Applications Of The Scientific Method Paper 3-5 Pages

SCI 110Course

 

 

http://create.mcgraw-hill.com

Copyright by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher.

This McGraw-Hill Create text may include materials submitted to McGraw-Hill for publication by the instructor of this course. The instructor is solely responsible for the editorial content of such materials. Instructors retain copyright of these additional materials.

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

iii

 

 

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

oo d

Ai r

Jerusalem

Earthly Paradise

H em

isphere

of Earth

Fire

Confirming Pages

1

1

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.

kra1392X_ch01_001-026.indd 1kra1392X_ch01_001-026.indd 1 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 1

 

 

Confirming Pages

2 Chapter 1 The Scientific Method

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

kra1392X_ch01_001-026.indd 2kra1392X_ch01_001-026.indd 2 30/11/12 7:31 PM30/11/12 7:31 PM

2 SCI 110

 

 

Confirming Pages

How Scientists Study Nature 3

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.”

kra1392X_ch01_001-026.indd 3kra1392X_ch01_001-026.indd 3 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 3

 

 

Confirming Pages

4 Chapter 1 The Scientific Method

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

kra1392X_ch01_001-026.indd 4kra1392X_ch01_001-026.indd 4 30/11/12 7:31 PM30/11/12 7:31 PM

4 SCI 110

 

 

Confirming Pages

How Scientists Study Nature 5

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.

kra1392X_ch01_001-026.indd 5kra1392X_ch01_001-026.indd 5 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 5

 

 

Confirming Pages

6 Chapter 1 The Scientific Method

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 .)

kra1392X_ch01_001-026.indd 6kra1392X_ch01_001-026.indd 6 30/11/12 7:31 PM30/11/12 7:31 PM

6 SCI 110

 

 

Confirming Pages

The Solar System 7

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.

kra1392X_ch01_001-026.indd 7kra1392X_ch01_001-026.indd 7 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 7

 

 

Confirming Pages

8 Chapter 1 The Scientific Method

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?”

kra1392X_ch01_001-026.indd 8kra1392X_ch01_001-026.indd 8 30/11/12 7:31 PM30/11/12 7:31 PM

8 SCI 110

 

 

Confirming Pages

The Solar System 9

system could be made still more complicated, or it could be replaced by a different model of the universe.

Nicolaus Copernicus, a versatile and energetic Pole of the early sixteenth century, chose the second approach. Let us consider the earth, said Copernicus, as one of the planets, a sphere rotating once a day on its axis. Let us imagine that all the planets, including the earth, circle the sun ( Fig.  1-8 ), that the moon circles the earth, and that the stars are all far away. In this model, it is the earth’s rotation that explains

Figure 1-7 The ptolemaic system, showing the assumed arrangement of the members of the solar system within the celestial sphere. Each planet is supposed to travel around the earth in a series of loops, while the orbits of the sun and moon are circular. Only the planets known in Ptolemy’s time are shown. The stars are all supposed to be at the same distance from the earth.

Figure 1-8 The copernican system. The planets, including the earth, are supposed to travel around the sun in circular orbits. The earth rotates daily on its axis, the moon revolves around the earth, and the stars are far away. All planets in the solar system are shown here. There are also a number of dwarf planets, such as Pluto; see Sec. 17.11. The actual orbits are ellipses and are not spaced as shown here, though they do lie in approximately the same plane.

kra1392X_ch01_001-026.indd 9kra1392X_ch01_001-026.indd 9 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 9

 

 

Confirming Pages

10 Chapter 1 The Scientific Method

the daily rising and setting of celestial objects, not the motions of these objects. The apparent shifting of the sun among the stars is due to the earth’s motion in its orbit. As the earth swings around the sun, we see the sun changing its position against the background of the stars. The moon’s gradual eastward drift is mainly due to its orbital motion. Apparently irregular movements of the planets are really just combinations of their motions with our own shifts of position as the earth moves.

The copernican system offended both Protestant and Catholic religious lead- ers, who did not want to see the earth taken from its place at the hub of the universe. The publication of Copernicus’s manuscript began a long and bitter argument. To us, growing up with the knowledge that the earth moves, it seems odd that this straight- forward idea was so long and so violently opposed. But in the sixteenth century good arguments were available to both sides.

Consider, said supporters of Ptolemy, how fast the earth’s surface must move to complete a full turn every 24 h. Would not everything loose be flung into space by this whirling ball, just as mud is thrown from the rim of a carriage wheel? And would not such dizzying speeds produce a great wind to blow down buildings, trees, plants? The earth does spin rapidly, replied the followers of Copernicus, but the effects are counterbalanced by whatever force it is that holds our feet to the ground. Besides, if the speed of the earth’s rotation is a problem, how much more of a problem would be the tremendous speeds of the sun, stars, and planets if they revolve, as Ptolemy thought, once a day around a fixed earth?

1.6 Kepler’s Laws How the Planets Actually Move Fortunately, improvements in astronomical measurements—the first since the time of the Greeks—were not long in coming. Tycho Brahe (1546–1601), an astronomer working for the Danish king, built an observatory on the island of Hven near Copen- hagen in which the instruments were remarkably precise ( Fig. 1-9 ). With the help of these instruments, Brahe, blessed with exceptional eyesight and patience, made thousands of measurements, a labor that occupied much of his life. Even without the

B I O G R A P H Y

currency reform, but much of his time was devoted to developing the idea that the planets move around the sun rather than around the earth. The idea was not new—the ancient Greeks were aware of it—but Copernicus went fur- ther and worked out the planetary orbits and speeds in detail. Although a summary of his results had been circulated in manuscript form earlier, not until a few weeks before his death was Copernicus’s De Revolutionibus Orbium Coelestium published in book form.

Today De Revolutionibus is recog- nized as one of the foundation stones of modern science, but soon after its appearance it was condemned by the Catholic Church (which did not lift its ban until 1835) and had little

impact on astronomy until Kepler further developed its concepts over a half century later.

When Columbus made his first voy- age to the New World Copernicus was a student in his native Poland. In the years that followed intellec- tual as well as geographical horizons receded before eager explorers. In 1496 Copernicus went to Italy to learn medicine, theology, and astron- omy. Italy was then an exciting place to be, a place of business expansion and conflicts between rival cities, great fortunes and corrupt govern- ments, brilliant thinkers and inspired artists such as Leonardo da Vinci and Michelangelo.

After 10 years in Italy Copernicus returned to Poland where he prac- ticed medicine, served as a canon in the cathedral of which his uncle was the bishop, and became involved in

Nicolaus Copernicus (1473–1543)

Leap Years

A day is the time needed for the earth to make a complete turn on its axis, and a year is the time it needs to complete an orbit around the sun. The length of the year is slightly less than 365 days and 6 hours. Thus adding an extra day to February every 4 years (namely those years evenly divisible by 4, which are accordingly called leap years ) keeps the seasons from shifting around the calendar.

The remaining discrepancy adds up to a full day too much every 128 years. To take care of most of this discrepancy, century years not divisible by 400 will not be leap years; thus 2000 was a leap year but 2100 will not be one.

kra1392X_ch01_001-026.indd 10kra1392X_ch01_001-026.indd 10 30/11/12 7:31 PM30/11/12 7:31 PM

10 SCI 110

 

 

Confirming Pages

The Solar System 11

telescope, which had not yet been invented, Tycho’s observatory was able to deter- mine celestial angles to better than 1 __ 100 of a degree.

At his death in 1601, Brahe left behind his own somewhat peculiar model of the solar system, a body of superb data extending over many years, and an assistant named Johannes Kepler. Kepler regarded the copernican scheme “with incredible and ravishing delight,” in his words, and fully expected that Brahe’s improved figures would prove Copernicus correct once and for all. But this was not the case; after 4 years of work on the orbit of Mars alone, Kepler could not get Brahe’s data to fit any of the models of the solar system that had by then been proposed.

If the facts do not agree with the theory, then the scientific method requires that the theory, no matter how attractive, must be modified or discarded. Kepler then began to look for a new cosmic design that would fit Brahe’s observations better.

The First Law After considering every possibility, which meant years of drudg- ery in making calculations by hand, Kepler found that circular orbits for the planets were out of the question even when modified in various ways. He abandoned circular orbits reluctantly, for he was something of a mystic and believed, like Copernicus and the Greeks, that circles were the only fitting type of path for celestial bodies. Kepler then examined other geometrical figures, and here he found the key to the puzzle ( Fig. 1-10 ). According to Kepler’s first law:

The Second Law Even this crucial discovery was not enough, as Kepler realized, to establish the courses of the planets through the sky. What was needed next was a way to relate the speeds of the planets to their positions in their elliptical orbits. Kepler could not be sure a general relationship of this kind even existed, and he was overjoyed when he had figured out the answer, known today as Kepler’s second law:

The paths of the planets around the sun are ellipses with the sun at one focus.

Figure 1-9 A 1598 portrait of Tycho Brahe in his observatory. The man at the right is determining the position of a celestial body by shifting a sighting vane along a giant protractor until the body is visible through the aperture at upper left. There were four of each kind of instrument in the observatory, which were used simultaneously for reliable measurements.

Figure 1-10 To draw an ellipse, place a loop of string over two tacks a short distance apart. Then move a pencil as shown, keeping the string taut. By varying the length of the string, ellipses of different shapes can be drawn. The points in an ellipse corresponding to the positions of the tacks are called focuses; the orbits of the planets are ellipses with the sun at one focus, which is Kepler’s first law.

A planet moves so that its radius vector sweeps out equal areas in equal times.

kra1392X_ch01_001-026.indd 11kra1392X_ch01_001-026.indd 11 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 11

 

 

Confirming Pages

12 Chapter 1 The Scientific Method

The radius vector of a planet is an imaginary line between it and the sun. Thus in Fig. 1-11 each of the shaded areas is covered in the same period of time. This means that each planet travels faster when it is near the sun than when it is far away. The earth, for instance, has a speed of 30 km/s when it is nearest the sun and 29 km/s when it is farthest away, a difference of over 3 percent.

The Third Law A great achievement, but Kepler was not satisfied. He was obsessed with the idea of order and regularity in the universe, and spent 10 more years making calculations. It was already known that, the farther a planet is from the sun, the longer it takes to orbit the sun. Kepler’s third law of planetary motion gives the exact relationship:

In equation form, this law states that

(Period of planet)2

___________________ (Average orbit radius)3

5 same value for all the planets

The period of a planet is the time needed for it to go once around the sun; in the case of the earth, the period is 1 year. Figure 1-12 illustrates Kepler’s third law. Table 17-1 gives the values of the periods and average orbit radii for the planets.

At last the solar system could be interpreted in terms of simple motions. Plan- etary positions computed from Kepler’s ellipses agreed not only with Tycho’s data but also with observations made thousands of years earlier. Predictions could be made of positions of the planets in the future—accurate predictions this time, no longer

The ratio between the square of the time needed by a planet to make a revolution around the sun and the cube of its average distance from the sun is the same for all the planets.

Figure 1-11 Kepler’s second law. As a planet goes from a to b in its orbit, its radius vector (an imaginary line joining it with the sun) sweeps out the area A. In the same amount of time the planet can go from c to d, with its radius vector sweeping out the area B, or from e to f, with its radius vector sweeping out the area C. The three areas A, B, and C are equal.

B I O G R A P H Y

party given by the Emperor of Bohe- mia), Kepler replaced him at the observatory and gained access to all of Brahe’s data, the most complete and accurate set then in existence.

Kepler felt that the copernican model of the solar system was not only capable of better agreement with the data than had yet been achieved but also contained within it yet- undiscovered regularities. Many years of labor resulted in three laws of plan- etary motion that fulfilled Kepler’s vision and were to bear their ultimate fruit in Newton’s law of gravity.

Kepler also found time to prepare new tables of planetary positions, to explain how telescopes produce magnified images, to father 13 chil- dren, and to prepare horoscopes for the Emperor of Bohemia, the main reason for his employment (as it had been for Brahe). In 1619 he suggested

that comet tails point away from the sun because of a “solar breeze,” a good guess (see Sec. 17.2) though he could not know its nature. A year later Kepler’s mother was accused of being a witch, but he was able to get her acquitted.

As a child, Kepler, who was born in Germany, was much impressed by seeing a comet and a total eclipse of the moon. In college, where astron- omy was his worst subject, Kepler concentrated on theology, but his first job was as a teacher of mathematics and science in Graz, Austria. There he pondered the copernican system and concluded that the sun must exert a force (which he later thought was magnetic) on the planets to keep them in their orbits.

Kepler also devised a geometri- cal scheme to account for the spacing of the planetary orbits and put all his ideas into a book called The Cosmic Mystery. Tycho Brahe, the Danish astronomer, read the book and took Kepler on as an assistant in his new observatory in Prague in what was then Bohemia. Upon Brahe’s death (the result of drinking too much at a

Johannes Kepler (1571–1630)

kra1392X_ch01_001-026.indd 12kra1392X_ch01_001-026.indd 12 30/11/12 7:31 PM30/11/12 7:31 PM

12 SCI 110

 

 

Confirming Pages

The Solar System 13

approximations. Furthermore, Kepler’s laws showed that the speed of a planet in dif- ferent parts of its orbit was governed by a simple rule and that the speed was related to the size of the orbit.

1.7 Why Copernicus Was Right Evidence Was Needed That Supported His Model While Contradicting Ptolemy’s Model It is often said that Kepler proved that Copernicus was “right” and that Ptolemy was “wrong.” True enough, the copernican system, by having the planets move around the sun rather than around the earth, was simpler than the ptolemaic system. As modified by Kepler, the copernican system was also more accurate. However, the ptolemaic system could also be modified to be just as accurate, though in a very much more complicated way. Astronomers of the time squared themselves both with the practical needs of their profession and with the Church by using the copernican system for calculations while asserting the truth of the ptolemaic system.

Figure 1-12 Kepler’s third law states that the ratio T 2 / R 3 is the same for all the planets.

Example 1.1

Kepler’s laws should be obeyed by all satellite systems, not just the solar system. In the seventeenth century the French astronomer Cassini discovered four of Saturn’s satellites (more have been discovered since). The names, periods, and orbit radii of these satellites are as follows: Tethys 1.89 days Rhea 4.52 days

2.95 3 105 km 5.27 3 105 km Dione 2.74 days Iapetus 79.30 days

3.77 3 105 km 35.60 3 105 km Verify that Kepler’s third law holds for these satellites.

Solution What we must do is calculate the ratio T 2 / R 3 for each satellite. The result for Tethys is

(1.89 days)2

______________ (2.95 3 105 km)3

5 1.40 3 10216 days2/km3

The ratio turns out to be the same for the other satellites as well, so we conclude that Kepler’s third law holds for this satellite system. [Calculations that involve powers of 10 are discussed in the Math Refresher at the end of this book. We note that (10 5 ) 3   5  10 3(5)   5  10 15 and 1/10 15   5  10 2 15 .]

Occam’s Razor

In science, as a general rule, the simplest explanation for a phe- nomenon is most likely to be cor- rect: less is more. This principle was first clearly expressed by the medieval philosopher William of Occam (or Ockham), who was born in England in 1280. In 1746 the French philosopher Etienne de Condillac called the prin- ciple Occam’s razor, an elegant metaphor that suggests cutting away unnecessary complications to get at the heart of the matter. Copernicus was one of many successful users of Occam’s razor. To be sure, as when shaving with an actual razor, it is possible to go too far; as the mathematician Alfred Whitehead said, “Seek simplicity, and distrust it.”

kra1392X_ch01_001-026.indd 13kra1392X_ch01_001-026.indd 13 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 13

 

 

Confirming Pages

14 Chapter 1 The Scientific Method

The copernican system is attractive because it accounts in a straightforward way for many aspects of what we see in the sky. However, only observations that contradict the ptolemaic system can prove it wrong. The copernican system is today considered correct because there is direct evidence of various kinds for the motions of the planets around the sun and for the rotation of the earth. An example of such evidence is the change in apparent position of nearby stars relative to the background of distant ones as the earth revolves around the sun ( Fig. 1-13 ), an effect called parallax; see Sec. 18.8. Shifts of this kind are small because all stars are far away, but they have been found.

As we know from everyday experience, and as we shall learn in a more precise way in Chap. 2, a force is needed to cause something to move in a curved path ( Fig. 1-14 ). The planets are no exception to this rule: a force of some kind must be acting to hold them in their orbits around the sun. Three centuries ago Isaac Newton had the inspired idea that this force must have the same character as the familiar force of gravity that pulls things to the earth’s surface.

1.8 What Is Gravity? A Fundamental Force Perhaps, thought Newton, the moon revolves around the earth much as the ball in Fig. 1-14 revolves around the hand holding the string, with gravity taking the place

UNIVERSAL GRAVITATION

Figure 1-13 As a consequence of the earth’s motion around the sun, nearby stars shift in apparent position relative to distant stars. The effect is known as parallax.

Distant stars

Nearby star

Sun

As seen from earth

1

2

E1

E2

Until only a few hundred years ago, astronomy was almost entirely in the service of astrology. The wealth of precise astronomical measurements that ancient civilizations compiled had as their purpose interpreting the ways of the gods.

Almost nobody today takes seri- ously the mythology of old. Although the basis of the connection has dis- appeared, however, some people still believe that the position in the sky of various celestial bodies at certain

times controls the world we live in and our individual destinies as well.

It does not seem very gracious for contemporary science to dismiss astrology in view of the great debt astronomy owes its practitioners of long ago. However, it is hard to have confidence in a doctrine that, for all its internal consistency and often delight- ful notions, nevertheless lacks any basis in scientific theory or observation and has proved no more useful in predict- ing the future than a crystal ball.

To our ancestors of thousands of years ago, things happened in the world because gods caused them to hap- pen. Famine and war, earthquake and eclipse—any conceivable catastrophe— all occurred under divine control. In time the chief gods were identified with the sun, the moon, and the five planets visible to the naked eye: Mer- cury, Venus, Mars, Jupiter, and Saturn. Early observers of the sky were primar- ily interested in finding links between celestial events and earthly ones, a study that became known as astrology.

Astrology

kra1392X_ch01_001-026.indd 14kra1392X_ch01_001-026.indd 14 30/11/12 7:31 PM30/11/12 7:31 PM

14 SCI 110

 

 

Confirming Pages

Universal Gravitation 15

of the pull of the string. In other words, perhaps the moon is a falling object, pulled to the earth just as we are, but moving so fast in its orbit that the earth’s pull is just enough to keep the moon from flying off ( Fig. 1-15 ). The earth and its sister planets might well be held in their orbits by a stronger gravitational pull from the sun. These notions turned out to be true, and Newton was able to show that his detailed theory of gravity accounts for Kepler’s laws.

It is worth noting that Newton’s discovery of the law of gravity depended on the copernican model of the solar system. “Common sense” tells us that the earth is the stationary center of the universe, and people were once severely punished for believing otherwise. Clearly the progress of our knowledge about the world we live in depends upon people, like Copernicus, who are able to look behind the screen of appearances that make up everyday life and who are willing to think for themselves.

Fundamental Forces Gravity is a fundamental force in the sense that it can- not be explained in terms of any other force. Only four fundamental forces are known: gravitational, electromagnetic, weak, and strong. These forces are respon- sible for everything that happens in the universe. Gravitational forces act between all bodies everywhere and hold together planets, stars, and the giant groups of stars called galaxies. Electromagnetic forces, which (like gravity) are unlimited in range, act between electrically charged particles and govern the structures and behav- ior of atoms, molecules, solids, and liquids. When a bat hits a ball, the interaction between them can be traced to electromagnetic forces. The weak and strong forces have very short ranges and act inside atomic nuclei. (Fundamental forces are fur- ther discussed in Sec. 8.14.)

The Law of Gravity Is the Same Everywhere How can we be sure that New- ton’s law of gravity, which fits data on the solar system, also holds throughout the rest of the universe? The evidence for this generalization is indirect but persua- sive. For instance, many double stars are known in which each member of the pair revolves around the other, which means some force holds them together. Through- out the universe stars occur in galaxies, and only gravity could keep them assem- bled in this way.

But is the gravity that acts between stars the same as the gravity that acts in the solar system? Analyzing the light and radio waves that reach us from space shows that the matter in the rest of the universe is the same as the matter found on the earth. If we are to believe that the universe contains objects that do not obey Newton’s law of grav- ity, we must have evidence for such a belief—and there is none. This line of thought may not seem as positive as we might prefer, but taken together with various theoreti- cal arguments, it has convinced nearly all scientists that gravity is the same everywhere.

Figure 1-14 An inward force is needed to keep an object moving in a curved path. The force here is provided by the string. If no force acts on it, a moving object will continue moving in a straight line at constant speed. (This is Newton’s first law of motion and is discussed in Sec. 2.7.)

Figure 1-15 The gravitational pull of the earth on the moon causes the moon to move in an orbit around the earth. If the earth exerted no force on the moon, the moon would fly off into space. If the moon had no orbital motion, it would fall directly to the earth.

kra1392X_ch01_001-026.indd 15kra1392X_ch01_001-026.indd 15 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 15

 

 

Confirming Pages

16 Chapter 1 The Scientific Method

1.9 Why the Earth Is Round The Big Squeeze A sign of success of any scientific theory is its ability to account for previously myste- rious findings. One such finding is the roundness of the earth ( Fig. 1-16 ), which was known by the Greeks as long ago as the fifth century b.c. ( Fig. 1-17 ). Early thinkers believed the earth was round because a sphere is the only “perfect” shape, a vague idea that actually explains nothing. In fact, the earth is round because gravity squeezes it into this shape.

As shown in Fig. 1-18 , if any part of the earth were to stick out very much, the gravitational attraction of the rest of the earth would pull downward on the projec- tion. The material underneath would then flow out sideways until the projection became level or nearly so. The downward forces around the rim of a deep hole would similarly cause the surrounding material to flow into it. The same argument applies to the moon, the sun, and the stars.

Such irregularities as mountains and ocean basins are on a very small scale compared with the earth’s size. The total range from the Pacific depths to the summit of Everest is less than 20 km, not much compared with the earth’s radius of 6400 km.

Figure 1-16 Astronauts in the Apollo 11 spacecraft saw this view of the earth as they orbited the moon, part of whose bleak landscape appears in the foreground. The earth is indeed round.

B I O G R A P H Y

tea, under some apple trees . . . he told me he was just in the same situation when the notion of gravitation came into his mind. ‘Why should that apple always descend perpendicularly to the ground,’ thought he to himself.”

When Cambridge University reopened, Newton went back and 2 years later became professor of mathematics there. He lived qui- etly and never married, carrying out experimental as well as theoretical research in many areas of physics; a reflecting telescope he made with his own hands was widely admired.

Especially significant was New- ton’s development of the laws of motion (see Chap. 2), which showed exactly how force and motion are related, and his application of them to a variety of problems. Newton collected the results of his work on mechanics in the Principia, a sci- entific classic that was published in 1687. A later book, Opticks, summa- rized his efforts in this field. Newton also spent much time on chemistry, though here with little success.

After writing the Principia, New- ton began to drift away from science.

He became a member of Parliament in 1689 and later an official, eventu- ally the Master, of the British Mint. At the Mint Newton helped reform the currency (one of Kepler’s interests, too) and fought counterfeiters. New- ton’s spare time in his last 30 years was mainly spent in trying to date events in the Bible. He died at 85, a figure of honor whose stature remains great to this day.

Although his mother wanted him to stay on the family farm in England, the young Newton showed a talent for science and went to Cambridge Uni- versity for further study. An outbreak of plague led the university to close in 1665, the year Newton graduated, and he returned home for 18 months.

In that period Newton came up with the binomial theorem of algebra; invented calculus, which gave science and engineering a new and powerful mathematical tool; discovered the law of gravity, thereby not only showing why the planets move as they do but also providing the key to understand- ing much else about the universe; and demonstrated that white light is a composite of light of all colors—an amazing list. As Newton later wrote, “In those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since.”

Legend has it that Newton’s inter- est turned to gravity when he was struck on the head by a falling apple. Newton’s own recollection was given to a visiting friend, who reported that “We went into the garden and drank

Isaac Newton (1642–1727)

kra1392X_ch01_001-026.indd 16kra1392X_ch01_001-026.indd 16 30/11/12 7:31 PM30/11/12 7:31 PM

16 SCI 110

 

 

Confirming Pages

Universal Gravitation 17

Figure 1-17 In the distant past evidence for the spherical shape of the earth came from travelers who found that, when they went north, more stars stayed above the horizon all night, and that, when they went south, additional stars became visible. Eratosthenes (276–194 B.C. ) determined the earth’s size with remarkable accuracy by comparing the length of the sun’s shadow at noon on the same day in two places on the same north-south line.

Polaris

Horizon

Horizon

View from B

View from A

Polaris

H orizon A

Apparent paths of stars

Horizon B

Figure 1-18 Gravity forces the earth to be round. (a) How a large bump would be pulled down. (b) How a large hole would be filled in.

The earth is not a perfect sphere. The reason was apparent to Newton: since the earth is spinning rapidly, inertia causes the equatorial portion to swing outward, just as a ball on a string does when it is whirled around. As a result the earth bulges slightly at the equator and is slightly flattened at the poles, much like a grapefruit. The total distortion is not great, for the earth is only 43 km wider than it is high ( Fig. 1-19 ). Venus, whose “day” is 243 of our days, turns so slowly that it has almost no distortion. Saturn, at the other extreme, spins so rapidly that it is almost 10 per- cent out of round.

kra1392X_ch01_001-026.indd 17kra1392X_ch01_001-026.indd 17 30/11/12 7:31 PM30/11/12 7:31 PM

The Physical Universe, 15th Edition 17

 

 

Confirming Pages

18 Chapter 1 The Scientific Method

Figure 1-19 The influence of its rotation distorts the earth. The effect is greatly exaggerated in the figure; the equatorial diameter of the earth is actually only 43 km (27 mi) more than its polar diameter.

Actual shape of earth Perfect sphere 1.10 The Tides

Up and Down Twice a Day Those of us who live near an ocean know well the rhythm of the tides, the twice-daily rise and fall of water level. Usually the change in height is no more than a few meters, but in some regions—the Bay of Fundy in eastern Canada is one—the total range can be over 20 m. The gravitational pull of the moon is what causes the advance and retreat of the oceans on this grand scale.

The moon gravitationally attracts different parts of the earth to different extents. In Fig. 1-20 the moon’s tug is strongest at A, which is closest, and weakest at B, which is far- thest away. Also, the rotation of the moon around the earth is too simple a picture—what actually happens is that both bodies rotate around the center of mass (CM) of the earth- moon system. (Think of the earth and the moon as opposite ends of a dumbbell. The CM is the balance point of the dumbbell; it is inside the earth 4700 km from its center.)

As it wobbles around the CM, the solid earth is pulled away from the water at B, where the moon’s tug is weakest, to leave the water there heaped up in a tidal bulge. At A, the greater tug of the moon dominates to cause a tidal bulge there as well. The bulges stay in place as the earth revolves under them to produce two high tides and two low tides at a given place every day ( Fig. 1-21 ).

Figure 1-20 The origin of the tides. The moon’s attraction for the waters of the earth is greatest at A, least at B. As the earth and moon rotate around the center of mass of the earth-moon system, which is located inside the earth, water is heaped up at A and B. The water bulges stay in place as the earth turns on its axis to produce two high and two low tides every day. As the earth turns under the bulges, friction between the oceans and the ocean floors slows down the earth’s rotation. As a result the tidal bulges lag slightly behind the earth-moon line. One effect of tidal friction is thus to lengthen the day. The rate of increase is a mere 1 s per day in every 43,500 years, but it adds up. Measurements of the daily growth markings on fossil corals show that the day was only 22 h long 380 million years ago. The other effect is that, because the tidal bulge facing the moon is behind the earth-moon line, the bulge exerts a force on the moon that pulls it slightly forward in its orbit, which causes the orbit to grow larger. As a result the moon is moving away from the earth at about 4 cm per year.

Figure 1-21 High and low water in the Bay of Fundy at Blacks Harbour in New Brunswick, Canada. Two tidal cycles occur daily.

kra1392X_ch01_001-026.indd 18kra1392X_ch01_001-026.indd 18 30/11/12 7:31 PM30/11/12 7:31 PM

18 SCI 110

 

 

Confirming Pages

Universal Gravitation 19

Spring and Neap Tides There is more to the story. The sun also affects the waters of the earth, but to a smaller extent than the moon even though the gravitational tug of the sun exceeds that of the moon. The reason is that what is involved in the tides is the difference between the attractions on the near and far sides of the earth, and this difference is greater for the moon because it is closer to the earth than the sun. About twice a month—when the sun, moon, and earth are in a straight line—solar tides add to lunar tides to give the especially high (and low) spring tides; see Fig. 1-22 . When the line between moon and earth is perpendicular to that between sun and earth, the tide-raising forces partly cancel to give neap tides, whose range is smaller than average.

1.11 The Discovery of Neptune Another Triumph for the Law of Gravity In Newton’s time, as in Ptolemy’s, only six planets were known: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. In 1781 a seventh, Uranus, was identified. Measure- ments during the next few years enabled astronomers to work out details of the new planet’s orbit and to predict its future positions in the sky. To make these predictions, not only the sun’s attraction but also the smaller attractions of the nearby planets Jupiter and Saturn had to be considered. For 40 years, about half the time needed for Uranus to make one complete revolution around the sun, calculated positions of the planet agreed well with observed positions.

Then a discrepancy crept in. Little by little Uranus moved away from its predicted path among the stars. The calculations were checked and rechecked, but no mistake could be found. There were two possibilities: either the law of gravity, on which the

Figure 1-22 Variation of the tides. Spring tides are produced when the moon is at M 1 or M 2 , neap tides when the moon is at M 3 or M 4 . The range between high and low water is greatest for spring tides.

kra1392X_ch01_001-026.indd 19kra1392X_ch01_001-026.indd 19 30/11/12 7:32 PM30/11/12 7:32 PM

The Physical Universe, 15th Edition 19

 

 

Confirming Pages

20 Chapter 1 The Scientific Method

calculations were based, was wrong, or else some unknown body was pulling Uranus away from its predicted path.

So firmly established was the law of gravitation that two young men, Urbain Leverrier in France and John Couch Adams in England, set themselves the task of calculating the orbit of an unknown body that might be responsible for the discrepan- cies in Uranus’s position. Adams sent a sketchy account of his studies to George Airy, England’s Astronomer Royal. Because the calculations were incomplete, although later found to be correct as far as they went, Airy asked for further details. Adams (who later blamed habitual lateness and a dislike of writing) did not respond.

A year later, in 1846, Leverrier, with no knowledge of Adams’s work, went further and proposed an actual position in the sky where the new planet should be found. He sent his result to a German astronomer, Johan Gottlieb Galle, who turned his telescope to the part of the sky where the new planet should appear. Very close to the position predicted by Leverrier, Galle found a faint object, which had moved slightly by the following night. This was indeed the eighth member of the sun’s family and was called Neptune. The theory of gravity had again successfully gone around the loop of the scientific method shown in Fig. 1-1 . In 2011 Neptune completed the first circuit of the sun since its discovery 165 years earlier.

When we say that the distance between Chicago and Minneapolis is 405 miles, what we are really doing is comparing this distance with a certain standard length called the mile. Standard quantities such as the mile are known as units. The result of every measurement thus has two parts. One is a number (405 for the Chicago-Minneapolis distance) to answer the question “How many?” The other is a unit (the mile in this case) to answer the question “Of what?”

1.12 The SI System All Scientists Use These Units The most widely used units today are those of the International System, abbreviated SI after its French name Système International d’Unités. Examples of SI units are the meter (m) for length, the second (s) for time, the kilogram (kg) for mass, the joule (J) for energy, and the watt (W) for power. SI units are used universally by scien- tists and in most of the world in everyday life as well. Although the British system of units, with its familiar foot and pound, remains in common use only in a few English- speaking countries, it is on the way out and eventually will be replaced by the SI. Since this is a book about science, only SI units will be used from here on.

The great advantage of SI units is that their subdivisions and multiples are in steps of 10, 100, 1000, and so on, in contrast to the irregularity of British units. In the case of lengths, for instance ( Fig. 1-23 ),

1 meter (m) 5 100 centimeters (cm) 1 kilometer (km) 5 1000 meters

whereas

1 foot (ft) 5 12 inches (in.) 1 mile (mi) 5 5280 feet

Table 1-1 lists the most common subdivisions and multiples of SI units. Each is designated by a prefix according to the corresponding power of 10. (Powers of 10 are widely used in science. What they mean and how to make calculations with them are reviewed in the Math Refresher at the back of the book starting on p. A-1.)

HOW MANY OF WHAT

kra1392X_ch01_001-026.indd 20kra1392X_ch01_001-026.indd 20 30/11/12 7:32 PM30/11/12 7:32 PM

20 SCI 110

 

 

Confirming Pages

How Many of What 21

Table 1-2 contains conversion factors for changing a length expressed in one sys- tem to its equivalent in the other. (More conversion factors are given inside the back cover of this book.) We note from the table that there are about 2 1 _ 2 cm in an inch, so a centimeter is roughly the width of a shirt button; a meter is a few inches longer than 3 feet; and a kilometer is nearly 2 _ 3 mile. Example 1.3 shows how conversion factors are used.

The meter and gram were new units. The ancient division of a day into 24 hours, an hour into 60 minutes, and a minute into 60 seconds was kept for the definition of the second as 1/(24)(60)(60) 5 1/86,400 of a day.

As more and more precision became needed, these definitions were modified several times. Today the second is specified in terms of the microwave radiation given off under certain circumstances by one type of cesium atom, 133Cs: 1 s equals the time needed for 9,192,631,770 cycles of this radiation to be emitted.

The meter, which for convenience had become the distance between two scratches on a platinum-iridium bar

kept at Sèvres, France, is now the dis- tance traveled in 1/299,792,458 s by light in a vacuum. There are approxi- mately 3.28 feet in a meter.

The kilogram (km) is the mass of a platinum-iridium cylinder 39 mm in diameter and 39 mm high at Sèvres. Despite much effort, a unit of mass based on a physical property measurable anywhere has not proved practical as yet. As dis- cussed in Sec. 2.10, mass and weight are not the same. The weight of a given mass is the force with which gravity attracts it to the earth; the weight of 1 kg is 2.2 pounds on the earth’s surface and decreases with altitude (see Fig. 2-38).

SI units are derived from the units of the older metric system. This system was introduced in France at the end of the eighteenth century to replace the hodgepodge of traditional units, often different in different countries and even in different parts of the same country, that was making commerce and industry difficult.

The meter (m), the standard of length, was originally defined as one ten-millionth of the distance from the equator to the North Pole. The gram (g), the standard of mass, was defined as the mass of 1 cubic centi- meter (cm3) of water; 1 cm3 is the vol- ume of a cube 1 cm (0.01 m) on each edge, and 1 kilogram 5 1000 grams.

Meter, Kilogram, Second

Figure 1-23 There are 1000 meters in a kilometer and 100 centimeters in a meter.

Table 1-1 Subdivisions and Multiples of SI Units (The Symbol m Is the Greek Letter “mu”)

Prefix Power of 10 Abbreviation Pronunciation Common Name

Pico- 10−12 p pee’ koe Trillionth Nano- 10−9 n nan’ oe Billionth Micro- 10−6 m my’ kroe Millionth Milli- 10−3 m mil’ i Thousandth Centi- 10−2 c sen’ ti Hundredth Hecto- 102 h hec’ toe Hundred Kilo- 103 k kil’ oe Thousand Mega- 106 M meg’ a Million Giga- 109 G ji’ ga Billion Tera- 1012 T ter’ a Trillion

kra1392X_ch01_001-026.indd 21kra1392X_ch01_001-026.indd 21 30/11/12 7:32 PM30/11/12 7:32 PM

The Physical Universe, 15th Edition 21

 

 

Confirming Pages

22 Chapter 1 The Scientific Method

Significant Figures In Example 1-3 the distance expressed in centimeters is 8.78  3  10 4  cm. Does this mean that d   5  87,800 cm exactly?

The answer is, not necessarily. We are only sure of the three digits 8, 7, and 8. By writing d   5  8.78  3  10 4  cm we can see just how precisely the distance is being expressed. If we needed less precision, we could round off the value of d to 8.8  3  10 4  cm. How- ever, we could not write d   5  8.780  3  10 4  cm because this implies greater precision than that of the original statement.

The accurately known digits in a number, plus one uncertain digit, are its significant figures. When quantities are used in calculations, the result is no more accurate than the quantity with the largest uncertainty. Suppose a 65-lb girl picks up a 0.23-lb apple. The total weight of the girl  1  apple is still 65 lb because all we know about the girl’s weight is that it is somewhere between 64.5 and 65.5 lb, which means an uncertainty greater than the apple’s weight. If the girl’s weight is instead known to be 65.0 lb, the mass of girl  1  apple is 65.2 lb; if her weight is instead known to be 65.00 kg, the weight of girl  1  apple is 65.23 kg. Thus

65 lb 1 0.23 lb 5 65 lb 65.0 lb 1 0.23 lb 5 65.2 lb

65.00 lb 1 0.23 lb 5 65.23 lb

Significant figures must be taken into account in multiplication and division also. For example, in part (b) of Example 1-3, the actual result of the calculation is

d 5 (0.878 km)(0.621 mi/km) 5 0.545238 mi

Example 1.2

How many nanometers are in a kilometer?

Solution A nanometer is a billionth (10 2 9 ) of a meter and a kilometer is a thousand (10 3 ) meters. Hence

kilometer _________ nanometer 5 103 m _______

1029 m 5 1012

There are 10 12 —a trillion—nanometers in a kilometer. [We note from the Math Refresher that 10 n /10 m   5  10 n 2 m , so here 10 3 /10 2 9   5  10 3 2 ( 2 9)   5  10 3 1 9   5  10 12 .]

Table 1-2 Conversion Factors for Length

Multiply a Length Expressed in By

To Get the Same Length Expressed in

Centimeters 0.394 in. ___ cm Inches

Meters 39.4 in. ___ m Inches

Meters 3.28 ft __ m Feet

Kilometers 0.621 mi ___ km

Miles

Inches 2.54 cm ___ in. Centimeters

Feet 30.5 cm ___ ft

Centimeters

Feet 0.305 m __ ft

Meters

Miles 1.61 km ___ mi Kilometers

kra1392X_ch01_001-026.indd 22kra1392X_ch01_001-026.indd 22 30/11/12 7:32 PM30/11/12 7:32 PM

22 SCI 110

 

 

Confirming Pages

Important Terms and Ideas 23

Because both the initial numbers had only three significant figures, the result can only have three also, so it was given as d   5  0.545 mi.

When a calculation has several steps, it is a good idea to keep an extra digit in the intermediate steps. Then, at the end, the final result can be rounded off to the correct number of significant figures.

For simplicity, in this book zeros after the decimal point have usually been omit- ted from values given in problems. For instance, it should be assumed that when a length of 7 m is stated, what is really meant is 7.000 . . . m.

Example 1.3

A few years ago a NASA official quoted a distance of 878 m to a reporter and added, “I don’t know what this is in terms of kilometers or miles.” Let us help him.

Solution (a) Since 1 km  5  10 3  m  5  1000 m, the distance in kilometers is

d 5 878 m__________ 1000 m/km

5 0.878 km

We note that 1______

m/km 5 km___m

and therefore m______

m/km 5

(m)(km)________ m 5 km

If instead we wanted this distance in centimeters, we would proceed in this way:

d 5 (878 m)(102 cm/m) 5 878 3 102 cm 5 (8.78 3 102)(102) cm 5 8.78 3 10212 cm 5 8.78 3 104 cm

This is the usual way such a quantity would be expressed. The Math Refresher at the end of the book might come in handy here. (b) From Table 1-2 the conversion factor we need is 0.621 mi/km, so

d 5 (0.878 km) ( 0.621 mi___km ) 5 0.545 mi

forces the sun exerts on the planets are what hold them in their orbits. Kepler’s laws are explained by the law of gravity.

The tides are periodic rises and falls of sea level caused by differences in the gravitational pulls of the moon and sun. Water facing the moon is attracted to it more than the earth itself is, and the earth moves away from water on its far side. The correspond- ing effect of the sun is smaller than that of the moon and acts to increase or decrease tidal ranges, depending on the relative posi- tions of the moon and sun.

To measure something means to compare it with a standard quantity of the same kind called a unit. The SI system of units is used everywhere by scientists and in most of the world in every- day life as well. The SI unit of length is the meter (m).

The significant figures in a number are its accurately known digits. When numbers are combined arithmetically, the result has as many significant figures as those in the number with the fewest of them.

The scientific method of studying nature has four steps: (1) formulating a problem; (2) observation and experiment; (3) interpreting the results; (4) testing the interpretation by further observation and experiment. When first proposed, a scientific interpretation is called a hypothesis. After thorough checking, it becomes a law if it states a regularity or relationship, or a theory if it uses general considerations to account for specific phenomena.

Polaris, the North Star, lies almost directly above the North Pole. A constellation is a group of stars that form a pattern in the sky. The planets are heavenly bodies that shift their positions regularly with respect to the stars.

In the ptolemaic system, the earth is stationary at the center of the universe. In the copernican system, the earth rotates on its axis and, with the other planets, revolves around the sun. Obser- vational evidence supports the copernican system.

Kepler’s laws are three regularities that the planets obey as they move around the sun.

Newton’s law of gravity describes the attraction all bod- ies in the universe have for one another. The gravitational

Important Terms and Ideas

kra1392X_ch01_001-026.indd 23kra1392X_ch01_001-026.indd 23 30/11/12 7:32 PM30/11/12 7:32 PM