The physical universe 15th edition pdf

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ISBN-10: ISBN-13:

2013

1121838936 9781121838932

Contents

1. The Scientific Method 1 2. Section for Chapter 1 27 3. Motion 29 4. Section for Chapter 2 65 5. Energy 68 6. Section for Chapter 3 97

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Credits

1. The Scientific Method: Chapter 1 from The Physical Universe, 15th Edition by Krauskopf, Beiser, 2014 1 2. Section for Chapter 1: Chapter from The Physical Universe, 15th Edition by Krauskopf, Beiser, 2014 27 3. Motion: Chapter 2 from The Physical Universe, 15th Edition by Krauskopf, Beiser, 2014 29 4. Section for Chapter 2: Chapter from The Physical Universe, 15th Edition by Krauskopf, Beiser, 2014 65 5. Energy: Chapter 3 from The Physical Universe, 15th Edition by Krauskopf, Beiser, 2014 68 6. Section for Chapter 3: Chapter from The Physical Universe, 15th Edition by Krauskopf, Beiser, 2014 97

iv

Hell

I Sphe re of the Moon

II Sphe re of Mercury

III Sph ere of Venus

IV Sph ere of the Sun

V Spher e of Mars

VI Spher e of Jupiter

of SaturnVI II Sph

ere of the fixed stars. The Zodiac

IX Cry stalline sphere. Primum Mobile

VII Sphe re

Purgatory

He mis

pher e

of wa

ter

The D ark

W

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Ai r

Jerusalem

Earthly Paradise

H em

isphere

of Earth

Fire

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How Scientists Study Nature 1.1 The Scientific Method

Four Steps • What the scientific method is. • The difference between a law and a

theory. • The role of models in science.

1.2 Why Science Is Successful Science Is a Living Body of Knowledge, Not a Set of Frozen Ideas

• Why the scientific method is so success- ful in understanding the natural world.

The Solar System 1.3 A Survey of the Sky

Everything Seems to Circle the North Star

• Why Polaris seems almost stationary in the sky.

• How to distinguish planets from stars without a telescope.

1.4 The Ptolemaic System The Earth as the Center of the Universe

• How the ptolemaic system explains the astronomical universe.

1.5 The Copernican System A Spinning Earth That Circles the Sun

• How the copernican system explains the astronomical system.

1.6 Kepler’s Laws How the Planets Actually Move

• The significance of Kepler’s laws. 1.7 Why Copernicus Was Right

Evidence Was Needed That Supported His Model While Contradicting Ptolemy’s Model

• How parallax decides which system provides the best explanation for what we see.

Universal Gravitation 1.8 What Is Gravity?

A Fundamental Force • Why gravity is a fundamental force.

1.9 Why the Earth Is Round The Big Squeeze

• What keeps the earth from being a perfect sphere.

1.10 The Tides Up and Down Twice a Day

• The origin of the tides. • The difference between spring and

neap tides and how it comes about.

1.11 The Discovery of Neptune Another Triumph for the Law of Gravity

• The role of the scientific method in finding a hitherto unknown planet.

How Many of What 1.12 The SI System

All Scientists Use These Units • How to go from one system of units to

another. • The use of metric prefixes for small and

large quantities. • What significant figures are and how to

calculate with them.

CHAPTER OUTLINE AND GOALS

Your chief goal in reading each section should be to understand the important findings and ideas indicated (•) below.

The Scientific Method

Medieval picture of the universe.

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All of us belong to two worlds, the world of people and the world of nature. As mem- bers of the world of people, we take an interest in human events of the past and present and find such matters as politics and economics worth knowing about. As members of the world of nature, we also owe ourselves some knowledge of the sciences that seek to understand this world. It is not idle curiosity to ask why the sun shines, why the sky is blue, how old the earth is, why things fall down. These are serious ques- tions, and to know their answers adds an important dimension to our personal lives.

We are made of atoms linked together into molecules, and we live on a planet circling a star—the sun—that is a member of one of the many galaxies of stars in the universe. It is the purpose of this book to survey what physics, chemistry, geology, and astronomy have to tell us about atoms and molecules, stars and galaxies, and everything in between. No single volume can cover all that is significant in this vast span, but the basic ideas of each science can be summarized along with the raw mate- rial of observation and reasoning that led to them.

Like any other voyage into the unknown, the exploration of nature is an adven- ture. This book records that adventure and contains many tales of wonder and dis- covery. The search for knowledge is far from over, with no end of exciting things still to be found. What some of these things might be and where they are being looked for are part of the story in the chapters to come.

Every scientist dreams of lighting up some dark corner of the natural world—or, almost as good, of finding a dark corner where none had been suspected. The most careful observations, the most elaborate calculations will not be fruitful unless the right questions are asked. Here is where creative imagination enters science, which is why many of the greatest scientific advances have been made by young, nimble minds.

Scientists study nature in a variety of ways. Some approaches are quite direct: a geologist takes a rock sample to a laboratory and, by inspection and analysis, finds out what it is made of and how and when it was probably formed. Other approaches are indirect: nobody has ever visited the center of the earth or ever will, but by com- bining a lot of thought with clues from different sources, a geologist can say with near certainty that the earth has a core of molten iron.

No matter what the approaches to particular problems may be, however, the work scientists do always fits into a certain pattern of steps. This pattern, a general scheme for gaining reliable information about the universe, has become known as the scientific method.

1.1 The Scientific Method Four Steps We can think of the scientific method in terms of four steps: (1) formulating a problem, (2) observation and experiment, (3) interpreting the data, and (4) testing the interpre- tation by further observation and experiment to check its predictions. These steps are often carried out by different scientists, sometimes many years apart and not always in this order. Whatever way it is carried out, though, the scientific method is not a mechanical process but a human activity that needs creative thinking in all its steps. Looking at the natural world is at the heart of the scientific method, because the results of observation and experiment serve not only as the foundations on which scientists build their ideas but also as the means by which these ideas are checked ( Fig. 1-1 ).

1. Formulating a problem may mean no more than choosing a certain field to work in, but more often a scientist has in mind some specific idea he or she wishes to investigate. In many cases formulating a problem and interpreting the data overlap.

HOW SCIENTISTS STUDY NATURE

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The scientist has a speculation, perhaps only a hunch, perhaps a fully developed hypothesis, about some aspect of nature but cannot come to a definite conclusion without further study.

2. Observation and experiment are carried out with great care. Facts about nature are the building blocks of science and the ultimate test of its results. This insis- tence on accurate, objective data is what sets science apart from other modes of intellectual endeavor.

3. Interpretation may lead to a general rule or law to which the data seem to con- form. Or it may be a theory, which is a more ambitious attempt to account for what has been found in terms of how nature works. In any case, the interpreta- tion must be able to cover new data obtained under different circumstances. As put forward orginally, a scientific interpretation is usually called a hypothesis.

4. Testing the interpretation involves making new observations or performing new experiments to see whether the interpretation correctly predicts the results. If the results agree with the predictions, the scientist is clearly on the right track. The new data may well lead to refinements of the original idea, which in turn must be checked, and so on indefinitely.

The Laws of Nature The laws of a country tell its citizens how they are supposed to behave. Different countries have different laws, and even in one country laws are changed from time to time. Furthermore, though he or she may be caught and pun- ished for doing so, anybody can break any law at any time.

The laws of nature are different. Everything in the universe, from atoms to gal- axies of stars, behaves in certain regular ways, and these regularities are the laws of nature. To be considered a law of nature, a given regularity must hold everywhere at all times within its range of applicability.

The laws of nature are worth knowing for two reasons apart from satisfying our curiosity about how the universe works. First, we can use them to predict phenomena not yet discovered. Thus Isaac Newton’s law of gravity was applied over a century ago to apparent irregularities in the motion of the planet Uranus, then the farthest known planet from the sun. Calculations not only showed that another, more distant planet should exist but also indicated where in the sky to look for it. Astronomers who looked there found a new planet, which was named Neptune.

Figure 1-1 The scientific method. No hypothesis is ever final because future data may show that it is incorrect or incomplete. Unless it turns out to be wrong, a hypothesis never leaves the loop of experiment, interpretation, testing. Of course, the more times the hypothesis goes around the loop successfully, the more likely it is to be a valid interpretation of nature. Experiment and hypothesis thus evolve together, with experiment having the final word. Although a hypothesis may occur to a scientist as he or she studies experimental results, often the hypothesis comes first and relevant data are sought afterward to test it.

Observation and Experiment

Collecting the data that bear upon the problem

Testing the Interpretation

Predicting the results of new experiments on the basis of the hypothesis

Interpretation

Explaining the data in terms of a hypothesis about how nature works

Statement of Problem What is the question being asked of nature? Are there any preliminary hypotheses?

Finding the Royal Road

Hermann von Helmholtz, a nine- teenth century German physicist and biologist, summed up his experience of scientific research in these words: “I would compare myself to a mountain climber who, not knowing the way, ascends slowly and toilsomely and is often compelled to retrace his steps because his progress is blocked; who, sometimes by rea- soning and sometimes by acci- dent, hits upon signs of a fresh path, which leads him a little farther; and who, finally, when he has reached his goal, discov- ers to his annoyance a royal road which he might have followed if he had been clever enough to find the right starting point at the beginning.”

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Second, the laws of nature can give us an idea of what goes on in places we cannot examine directly. We will never visit the sun’s interior (much too hot) or the interior of an atom (much too small), but we know a lot about both regions. The evidence is indirect but persuasive.

Theories A law tells us what; a theory tells us why. A theory explains why cer- tain events take place and, if they obey a particular law, how that law originates in terms of broader considerations. For example, Albert Einstein’s general theory of relativity interprets gravity as a distortion in the properties of space and time around a body of matter. This theory not only accounts for Newton’s law of gravity but goes further, including the prediction—later confirmed—that light should be affected by gravity.

As the French mathematician Henri Poincaré once remarked, “Science is built with facts just as a house is built with bricks, but a collection of facts is not a science any more than a pile of bricks is a house.”

Models It may not be easy to get a firm intellectual grip on some aspect of nature. Therefore a model —a simplified version of reality—is often part of a hypothesis or theory. In developing the law of gravity, Newton considered the earth to be perfectly round, even though it is actually more like a grapefruit than like a billiard ball. New- ton regarded the path of the earth around the sun as an oval called an ellipse, but the actual orbit has wiggles no ellipse ever had. By choosing a sphere as a model for the earth and an ellipse as a model for its orbit, Newton isolated the most important fea- tures of the earth and its path and used them to arrive at the law of gravity.

If Newton had started with a more realistic model—a somewhat squashed earth moving somewhat irregularly around the sun—he probably would have made little progress. Once he had formulated the law of gravity, Newton was then able to explain how the spinning of the earth causes it to become distorted into the shape of a grape- fruit and how the attractions of the other planets cause the earth’s orbit to differ from a perfect ellipse.

1.2 Why Science Is Successful Science Is a Living Body of Knowledge, Not a Set of Frozen Ideas What has made science such a powerful tool for investigating nature is the constant testing and retesting of its findings. As a result, science is a living body of information and not a collection of dogmas. The laws and theories of science are not necessarily the final word on a subject: they are valid only as long as no contrary evidence comes to light. If such contrary evidence does turn up, the law or theory must be modified or even discarded. To rock the boat is part of the game; to overturn it is one way to win. Thus science is a self-correcting search for better understanding of the natural world, a search with no end in sight.

Experiment Is the Test

A master of several sciences, Michael Faraday is best remem- bered for his discoveries in electricity and magnetism (see biography in Sec. 6.18). This statement appears in the entry for March 19, 1849 in his labora- tory notebook: “Nothing is too wonderful to be true if it be con- sistent with the laws of nature, and . . . experiment is the best test of such consistency.”

Faraday was a Fellow of Brit- ain’s Royal Society, which was founded in 1660 to promote the use of observation and experi- ment to study the natural world. The oldest scientific organiza- tion in the world, the Royal Society has as its motto Nullus in Verba —Latin for “Take nobody’s word for it.” On its 350th anni- versary, the Royal Society held a celebration of “the joy and vital- ity of science, its importance to society and culture, and its role in shaping who we are and who we will become.”

the point is that it is a large-scale framework of ideas and relationships.

To people ignorant of science, a theory is a suggestion, a proposal, what in science is called a hypothesis. For instance, believers in creationism, the unsupported notion that all living things simultaneously appeared on

earth a few thousand years ago, scorn Darwin’s theory of evolution (see Sec. 16.8) as “just a theory” despite the wealth of evidence in its favor and its bedrock position in modern biology. In fact, few aspects of our knowledge of the natural world are as solidly established as the theory of evolution.

In science a theory is a fully developed logical structure based on general principles that ties together a variety of observations and experimental findings and permits as-yet-unknown phenomena and connections to be predicted. A theory may be more or less speculative when proposed, but

Theory

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Scientists are open about the details of their work, so that others can follow their thinking and repeat their experiments and observations. Nothing is accepted on any- body’s word alone, or because it is part of a religious or political doctrine. “Com- mon sense” is not a valid argument, either; if common sense were a reliable guide, we would not need science. What counts are definite measurements and clear reasoning, not vague notions that vary from person to person.

The power of the scientific approach is shown not only by its success in under- standing the natural world but also by the success of the technology based on sci- ence. It is hard to think of any aspect of life today untouched in some way by science. The synthetic clothing we wear, the medicines that lengthen our lives, the cars and airplanes we travel in, the telephone, Internet, radio, and television by which we communicate—all are ultimately the products of a certain way of thinking. Curiosity and imagination are part of that way of thinking, but the most important part is that nothing is ever taken for granted but is always subject to test and change.

Religion and Science In the past, scientists were sometimes punished for daring to make their own interpretations of what they saw. Galileo, the first modern scientist (see biography in Sec. 2.5), was forced by the Roman Catholic Church in 1633 under threat of torture to deny that the earth moves about the sun. Even today, attempts are being made to compel the teaching of religious beliefs—for instance, the story of the Creation as given in the Bible—under the name of science. But “creation science” is a contradiction in terms. The essence of science is that its results are open to change in the light of new evidence, whereas the essence of creationism is that it is a fixed doctrine with no basis in observation. The scientific method has been the means of liberating the world from ignorance and superstition. To discard this method in favor of taking at face value every word in the Bible is to replace the inquiring mind with a closed mind.

Those who wish to believe that the entire universe came into being in 6 days a few thousand years ago are free to do so. What is not proper is for certain politi- cians (whom Galileo would recognize if he were alive today) to try to turn back the intellectual clock and compel such matters of faith to be taught in schools along- side or even in place of scientific concepts, such as evolution (see Sec. 16.8), that have abundant support in the world around us. To anyone with an open mind, the evidence that the universe and its inhabitants have developed over time and con- tinue to do so is overwhelming, as we shall see in later chapters. Nothing stands still. The ongoing evolution of living things is central to biology; the ongoing evo- lution of the earth is central to geology; the ongoing evolution of the universe is central to astronomy.

Many people find religious beliefs important in their lives, but such beliefs are not part of science because they are matters of faith with ideas that are meant to be accepted without question. Skepticism, on the other hand, is at the heart of science. Science follows where evidence leads; religion has fixed principles. It is entirely possible—and indeed most religious people do this—to consult sacred texts for inspiration and guidance while accepting that observation and reason represent the path to another kind of understanding. But religion and science are not inter- changeable because their routes and destinations are different—which means that science classrooms are not the place to teach religion. To mix the religious and the scientific ways of looking at the world is good for neither, particularly if compul- sion is involved.

Advocates of creationism (or “intelligent design”) assert that evolution is an atheistic concept. Yet religious leaders of almost all faiths see no conflict between evolution and religious belief. According to Cardinal Paul Poupard, head of the Roman Catholic Church’s Pontifical Council for Culture, “we . . . know the dan- gers of a religion that severs its links with reason and becomes prey to fundamen- talism. The faithful have the obligation to listen to that which secular modern science has to offer.”

Degrees of Doubt

Although in principle every- thing in science is open to ques- tion, in practice many ideas are not really in doubt. The earth is certainly round, for instance, and the planets certainly revolve around the sun. Even though the earth is not a perfect sphere and the planetary orbits are not per- fect ellipses, the basic models will always be valid.

Other beliefs are less firm. An example is the current picture of the future of the universe. Quite convincing data suggest that the universe has been expand- ing since its start in a “big bang” about 13.7 billion years ago. What about the future? It seems likely from the latest measurements that the expansion will continue forever, but this conclusion is still tentative and is under active study by astronomers today.

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Each day the sun rises in the east, sweeps across the sky, and sets in the west. The moon, planets, and most stars do the same. These heavenly bodies also move relative to one another, though more slowly.

There are two ways to explain the general east-to-west motion. The most obvi- ous is that the earth is stationary and all that we see in the sky revolves around it. The other possibility is that the earth itself turns once a day, so that the heavenly bodies only appear to circle it. How the second alternative came to be seen as correct and how this finding led to the discovery of the law of gravity are important chapters in the history of the scientific method.

1.3 A Survey of the Sky Everything Seems to Circle the North Star One star in the northern sky seems barely to move at all. This is the North Star, or Polaris, long used as a guide by travelers because of its nearly unchanging position. Stars near Polaris do not rise or set but instead move around it in circles ( Fig. 1-2 ). These circles carry the stars under Polaris from west to east and over it from east to west. Farther from Polaris the circles get larger and larger, until eventually they dip below the horizon. Sun, moon, and stars rise and set because their circles lie partly below the horizon. Thus, to an observer north of the equator, the whole sky appears to revolve once a day about this otherwise ordinary star.

Why does Polaris occupy such a central position? The earth rotates once a day on its axis, and Polaris happens by chance to lie almost directly over the North Pole. As the earth turns, everything else around it seems to be moving. Except for their circular motion around Polaris, the stars appear fixed in their positions with respect to one another. Stars of the Big Dipper move halfway around Polaris between every sunset and sunrise, but the shape of the Dipper itself remains unaltered. (Actually, as discussed later, the stars do change their relative positions, but the stars are so far away that these changes are not easy to detect.)

Constellations Easily recognized groups of stars, like those that form the Big Dip- per, are called constellations ( Fig. 1-3 ). Near the Big Dipper is the less conspicuous Little Dipper with Polaris at the end of its handle. On the other side of Polaris from

Figure 1-2 Time exposure of stars in the northern sky. The trail of Polaris is the bright arc slightly to the left of the center of the larger arcs. The dome in the foreground houses one of the many telescopes on the summit of Mauna Kea, Hawaii. This location is favored by astronomers because observing conditions are excellent there. The lights of cars that moved during the exposure are responsible for the yellow traces near the dome.

THE SOLAR SYSTEM

What the Constitution Says

The founders of the United States of America insisted on the separation of church and state, a separation that is part of the Con- stitution. What happens in coun- tries with no such separation, in the past and in the present, testi- fies to the wisdom of the founders.

In 1987 the U.S. Supreme Court ruled that teaching cre- ationism in the public schools is illegal because it is a purely reli- gious doctrine. In response, the believers in creationism changed its name to “intelligent design” without specifying who the designer was or how the design was put into effect. Their sole argument is that life is too com- plex and diverse to be explained by evolution, when in fact this is precisely what evolution does with overwhelming success. Nev- ertheless, attempts have continued to be made to include intelligent design in science classes in public schools. All such attempts have been ruled illegal by the courts. (For more, see Sec. 1.2 at www. mhhe.com/krauskopf .)

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the Big Dipper are Cepheus and the W-shaped Cassiopeia, named, respectively, for an ancient king and queen of Ethiopia. Next to Cepheus is Draco, which means dragon.

Elsewhere in the sky are dozens of other constellations that represent animals, heroes, and beautiful women. An especially easy one to recognize on winter eve- nings is Orion, the mighty hunter of legend. Orion has four stars, three of them quite bright, at the corners of a warped rectangle with a belt of three stars in line across its middle ( Fig. 1-4 ). Except for the Dippers, a lot of imagination is needed to connect a given star pattern with its corresponding figure, but the constellations nevertheless are useful as convenient labels for regions of the sky.

Sun and Moon In their daily east-west crossing of the sky, the sun and moon move more slowly than the stars and so appear to drift eastward relative to the con- stellations. In the same way, a person on a train traveling west who walks toward the rear car is moving east relative to the train although still moving west relative to the ground. In the sky, the apparent eastward motion is most easily observed for the moon. If the moon is seen near a bright star on one evening, by the next evening it will be some distance east of that star, and on later nights it will be farther and farther to the east. In about 4 weeks the moon drifts eastward completely around the sky and returns to its starting point.

The sun’s relative motion is less easy to follow because we cannot observe directly which stars it is near. But if we note which constellations appear where the sun has just set, we can estimate the sun’s location among the stars and follow it from day to day. We find that the sun drifts eastward more slowly than the moon, so slowly that the day-to-day change is scarcely noticeable. Because of the sun’s motion each constellation appears to rise about 4 min earlier each night, and so, after a few weeks or months, the appearance of the night sky becomes quite different from what it was when we started our observations.

By the time the sun has migrated eastward completely around the sky, a year has gone by. In fact, the year is defined as the time needed for the sun to make such an apparent circuit of the stars.

Figure 1-4 Orion, the mighty hunter. Betelgeuse is a bright red star, and Bellatrix and Rigel are bright blue stars. Stars that seem near one another in the sky may actually be far apart in space. The three stars in Orion’s belt, for instance, are in reality at very different distances from us.

Figure 1-3 Constellations near Polaris as they appear in the early evening to an observer who faces north with the figure turned so that the current month is at the bottom. Polaris is located on an imaginary line drawn through the two “pointer” stars at the end of the bowl of the Big Dipper. The brighter stars are shown larger in size.

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Figure 1-5 Apparent path of a planet in the sky looking south from the northern hemisphere of the earth. The planets seem to move eastward relative to the stars most of the time, but at intervals they reverse their motion and briefly move westward. Apparent path

of a planet

Planets Five other celestial objects visible to the naked eye also shift their positions with respect to the stars. These objects, which themselves resemble stars, are planets (Greek for “wanderer”) and are named for the Roman gods Mercury, Venus, Mars, Jupiter, and Saturn. Like the sun and moon, the planets shift their positions so slowly that their day-to-day motion is hard to detect. Unlike the sun, they move in complex paths. In general, each planet drifts eastward among the stars, but its relative speed var- ies and at times the planet even reverses its relative direction to head westward briefly. Thus the path of a planet appears to consist of loops that recur regularly, as in Fig. 1-5 .

1.4 The Ptolemaic System The Earth as the Center of the Universe Although the philosophers of ancient Greece knew that the apparent daily rotation of the sky could be explained by a rotation of the earth, most of them preferred to regard the earth as stationary. The scheme most widely accepted was originally the work of Hippar- chus. Ptolemy of Alexandria ( Fig. 1-6 ) later included Hipparchus’s ideas into his Almagest, a survey of astronomy that was to be the standard reference on the subject for over a thou- sand years. This model of the universe became known as the ptolemaic system.

The model was intricate and ingenious ( Fig. 1-7 ). Our earth stands at the center, motionless, with everything else in the universe moving about it either in circles or in combinations of circles. (To the Greeks, the circle was the only “perfect” curve, hence the only possible path for a celestial object.) The fixed stars are embedded in a huge crystal sphere that makes a little more than a complete turn around the earth each day. Inside the crystal sphere is the sun, which moves around the earth exactly once a day. The dif- ference in speed between sun and stars is just enough so that the sun appears to move eastward past the stars, returning to a given point among them once a year. Near the earth in a small orbit is the moon, revolving more slowly than the sun. The planets Venus and Mercury come between moon and sun, the other planets between sun and stars.

To account for irregularities in the motions of the planets, Ptolemy imagined that each planet moves in a small circle about a point that in turn follows a large circle about the earth. By a combination of these circular motions a planet travels in a series of loops. Since we observe these loops edgewise, it appears to us as if the planets move with variable speeds and sometimes even reverse their directions of motion in the sky.

From observations made by himself and by others, Ptolemy calculated the speed of each celestial object in its assumed orbit. Using these speeds he could then figure out the location in the sky of any object at any time, past or future. These calcu- lated positions checked fairly well, though not perfectly, with positions that had been recorded centuries earlier, and the predictions also agreed at first with observations made in later years. So Ptolemy’s system fulfilled all the requirements of a scientific theory: it was based on observation, it accounted for the celestial motions known in his time, and it made predictions that could be tested in the future.

1.5 The Copernican System A Spinning Earth That Circles the Sun By the sixteenth century it had become clear that something was seriously wrong with the ptolemaic model. The planets were simply not in the positions in the sky predicted for them. The errors could be removed in two ways: either the ptolemaic

Figure 1-6 Ptolemy ( A.D. 100–170).

The Temple of the Sun

Here is how Copernicus summed up his picture of the solar system: “Of the moving bodies first comes Saturn, who completes his circuit in 30 years. After him Jupiter, moving in a 12-year revolution. Then Mars, who revolves bien- nially. Fourth in order an annual cycle takes place, in which we have said is contained the earth, with the lunar orbit as an epicy- cle, that is, with the moon mov- ing in a circle around the earth. In the fifth place Venus is carried around in 9 months. Then Mer- cury holds the sixth place, circu- lating in the space of 80 days. In the middle of all dwells the Sun. Who indeed in this most beauti- ful temple would place the torch in any other or better place than one whence it can illuminate the whole at the same time?”