptolemy's astronomical ambitions included not only accounting for past and present celestial motions, but also predicting future celestial and planetary motions as well. As new and more precise data became available, Ptolemy's eccentrics, equants, and epicycles would be adjusted to fit that data if necessary. All in all, the theory of Ptolemy became quite accurate and extremely useful (e.g., it could be used as a basis for keeping track of time). If Ptolemaic geocentric theory was to be dethroned and replaced by another theory, it would have to be for powerful and practical reasons. For in addition to its entrenchment and pedigree within the scientific community, the Ptolemaic-Aristotelian cosmological model had been embraced as a theory of the heavens by Christianity.

The Copernican Heliocentrism: A Revolution in Astronomy and Physics

Between the time of Ptolemy and Copernicus, astronomy underwent more than a millennium of normal geocentric activity in which the principles of the theory went relatively unquestioned, and in which most of the research and investigative work was aimed at applying the theory and not undermining it. There were some minor rumblings about geocentrism during this time, most notably from Nicholas Oresme in the fourteenth century and Nicholas of Cusa in the fifteenth. However, neither man rejected geocentrism. But Oresme's views at least can be characterized as a definite stepping stone on the conceptual path to heliocentrism. He argued in his Le Livre du ciel et du monde that observed astronomical phenomena can be explained in a computationally equivalent manner by the assumption of a rotating earth or by the rotation of the heavens about the earth. He further argued that it would not be possible by reason or experience to confirm either hypothesis. Concerning the argument that only a motionless earth squared with Aristotelian physics, Oresme pointed out that such physical reasoning was based upon a theory of motion that had never been confirmed.

Despite his concerns, Oresme never really considered committing himself to the reality of a rotating earth. By the turn of the sixteenth century, geocentrism was as entrenched as a scientific paradigm could possibly be. However, it was also at this time that the first difficulties with Ptolemy's astronomy began to appear. For example, predictions of planetary locations were becoming noticeably inaccurate.

Early in the sixteenth century a Polish clergyman name Nicholaus Copernicus set out to revise the existing astronomical tables and remove the inaccuracies therein. He was a realist who believed that if he could hit upon "the one true form of the heavens," he could bring perfect accuracy to astronomy. But Copernicus quickly realized that the problems with Ptolemy's astronomy involved much more than the sizes and speeds of epicycles. To him, Ptolemy's astronomy seemed to be internally inconsistent and incoherent. In his efforts to "save the phenomena," Ptolemy had sometimes used incompatible hypotheses for the same heavenly body to account for different sets of data. In addition, his system showed a strange kind of incoherence in the orbital times of the heavenly bodies. The moon, which was closest to the earth, completed its orbit in four weeks, while the sun, which was farther away, took only one day. Jupiter, one of the outer planets, spent 300 years completing its trips around the earth, while the celestial sphere, the farthest body from the earth, completed its revolution in just one day.

As a realist, Copernicus felt that the elimination of these internal problems would lead to a greater precision and accuracy in astronomy. Placing the sun in the center of the universe and giving the earth two motions, a rotation on an axis and an orbit about the sun, he found that he could account for all the data associated with each heavenly body without resorting to inconsistent hypotheses. Further, he found that, with the sun as the central reference point, the orbital speeds of the planets varied inversely with their distance from the sun, and that the apparent retrograde motion of the outer planets was due to these variations in orbital speeds. He was even able to eliminate the awkward equant points and return astronomy to the "strict" use of uniform circular motion. Certainly Copernicus's system had an internal coherence that Ptolemy's system did not. But he still had to use a complex array of cycles and epicycles, and so his theory retained an air of artificiality.

Despite his success in bringing coherence and consistency to astronomy, Copernicus was not able to shed new light on the problems that plagued a moving earth theory. To explain why we do not experience any dynamical effects due to the motion of the earth, he suggested that the atmosphere and everything in it participates in these motions, but he did not tell us why this happened. The earth does not disintegrate as it rotates for the same reason that the celestial sphere did not disintegrate in the old view, whatever that reason was. Stellar parallax was not observed, he said, because of the immense size of the universe, ignoring the attendant problems with this view. But the biggest problem for Copernicus and his moving earth theory was this: in the end his astronomical system was not significantly simpler nor more accurate than the revised Ptolemaic view of his time. Since he had set the accuracy of prediction as the crucial test for his theory, Copernicus realized that he did not have a strong enough argument to get the approval of the scientific community.

Copernicus developed his heliocentric theory between 1510 and 1514. During that time he prepared his Commentariolus, or First Commentary, which contained his basic assumptions and arguments. Although Copernicus circulated the Commentariolus among some of his friends and students, he refrained from publishing it primarily because its basic hypothesis was at odds with Christian theology. During the next twenty years, Copernicus prepared his definitive work, De Revolutionibus Orbium Caelestium. In 1540, an enthusiastic disciple Georg Joachim Rheticus, published a brief technical description of Copernicus's heliocentric system called Narratio Prima, which set the stage for the publication of De Revolutionibus in 1543. When it was finally published, it was accompanied by an unsigned preface written by a friend of Copernicus named Andreas Osiander. In the preface Osiander sought to deflect any potential criticisms from Aristotelians and theologians by suggesting that the heliocentric theory was not necessarily true but was of considerable instrumental value; it provided, for example, a correct basis for calculation and was "more convenient" to use. Once published, the De Revolutionibus did not cause much of a stir in either religious or scientific circles.

Brahe and Kepler

Copernicus died believing that the moving earth hypothesis was correct. But he had not convinced the scientific community. It took the next hundred years and the work of four exceptional scientists to tip the argument in his favor.

Tycho Brahe was a first-rate astronomer of the late sixteenth century who continually made systematic and sophisticated observations and measurements of the heavens over long periods of time. From his observations he was able to conclude that if the earth moved in orbit about the sun, as Copernicus suggested, it would travel approximately 200 million miles in a year. Brahe could not understand why, if the earth traveled so far, that stellar parallax would not be observed. In the end he offered a hybrid theory in which the other planets (Mercury, Venus, Mars, Jupiter, and Saturn) all orbited the sun while the sun orbited the stationary earth. The celestial sphere was retained to carry the stars around the earth.

Although he could not accept the Copernican hypothesis, Brahe did make two extraordinary observations that began the process that led to the ultimate rejection of the Aristotelian-Ptolemaic universe. In 1572 he observed a bright new star that remained visible even during the day for a brief period of time. We now know that star to have been a supernova. What these phenomena showed clearly was that changes did occur in the heavens, even radical changes. The heavens were not the immutable region that Aristotle had envisioned.

In 1577 Brahe began careful calculations of the motions of comets. After three years of study he was able to prove that the comets moved well into the heavens beyond the orbits of the moon and several of the planets. This was further evidence that the hollow transparent spheres of Aristotle did not exist.

But perhaps the greatest contribution of Brahe to astronomy was the great fund of information about the heavens that he passed on to his research assistant Johannes Kepler. Unlike his teacher, Kepler was a convinced Copernican. Upon studying the planetary records within the perspective of a moving earth theory, Kepler confirmed that the farther the planets were from the sun the more slowly they moved in orbit. His conclusion was that some force or power in the sun was moving the planets and that this force or power diminished with distance. For the first time the sun was seen as a controlling factor in the planetary motions.

Kepler's originality and insight did not end there. Given the records of the motion of the planet Mars by Brahe for analysis, Kepler sought and found a single simple shape for the planet's orbit. This shape turned out to be an ellipse with the sun located at one of its focal points. If this were the actual motion of the planet Mars, then its velocity would have to vary in orbit. Kepler found that the speed of the planet Mars varied in proportion to its distance from the sun just as the speed of the different planets had varied in proportion to their distances. Kepler published these results in 1609 in a book called Astronomia Nova. The book contained his first two laws of planetary motions.

  1. Each planet describes an elliptical orbit with the sun at one of the focal points of the ellipse.
  2. The radius vector (line joining the sun and the planet) sweeps out equal areas in equal times. This is the distance-velocity law.

Ten years later Kepler added a third law of planetary motion: T2 is proportional to R3, where T is the time it takes for the planet to complete its orbit about the sun and R is the mean distance of the planet from the sun.

With these laws Kepler had placed heliocentrism in its final form. The sun was indeed central but not in the exact center of every planetary orbit. All the planets, including the earth, moved in orbits about the sun that were elliptical rather than circular. As accurate as this picture turned out to be, however, it was still far from achieving final acceptance.

Galileo and Newton

In the end it took two additional developments to guarantee heliocentrism a permanent place in the scientific world picture. The first development was the invention of the telescope in 1610. An Italian astronomer, Galileo, became aware that such an instrument had been produced in Holland and decided to build one himself to explore the heavens. With his telescope he observed mountains and valleys on the moon suggesting that the heavens were not unlike the earth. He observed the appearance and disappearance of dark spots on the sun, confirming that the heavens can undergo significant changes like earthly objects. These observations were enough to cause the rejection of the Aristotelian cosmology of a perfect heaven once and for all.

But that was just the beginning. Galileo also observed the phases of the planet Venus, which could only be explained if Venus was in orbit about the sun. He discovered four satellites or moons of the planet Jupiter and found that they were in orbit about that planet with velocities that varied with their distance. This showed that the earth was certainly not the center of all orbits, and by analogy it supported the heliocentric argument of Copernicus. Finally, Galileo's discovery of new stars indicated that stars were independent bodies at various distances from the earth. The celestial sphere was gone forever. This meant that the universe had no spatial boundary. Theoretically the universe was now considered to be infinitely large.

Based upon his telescopic discoveries, Galileo became a convinced Copernican and so sought to argue that case to the scientific community. In 1632 he published his Dialogue on the Two Chief World Systems, in which he gave a thorough critique of geocentrism from which it never recovered. He then went on to enrich the Copernican argument with his telescopic observations and his own analysis.

With the work of Galileo there was no doubt that Heliocentric Theory held the dominant position in astronomy. What was lacking was a physical theory to explain its main features. That theory was invented by Isaac Newton between 1666 and 1687. In those years Newton developed the first great science, the science of mechanics, which was published in 1687 with the title The Mathematical Principles of Natural Philosophy. In his science Newton sought to explain the motions of all material objects in the universe. He started by distinguishing natural states, which could maintain themselves, from coerced states, which required an outside force. Using absolute space as a theoretical reference frame, Newton held that rest and uniform rectilinear motion were natural states that could maintain themselves. Changes in those states, called accelerations, required an unbalanced force.

Unlike Aristotle, who saw circular motion as a natural state for the heavens, Newton saw the somewhat circular orbital motions of the planets as involving a constant acceleration directed toward the center of the orbits, the sun. Since he rejected any distinction between terrestrial and celestial mechanics, Newton felt that the force causing objects to fall in the vicinity of the earth was of the same nature as the force causing the planets to constantly change their direction of motion. This force, which he called gravity, was mathematically formalized in his Law of Universal Gravitation. According to the law, material objects appear to exert an attractive force upon one another that varies proportionally to the product of their masses and inversely with the distance between them squared. Newton was then able to show that his law of gravity, along with his three laws of motion, could explain Kepler's three laws of planetary motion. Thus the reason why the velocity of a planet in orbit varies inversely with its distance from the sun is because the attractive force of gravity between the sun and the planet diminishes with the distance. Heliocentrism now had a physical theory to explain its features.

The Final Word

In the end it was not the discovery of stellar parallax, or the development of a satisfactory explanation for why we have no experience of the double motion of the earth, that led to the complete acceptance of heliocentrism. Rather it was the fact that heliocentrism was consistent with the great new science of mechanics, while geocentrism was not, that ended the competition once and for all. When stellar parallax was finally observed in 1838 by the German astronomer Friedrich Bessel, it was anticlimactic. By then Heliocentric Theory had become a permanent part of the scientific landscape.

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