The Night Sky

Among the most predictable objects in the universe are the lights we see in the sky at night—the stars and planets. Modern men and women, living in large metropolitan areas, are no longer very conscious of the richness of the night sky's shifting patterns. But think about the last time you were out in the country on a clear moonless night, far from the lights of town. There, the stars seem very close, very real. Before the nineteenth-century development of artificial lighting, human beings often experienced jet-black skies filled with brilliant pinpoint stars.

The sky changes; it’s never quite the same from one night to the next. Living with this display all the time, our ancestors noticed regularities in the arrangement and movements of stars and planets, and they wove these almost lifelike patterns into their religion and mythology. They learned that when the Sun rose in a certain place, it was time to plant crops because spring was on its way. They learned to predict the times of the month when a full Moon would illuminate the ground, allowing them to continue harvesting and hunting after sunset. To these people, knowing the behavior of the sky was not an intellectual game or an educational frill, it was an essential part of their lives. It is no wonder, then, that astronomy, the study of objects in the heavens, was one of the first sciences to develop.

By relying on their observations and records of the regular motions of the stars and planets, ancient observers of the sky were perhaps the first humans to accept the most basic tenet of science:

Physical events are quantifiable and therefore predictable.

Without the predictability of physical events, the scientific method could not proceed.

Stonehenge

No symbol of humankind's early preoccupation with astronomy is more dramatic than Stonehenge, the great prehistoric stone monument on Salisbury Plain in southern England. The structure consists of a large circular bank of earth surrounding a ring of single upright stones, which in turn encircle a horseshoe-shaped structure of five giant stone archways. Each arch is constructed from three massive blocks—two vertical supports several meters tall capped by a great stone lintel. The open end of the horseshoe aligns with an avenue that leads northeast to another large stone, called the “heel stone” Stonehenge was built in spurts over a long period of time, starting in about 2800 bc. Despite various legends assigning it to the Druids, Julius Caesar, the magician Merlin (who was supposed to have levitated the stones from Ireland), or other mysterious unknown races, archaeologists have shown that Stonehenge was built by several groups of people, none of whom had a written language and some of whom even lacked metal tools. Why would these people expend such a great effort to erect one of the world's great monuments?

Stonehenge, like many similar structures scattered around the world, was built to mark the passage of time. It served as a giant calendar based on the movement of objects in the sky. The most famous astronomical function of Stonehenge was to mark the passage of the seasons. In an agricultural society, after all, one has to know when it's time to plant the crops, and one can't always tell by looking at the weather. At Stonehenge, this job was done by sighting through the stones. On midsummer's morning, for example, someone standing in the center of the monument will see the Sun rising directly over the heel stone.

Building a structure like Stonehenge required accumulation of a great deal of knowledge about the sky—knowledge that could have been gained only through many years of observation. Without a written language, people would have had to pass complex information about the movements of the Sun, the Moon, and the planets from one generation to the next. How else could they have aligned their stones so perfectly that modern-day Druids in England can still greet the midsummer sunrise over the heel stone?

If the universe was not regular and predictable, if repeated observation could not show us patterns that occur over and over again, the very concept of a monument like Stonehenge would be impossible. And yet, there it stands after almost 5,000 years, a testament to human ingenuity and to the possibility of predicting the behavior of the universe we live in.

Having made the point that Stonehenge functioned as a calendar, we must also point out that this doesn't mean it was only a calendar. The area around Stonehenge is littered with graves, and in 2009, archaeologists discovered holes that once held another stone circle—stones that were later incorporated into Stonehenge itself. The smaller circle may have functioned as a location for cremations, leading one archaeologist to suggest that Stonehenge served as the center of the “Land of the Dead” in ancient times.

The Discovery of the Spread of Disease

Observing nature is a crucial part of the scientific method. During the nineteenth century, for example, Europe experienced an epidemic of cholera, a severe and often fatal intestinal disease. No one knew the cause of the disease—the discovery of the germ theory of disease was still decades in the future. The very name of the disease is derived from the early days of medicine, when “choler” was seen as one of the “humors” that governed human health. But even without knowing the cause of the disease, physicians and scientists could observe the places and times when it occurred.

John Snow (1823–1858) was a distinguished London physician who is remembered in medicine as one of the pioneers in the new field of anesthesiology. He even attended the birth of Queen Victoria's last children, administering chloroform during labor. For many years, he had been convinced that the incidence of cholera was connected in some way to London's water supply. At that time, many people got their water from public pumps, and even water delivered to private homes came through a chaotic maze of pipes, so that water delivered to neighboring buildings could come from very different sources. Over the years, Snow patiently cataloged data on water sources and the frequent cholera outbreaks in the city.

In 1854, Snow made a dramatic discovery. He noticed that the incidence of cholera that year seemed to be concentrated around a place called Golden Square, a poor neighborhood where people drew their water from a place called the Broad Street pump. Upon investigation, Snow found that the square was surrounded by a large number of homes where human waste was dumped into backyard pits. He argued that these findings suggested the disease was somehow related to contamination of the water supply Driven by the accumulation of data like this, the city of London (and soon all major population centers) eventually began to require that human waste be carried away from dwellings into sewers and not just dumped into a river upstream of the intakes for the drinking water supply. Thus, Snow's discovery of a regularity in nature (in this case between disease and polluted water) was the foundation on which modern sanitation and public health systems are based.

Just as the builders of Stonehenge had no idea of the structure of the solar system or why the heavens behave as they do, Snow had no idea why keeping human waste out of the drinking water supply should eliminate a disease such as cholera. It wasn't until the early 1890s, in fact, that the German scientist Robert Koch first suggested that the disease was caused by a particular bacterium, Vibrio cholerae, that is carried in human waste. •

Science by the Numbers

Ancient Astronauts

Confronted by a monument such as Stonehenge, with its precise orientation and epic proportions, some people refuse to accept the notion that it could have been built by the ingenuity and hard work of ancient peoples. Instead, they assume that there must have been some outside intervention, frequently in the form of visitors from other planets whose handiwork survives in the monument today. Many ancient monuments, including the pyramids of Egypt, the Mayan temples of Central America, and the giant statues of Easter Island, have been ascribed to these mysterious aliens.

Such conjecture is unconvincing unless you first show that building the monument was beyond the capabilities of the indigenous people. Suppose, for example, that Columbus had found a glass-and-steel skyscraper when he landed in America. Both the ability to produce the materials (steel, glass, and plastic, for example) and the ability to construct a building dozens of stories tall were beyond the abilities of Native Americans at that time. A reasonable case could have been made for the intervention of ancient astronauts or some other advanced intelligence.

Is Stonehenge a similar case? The material, local stone, was certainly available to anyone who wanted to use it. Working and shaping stone was also a skill, albeit a laborious one, that was available to early civilizations. The key question, then, is whether people without steel tools or wheeled vehicles could have moved the stones from the quarry to the construction site (Figure 2-3 ).

The largest stone, about 10 meters (more than 30 feet) in length, weighs about 50 metric tons (50,000 kilograms, or about 100,000 pounds) and had to be moved over land some 30 kilometers (20 miles) from quarries to the north. Could this massive block have been moved by primitive people, equipped only with wood and ropes?

While Stonehenge was being built, it snowed frequently in southern England, so the stones could have been hauled on sleds. A single person can easily haul 100 kilograms on a sled (think of pulling a couple of your friends). How many people would it take to haul a 50,000-kilogram stone? Organizing 500 people for the job would have been a major social achievement, of course, but there's nothing physically impossible about it. So, although scientists cannot absolutely disprove the possibility that Stonehenge was constructed by some strange, forgotten technology, why should we invoke such alien intervention when the concerted actions of a dedicated, hard-working human society would have sufficed?

When confronted with phenomena in a physical world, we should accept the most straightforward and reasonable explanation as the most likely. This procedure is called Ockham's razor, after William of Ockham, a fourteenth-century English philosopher who argued that “postulates must not be multiplied without necessity”—that is, given a choice, the simplest solution to a problem is most likely to be right. Scientists thus reject the notion of ancient astronauts building Stonehenge, and they relegate such speculation to the realm of pseudoscience. •

The Birth of Modern Astronomy

Far from the city, when you look up at the night sky you see a dazzling array of objects. Thousands of visible stars fill the heavens and appear to move each night in stately circular arcs centered on the North Star. The relative positions of these stars never seem to change, and closely spaced groups of stars called constellations have been given names such as the Big Dipper and Leo the Lion. Moving across this fixed starry background are Earth's Moon, with its regular succession of phases, and a half-dozen planets that wander through the path in the sky known as the zodiac. You might also see swift streaking meteors or long-tailed comets—transient objects that grace the night sky from time to time.

What causes these objects to move, and what do those motions tell us about the universe in which we live?

The Historical Background: Ptolemy and Copernicus

Since before recorded history, people have observed the distinctive motions of objects in the sky and have tried to explain them. Most societies created legends and myths tied to these movements, and some (the Babylonians, for example) had long records of sophisticated astronomical observations. It was the Greeks, however, who devised the first astronomical explanations that incorporated elements of modern science.

Claudius Ptolemy, an Egyptian-born Greek astronomer and geographer who lived in Alexandria in the second century ad, proposed the first widely accepted explanation for complex celestial motions. Working with the accumulated observations of earlier Babylonian and Greek astronomers, he put together a singularly successful model—a theory, to use the modern term—about how the heavens had to be arranged to produce the display we see every night. In the Ptolemaic description of the universe, Earth sat unmoved at the center. Around it, on a concentric series of rotating spheres, moved the stars and planets. The model was carefully crafted to take account of observations. The planets, for example, were attached to small spheres rolling inside the larger spheres so that their uneven motion across the sky could be understood.

This system remained the best explanation of the universe for almost 1,500 years. It successfully predicted planetary motions, eclipses, and a host of other heavenly phenomena, and was one of the longest-lived scientific theories ever devised.

During the first decades of the sixteenth century, however, a Polish cleric by the name of Nicolaus Copernicus (1473–1543) considered a competing hypothesis that was to herald the end of Ptolemy's crystal spheres. His ideas were published in 1543 under the title On the Revolutions of the Heavenly Spheres. Copernicus retained the notions of a spherical universe with circular orbits, and even kept the ideas of spheres rolling within a sphere, but he asked a simple and extraordinary question: “Is it possible to construct a model of the heavens whose predictions are as accurate as Ptolemy's, but in which the Sun, rather than Earth, is at the center?” We do not know how Copernicus, a busy man of affairs in medieval Poland, conceived this question, nor do we know why he devoted his spare time for most of his adult life to answering it. We do know, however, that in 1543, for the first time in over a millennium, the Ptolemaic system was faced by a serious challengerObservations: Tycho Brahe and Johannes Kepler

With the publication of the Copernican theory, astronomers were confronted by two competing models of the universe. The Ptolemaic and Copernican systems differed in a fundamental way that had far-reaching implications about the place of humanity in the cosmos. They both described possible universes, but in one, Earth (and by implication humankind) was no longer at the center. The astronomers' task was to decide which model best describes the universe we actually live in.

To resolve the question, astronomers had to compare the predictions of the two competing hypotheses to the observations of what was actually seen in the sky. When they performed these observations, a fundamental problem became apparent. Although the two models made different predictions about the position of a planet at midnight, for example, or the time of moonrise, the differences were too small to be measured with equipment available at the time. The telescope had not yet been invented, but astronomers were skilled in recording planetary positions by depending entirely on naked-eye measurements with awkward instruments. Until the accuracy of measurement was improved, the question of whether Earth was at the center of the universe couldn't be decided.

The Danish nobleman Tycho Brahe (1546–1601) showed the way out of this impasse. Tycho, as he was known, is one of those people who, in addition to making important contributions to knowledge, led a truly bizarre life. As a young man, for example, he lost the bridge of his nose in a duel with a fellow student over who was the better mathematician; for the rest of his life he had to wear a metal prosthesis.

Tycho's scientific reputation was firmly established at the age of 25, when he observed and described a new star in the sky This dramatic discovery challenged the prevailing wisdom that the heavens are unchanging. Within the next 5 years, the Danish king had given him the island of Hveen off the coast of Denmark and funds to construct a royal observatory there.

Tycho built his career on the design and use of vastly improved observational instruments. He determined the position of each star or planet with a “quadrant,” a large, sloping device something like a gunsight, recording each position as two angles. If you were to do this today, you might, for example, measure one angle up from the horizon and a second angle around from due north. Tycho constructed his sighting device of carefully selected materials, and he learned to correct his measurements for thermal contraction—the slight shrinkage of brass and iron components that occurred during the cold Danish nights. Over a period of 25 years, he used these instruments to accumulate extremely accurate data on the positions of the planets. When Tycho died in 1601, his data passed into the hands of his assistant, Johannes Kepler (1571–1630), a skilled German mathematician who had joined Tycho 2 years before. Kepler analyzed Tycho Brahe's decades of planetary data in new ways, and he found that the data could be summarized in three mathematical statements about the solar system. Kepler's first and most important lawstates that all planets, including Earth, orbit the Sun in elliptical, not circular, paths. In this picture, the spheres-within-spheres are gone because ellipses fully account for the observed planetary motions. Not only do Kepler's laws give a better description of what is observed in the sky, but they present a simpler picture of the solar system as well.

Previous astronomers had assumed that planetary orbits must be perfect circles, and many believed on theological or philosophical grounds that Earth had to be the center of a spherical universe. In science, such assumptions of ideality may guide thinking, but they must be replaced when observations prove them wrong.

The work of Tycho Brahe and Johannes Kepler firmly established that Earth is not at the center of the universe, that planetary orbits are not circular, and that the answer to the contest between the Ptolemaic and Copernican universes is “neither of the above.” This research also illustrates a recurrent point about scientific progress. The ability to answer scientific questions, even questions dealing with the most fundamental aspects of human existence, often depends on the kinds of instruments scientists have at their disposal and on the ability of scientists to apply advanced mathematical reasoning to their data.

At the end of this historical episode, astronomers had Kepler's laws that describe how the planets in the solar system move, but they had no idea why planets behave the way they do. The answer to that question was to come from an unexpected source.

2.2 The Birth of Mechanics

Mechanics is an old word for the branch of science that deals with the motions of material objects. A rock rolling down a hill, a ball thrown into the air, and a sailboat skimming over the waves are all fit subjects for this science. Since ancient times, philosophers had speculated on why things move the way they do, but it wasn't until the seventeenth century that our modern understanding of the subject began to emerge.

Galileo Galilei

The Italian physicist and philosopher Galileo Galilei (1564–1642) was, in many ways, a forerunner of the modern scientist A professor of mathematics at the University of Padua, he quickly became an advisor to the powerful court of the Medici at Florence as well as a consultant at the Arsenal of Venice, the most advanced naval construction center in the world. He invented many practical devices, such as the first thermometer, the pendulum clock, and the proportional compass that craftsmen still use today. Galileo is also famous as the first person to record observations of the heavens with a telescope, which he built after hearing of the instrument from others. His astronomical writings, which supported the Sun-centered Copernican model of the universe, led to his trial by the Inquisition. Science in the Making

The Heresy Trial of Galileo

In spite of his great scientific advances, Galileo is remembered primarily because of his heresy trial in 1633. In 1610, Galileo had published a summary of his telescopic observations in The Starry Messenger. Some readers complained that these ideas violated Catholic Church doctrine, and in 1616, Galileo was called before the College of Cardinals. The Catholic Church supposedly warned Galileo not to discuss Copernican ideas unless he treated them as an unproven hypothesis.

In spite of these instructions, in 1632, Galileo published A Dialogue Concerning Two World Systems, which was a long defense of the Copernican system. This action led to the famous trial, at which Galileo purged himself of suspicion of heresy by denying that he held the views in his book. He was already an old man by this time, and he spent his last few years under house arrest in his villa near Florence.

The legend of Galileo's trial, in which an earnest seeker of truth is crushed by a rigid hierarchy, bears little resemblance to the historical events. The Catholic Church had not banned Copernican ideas. Copernicus, after all, was a savvy Church politician who knew how to get his ideas across without ruffling feathers. But Galileo's confrontational tactics—notably putting the Pope's favorite arguments into the mouth of a foolish character in the book—brought the predictable reaction.

A footnote: In 1992, the Catholic Church reopened the case of Galileo and, in effect, issued a retroactive “not guilty.” The grounds for the reversal were that the original judges had not separated questions of faith from questions of scientific fact. •

Speed, Velocity, and Acceleration

To lay the groundwork for understanding Galileo's study of moving objects (and ultimately to understand the workings of the solar system), we have to begin with precise definitions of three familiar terms: speed, velocity, and acceleration.

Speed and Velocity

Speed and velocity are everyday words that have precise scientific meanings. Speed is the distance an object travels divided by the time it takes to travel that distance. Velocity has the same numerical value as speed, but it is a quantity that also includes information on the direction of travel. The speed of a car might be 40 miles per hour, for example, while the velocity is 40 miles per hour due west. Quantities such as velocity that involve both a speed and a direction are called vectors. Velocity and speed are both measured in units of distance per time, such as meters per second, feet per second, or miles per hour.Acceleration

Acceleration is a measure of the rate of change of velocity. Whenever an object changes speed or direction, it accelerates. When you step on the gas pedal in your car, for example, the car accelerates forward. When you slam on the brakes, the car accelerates backward (what is sometimes called deceleration). When you go around a curve in your car, even if the car's speed stays exactly the same, the car is still accelerating because the direction of motion is changing. The most thrilling amusement park rides combine these different kinds of acceleration—speeding up, slowing down, and changing direction in bumps, tight turns, and rapid spins.

In words: Acceleration is the amount of change in velocity divided by the time it takes that change to occur.Like velocity, acceleration requires information about the direction, and it is therefore a vector.

When velocity changes, it may be by a certain number of feet per second or meters per second in each second. Consequently, the units of acceleration are meters per second squared, usually described as “meters per second per second” (and abbreviated m/s2), where the first “meters per second” refers to the velocity and the last “per second” refers to the time it takes for the velocity to change.

To understand the difference between acceleration and velocity, think about the last time you were behind the wheel of a car driving down a long, straight road. You glance at your speedometer. If the needle is unmoving (at 30 miles per hour, for example), you are moving at a constant speed. Suppose, however, that the needle isn't stationary on the speedometer scale (perhaps because you have your foot on the gas or on the brake). Your speed is changing and, by the preceding definition, you are accelerating. The higher the acceleration, the faster the needle moves. If the needle doesn't move, however, this doesn't mean you and the car aren't moving. As we know, an unmoving needle simply means that you are traveling at a constant speed. Motion at a constant speed in a single direction is called uniform motion.

The Founder of Experimental Science

Galileo devised an ingenious experiment to determine the relationships among distance, time, velocity, and acceleration. Many scientists now view Galileo's greatest achievement as this experimental work on the behavior of objects thrown or dropped on the surface of Earth. Greek philosophers, using pure reason, had taught that heavier objects must fall faster than light ones. In a series of classic experiments, Galileo showed that this was not the case—that at Earth's surface all objects accelerate at the same rate as they fall downward. Ironically, Galileo probably never performed the one experiment for which he is most famous—dropping two different weights from the Leaning Tower of Pisa to see which would land first.

To describe falling objects, it's necessary to make precise measurements of two variables: distance and time. Galileo and his contemporaries easily measured distance using rulers, but their timepieces were not precise enough to measure the brief times it took objects to fall straight down. Previous workers had simply observed the behavior of falling objects, but Galileo constructed a special apparatus designed purely to measure acceleration He slowed down the time of fall by rolling large balls down an inclined plane crafted of brass and hard wood, and measured the time of descent by listening to the “ping” as the ball rolled over wires stretched along its path. (The human ear is quite good at hearing equal time intervals.) The balls accelerated as they moved down the plane, and by increasing the angle of elevation of the plane, Galileo could increase that acceleration. At an elevation of 90 degrees, of course, the ball would fall freely.

Galileo's experiments convinced him that any object accelerating toward Earth's surface, no matter how heavy or light, falls with exactly the same constant acceleration. For balls on his plane, his results can be summarized in a simple equation:

In words: The velocity of an accelerating object that starts from rest is proportional to the length of time that it has been falling.

The velocity of Galileo's objects, of course, was always directed downward.

This equation tells us that an object that falls for 2 seconds achieves a velocity twice that of an object that falls for only 1 second, whereas one that falls for 3 seconds will be moving three times as fast as one that falls for only 1 second, and so on. The exact value of the velocity depends on the acceleration, which, in Galileo's experiment, depended on the angle of elevation of the plane.

In the special case where the ball is falling freely (i.e., when the plane is at 90 degrees), the acceleration is such an important number that it is given a specific letter of the alphabet, g. This value is the acceleration that all objects experience at Earth's surface. (Note that the Moon and other planets have their own very different surface accelerations; g applies only to Earth's surface.) The value of g can be determined by measuring the fall rate of objects in a laboratory, and it turns out to be. The Science of Life

Experiencing Extreme Acceleration

You experience accelerations every day of your life. Just lying in bed you feel acceleration equal to g, due to Earth's gravitational pull. When you travel in a car or plane, ride an elevator, and especially when you enjoy amusement park rides, your body is subjected to additional accelerations, though rarely exceeding 2 g. But jet pilots and astronauts experience accelerations many times that caused by Earth's gravitational pull during takeoffs, sharp turns, and emergency ejections. What happens to the human body under extreme acceleration, and how can equipment be designed to reduce the risk of injury? In the early days of rocket flights and high-speed jet design, government scientists had to know.

Controlled laboratory accelerations were produced by rocket sleds or centrifuges, which may reach accelerations exceeding 10 g. Researchers quickly discovered that muscles and bones behave as an effectively rigid framework. Sudden extreme acceleration, such as that experienced in a car crash, may cause damage, but these parts can withstand the more gradual changes in acceleration associated with flight.

The body's fluids, on the other hand, shift and flow under sustained acceleration. A pilot in a sharp curve will be pushed down into the seat and experience something like the feeling you get when an elevator starts upward. The blood in the arteries leading up to the brain will also be pushed down, and, if the acceleration is big enough, the net effect will be to drain blood temporarily from the brain. The heart simply can't push the blood upward hard enough to overcome the downward pull. As a result, a pilot may experience a blackout, followed by unconsciousness. Greater accelerations could be tolerated in the prone position adopted by the first astronauts, who had to endure sustained 8 g conditions during takeoffs.

One of the authors (J. T.) once rode in a centrifuge and experienced an 8 g acceleration. The machine itself was a gray, egg-shaped capsule located at the end of a long steel arm. When in operation, the arm moved in a horizontal circle. Funny things happen at 8 g. For example, the skin of your face is pulled down, so that it's hard to keep your mouth open to breathe. The added weight feels like a very heavy person sitting on your chest.

There is, however, one advantage to having had this particular experience. Now, whenever he encounters the question, “What is the most you have ever weighed?” on a medical form, the author can write “1,600 pounds.” 2.3 Isaac Newton and the Universal Laws of Motion

With Galileo's work, scientists began to isolate and observe the motion of material objects in nature and to summarize their results into mathematical relationships. As to why bodies should behave this way, however, they had no suggestions. And there was certainly little reason to believe that the measurements of falling objects at Earth's surface had anything at all to do with motions of planets and stars in the heavens.

The English scientist Isaac Newton (1642–1727), arguably the most brilliant scientist who ever lived , synthesized the work of Galileo and others into a statement of the basic principles that govern the motion of everything in the universe, from stars and planets to clouds, cannonballs, and the muscles in your body. These results, called Newton's laws of motion, sound so simple and obvious that it's hard to realize they represent the results of centuries of experiment and observation, and even harder to appreciate what an extraordinary effect they had on the development of science.

The young Newton was interested in mechanical devices and eventually enrolled as a student at Cambridge University. For most of the 1665–1666 school year, the university was closed due to a recurrence in England of the Great Plague that had devastated much of Europe in the past. Isaac Newton spent the time at a family farm in Lincolnshire, reading and thinking about the physical world. There he began thinking through his extraordinary discoveries in the nature of motion, as well as pivotal advances in optics and mathematics.

Three laws summarize Newton's description of motions.

The First Law

A moving object will continue moving in a straight line at a constant speed, and a stationary object will remain at rest, unless acted on by an unbalanced force.

Newton's first law seems to state the obvious: If you leave an object alone, it won't change its state of motion. In order to change it, you have to push it or pull it, thus applying a force. Yet virtually all scientists from the Greeks to Copernicus would have argued that the first law is wrong. They believed that because the circle is the most perfect geometrical shape, objects will move in circles unless something interferes. They also believed that heavenly objects would keep turning without any outside force acting (indeed, they had to believe this or face the question of why the heavens didn't slow down and stop).

Newton, basing his arguments on observations and the work of his predecessors, turned this notion around. An object left to itself will move in a straight line, and if you want to get it to move in a circle, you have to apply a force You know this is true—if you swing something around your head, it will move in a circle only as long as you hold on to it. Let go, and off it goes in a straight line.

This simple observation led Newton to recognize two different kinds of motion. An object is in uniform motion if it travels in a straight line at constant speed. All other motions are called acceleration. Accelerations can involve changes of speed, changes of direction, or both.

Newton's first law tells us that when we see acceleration, something must have acted to produce that change. We define a force as something that produces a change in the state of motion of an object. In fact, we will use the first law of motion extensively in this book to tell us how to recognize when a force, particularly a new kind of force, is acting.

The tendency of an object to remain in uniform motion is called inertia. A body at rest tends to stay at rest because of its inertia, while a moving body tends to keep moving because of its inertia. We often use this idea in everyday speech; for example, we may talk about the inertia in a company or government organization that is resistant to change. The Second Law

The acceleration produced on a body by a force is proportional to the magnitude of the force and inversely proportional to the mass of the object.

If Newton's first law of motion tells you when a force is acting, then the second law of motion tells you what the force does when it acts. This law conforms to our everyday experience: It's easier to lift a child than an adult, and easier to move a ballerina than a defensive tackle.

Newton's second law is often expressed as an equation.

In words: The greater the force, the greater the acceleration; but the more massive the object being acted on by a given force, the smaller the acceleration. This equation, well known to generations of physics majors, tells us that if we know the forces acting on a system of known mass, we can predict its future motion. The equation conforms to our experience that an object's acceleration is a balance between two factors: force and mass, which is related to the amount of matter in an object.

A force causes the acceleration. The greater the force, the greater the acceleration. The harder you throw a ball, the faster it goes. Mass measures the amount of matter in any object. The greater the object's mass, the more “stuff” you have to accelerate, the less effect a given force is going to have. A given force will accelerate a golf ball more than a bowling ball, for example. Newton's second law of motion thus defines the balance between force and mass in producing an acceleration.

Newton's first law defines the concept of force as something that causes a mass to accelerate, but the second law goes much further. It tells us the exact magnitude of the force necessary to cause a given mass to achieve a given acceleration. Because force equals mass times acceleration, the units of force must be the same as mass times acceleration. Mass is measured in kilograms (kg) and acceleration in meters per second per second (m/s2), so the unit of force is the “kilogram-meter-per-second-squared” (kg-m/s2). One kg-m/s2 is called the “newton.” The symbol for the newton is N. The second law of motion does not imply that every time a force acts, motion must result. A book placed on a table still feels the force of gravity, and you can push against a wall without moving it. In these situations, the atoms in the table or the wall shift around and exert their own force that balances the one that acts on them. It is only the net, or unbalanced, force that actually gives rise to acceleration.

The Third Law

For every action there is an equal and opposite reaction.

Newton's third law of motion tells us that whenever a force is applied to an object, that object simultaneously exerts an equal and opposite force. When you push on a wall, for example, it instantaneously pushes back on you; you can feel the force on the palm of your hand. In fact, the force the wall exerts on you is equal in magnitude (but opposite in direction) to the force you exert on it.

The third law of motion is perhaps the least intuitive of the three. We tend to think of our world in terms of causes and effects, in which big or fast objects exert forces on smaller, slower ones: a car slams into a tree, a batter drives the ball into deep left field, a boxer hits a punching bag But in terms of Newton's third law, it is equally valid to think of these events the “other way around.” The tree stops the car's motion, the baseball alters the swing of the bat, and the punching bag blocks the thrust of the boxer's glove, thus exerting a force and changing the direction and speed of the punch.

Forces always act simultaneously in pairs. You can convince yourself of this fact by thinking about any of your day's myriad activities. As you recline on a sofa reading this book, your weight exerts a force on the sofa, but the sofa exerts an equal and opposite force (called a contact force) on you, preventing you from falling to the floor The book feels heavy in your hands as it presses down, but your hands hold the book up, exerting an equal and opposite force. You may feel a slight draft from an open window or fan, but as the air exerts that gentle force on you, your skin just as surely exerts an equal and opposite force on the air, causing it to change its path.

It is important to realize that although forces of the same magnitude act on both objects—your hand and the wall, for example—the results of the action of those forces can be different, depending on the objects involved. When a bug hits the windshield of a car, for example, it exerts a force on the car at the same time the car exerts an equal and opposite force on it. The consequences of the action of those forces are quite different, however. The tiny deceleration of the car is imperceptible, but the bug is squashed.

It is also important to note that although the forces are equal and opposite, they do not cancel each other since they act on different objects. Newton's Laws at Work

Every motion in your life—indeed, every motion in the universe—involves the constant interplay of all three of Newton's laws. The laws of motion never occur in isolation but rather are interlocking aspects of every object's behavior. The interdependence of Newton's three laws of motion can be envisioned by a simple example. Imagine a boy standing on roller skates holding a stack of baseballs. He throws the balls, one by one. Each time he throws a baseball, the first law tells us that he has to exert a force so that the ball accelerates. The third law tells us that the baseball will exert an equal and opposite force on the boy. This force acting on the boy will, according to the second law, cause him to recoil backward.

Although the example of the boy and the baseballs may seem a bit contrived, it exactly illustrates the principle by which fish swim and rockets fly. As a fish moves its tail, it applies a force against the water. The water, in turn, pushes back on the fish and propels it forward. In a rocket motor, forces are exerted on hot gases, accelerating them out the tail end Isaac Newton's three laws of motion form a comprehensive description of all possible motions, as well as the forces that lead to them. In and of themselves, however, Newton's laws do not say anything about the nature of those forces. In fact, much of the progress of science since Newton's time has been associated with the discovery and elucidation of the forces of nature.

2.4 Momentum

Newton's laws tell us that the only way to change the motion of an object is to apply a force. We all have an intuitive understanding of this tendency. We sense, for example, that a massive object such as a large train, even if it is moving slowly, is very hard to stop. This knowledge is often used by people who make science fiction movies. It's almost a cliché now that when a spaceship is huge and bulky, the filmmakers supply a deep, rumbling soundtrack that mimics a slowly moving train. (In this case, artistic effect conflicts with the laws of nature because in the vacuum of space there can be no sound waves.)

At the same time, a small object moving very fast—a rifle bullet, for example—is very hard to stop as well. Thus, our everyday experience tells us that the tendency of a moving object to remain in motion depends both on the mass of the object and on its speed. The higher the mass and the higher the speed, the more difficult it is to stop the object or change its direction of motion.

Physicists encapsulate these notions in a quantity called linear momentum, which equals the product of an object's mass times its velocity. Conservation of Linear Momentum

We can derive a very important consequence from Newton's laws. If no external forces act on a system, then Newton's second law says that the change in the total momentum of a system is zero. When physicists find a quantity that does not change, they say that the quantity is conserved. The conclusion we have just reached, therefore, is called the law of conservation of linear momentum.

It's important to keep in mind that the law of conservation of momentum doesn't say that momentum can never change. It just says that it won't change unless an outside force is applied. If a soccer ball is rolling across a field and a player kicks it, a force is applied to the ball as soon as the player's foot touches it. At that moment, the momentum of the ball changes, and that change is reflected in its change of direction and speed.

You saw the consequences of the conservation of momentum the last time you watched a fireworks display The rocket arches up and explodes just at the moment that the rocket is stationary at the top of its path, at the instant when its total momentum is zero. After the explosion, brightly colored burning bits of material fly out in all directions. Each of these pieces has a mass and a velocity, so each has some momentum. Conservation of momentum, however, tells us that when we add up all the momenta of the pieces, they should cancel each other out and give a total momentum of zero. Thus, for example, if there is a 1-gram piece moving to the right at 10 meters per second, there has to be the equivalent of a 1-gram piece moving to the left at the same velocity. Thus, conservation of momentum gives fireworks their characteristic symmetric starburst pattern. Angular Momentum

Just as an object moving in a straight line will keep moving unless a force acts, an object that is rotating will keep rotating unless a twisting force called a torque acts to make it stop. A spinning top will keep spinning until the friction between its point of contact and the floor slows it down. A wheel will keep turning until friction in its bearing stops it. This tendency to keep rotating is called angular momentum.

Think about some common experiences with spinning objects. Two factors increase an object's angular momentum and thus make it more difficult to slow down and stop the rotating object. The first factor is simply the rate of spin; the faster an object spins, the harder it is to stop. The second, more subtle factor relates to the distribution of mass. Spinning objects with more mass, or with mass located farther away from the central axis of rotation, have greater angular momentum. Thus, a solid metal wheel has more angular momentum than an air-filled tire of the same diameter and rate of spin.

The consequences of the conservation of angular momentum you're most likely to experience occur when something happens to change a spinning object's distribution of mass. A striking illustration of this point can be seen in figure skating competitions. As a skater goes into a spin with her arms spread, she spins slowly. As she pulls her arms in tight to her body, her angular momentum must remain constant, since no outside force acts to affect the spin. Her rate of spin must increase. Technology

Inertial Guidance System

The conservation of angular momentum plays an important role in so-called inertial guidance systems for navigation in airplanes and satellites. The idea behind such systems is very simple. A massive object like a sphere or a flat circular disk is set into rotation inside a device in which very little resistance (that is, almost no torque) is exerted by the bearings. When such an object is set into rotation, its angular momentum continues to point in the same direction, regardless of how the spaceship moves around it. By sensing the constant rotation and seeing how it is related to the orientation of the satellite, engineers can tell which way the satellite is pointed. •

2.5 The Universal Force of Gravity

Gravity is the most obvious force in our daily lives. It holds you down in your chair and it keeps you from floating off into space. It guarantees that when you drop things they fall. The effects of what we call gravity were known to the ancients, and its quantitative properties were studied by Galileo and many of his contemporaries, but Isaac Newton revealed its universality.

By Newton's account, he experienced his great insight in an apple orchard. He saw an apple fall and, at the same time, saw the Moon in the sky behind it. He knew that in order for the Moon to keep moving in a circular path, a force had to be acting on it. He wondered whether the gravity that caused the apple to move downward could extend far outward to the Moon, supplying the force that kept it from flying off.

Look at the problem this way: If the Moon goes around Earth, then it isn't moving in a straight line. From the first law of motion it follows that a force must be acting on it. Newton hypothesized that this was the same force that made the apple fall—the familiar force of gravity. Eventually, Newton realized that the orbits of all the planets could be understood if gravity was not restricted to the surface of Earth but was a force found throughout the universe. He formulated this insight (an insight that has been overwhelmingly confirmed by observations) in what is called Newton's law of universal gravitation. •

In words: Between any two objects in the universe there is an attractive force (gravity) that is proportional to the masses of the objects and inversely proportional to the square of the distance between them. The Gravitational Constant, G

When we say that A is directly proportional to B, we mean that if A increases, B must increase by the same proportion. If A doubles, then B must double as well. We can state this idea in mathematical form by writing where k is a number known as the constant of proportionality between A and B. This equation tells us that if we know the constant k and either A or B, then we can calculate the exact value of the other. Thus, the constant of proportionality in a relationship is a useful thing to know.

The gravitational constant, G, is a constant of direct proportionality; it expresses the exact numerical relation between the masses of two objects and their separation, on the one hand, and the force between them on the other. Unlike g, however, which applies only to Earth's surface, G is a universal constant that applies to any two masses anywhere in the universe.

Henry Cavendish (1731–1810), a student at Cambridge University in England, first measured G in 1798 by using the experimental apparatus shown in Figure 2-19. Cavendish suspended a dumbbell made of two small lead balls by a stiff wire and fixed two larger lead spheres near the suspended balls. The gravitational attraction between the hanging lead balls and the fixed spheres caused the wire to twist slightly. By measuring the amount of twisting force, or torque, on the wire, Cavendish could calculate the gravitational force on the dumbbells. This force, together with knowledge of the masses of the dumbbells (m1 in the equation) and the heavy spheres (m2), as well as their final separation (d), gave him the numerical value of everything in Newton's law of universal gravitation except G, which he then calculated using simple arithmetic. In metric units, the value of G is 6.67 × 10−11 m3/s2-kg, or 6.67 × 10−11 N-m2/kg2 (recall that N is the symbol for a newton, the unit of force). This constant appears to be universal, holding true everywhere in our universe.

Weight and Gravity

The law of universal gravitation says that there is a force between any two objects in the universe: two dancers, two stars, this book and you—all exert forces on each other. The gravitational attraction between you and Earth would pull you down if you weren't standing on the ground. As it is, the ground exerts a force equal and opposite to that of gravity, a force you can feel in the soles of your feet. If you were standing on a scale, the gravitational pull of Earth would pull you down until a spring or other mechanism in the scale exerted the opposing force. In this case, the size of that counterbalancing force registers on a display and you call it your weight.

Weight, in fact, is just the force of gravity on an object located at a particular point. Weight depends on where you are; on the surface of Earth you weigh one thing, on the surface of the Moon another, and in the depths of interstellar space you would weigh next to nothing. You even weigh a little less on a high mountaintop than you do at sea level because you are farther from Earth's center. Weight contrasts with your mass (the amount of matter), which stays the same no matter where you go.

Big G and Little g

The law of universal gravitation, coupled with the experimental results on bodies falling near Earth, can be used to reveal a close relationship between the universal constant G and Earth's gravitational acceleration g. According to the law of universal gravitation, the gravitational force on an object of any mass at Earth's surface is where ME and RE are Earth's mass and radius, respectively. On the other hand, Newton's second law says that Equating the right sides of these two equations, Dividing both sides by mass, But the values of G, ME, and RE have been measured: Thus, the value of Earth's gravitational acceleration, g, can be calculated from Newton's universal equation for gravity.

This result is extremely important. For Galileo, g was a number to be measured, but whose value he could not predict. For Newtonians, on the other hand, g was a number that could be calculated purely from Earth's size and mass. Because we understand where g comes from, we can now predict the appropriate value of gravitational acceleration not only for Earth but also for any body in the universe, provided we know its mass and radius. Newton bequeathed a picture of the universe that is beautiful and ordered. The planets orbit the Sun in stately paths, forever trying to move off in straight lines, forever prevented from doing so by the inward tug of gravity. The same laws that operate in the cosmos operate on Earth, and these laws were discovered by the application of the scientific method. To a Newtonian observer, the universe was like a clock. It had been wound up and was ticking along according to God's laws. Newton and his followers were persuaded that in carrying out their work, they were discovering what was in the mind of God when the universe was created.

Of all celestial phenomena, none seemed more portentous and magical than comets, yet even these chance wanderers were subject to Newton's laws. In 1682, British astronomer Edmond Halley (1656–1742) used Newtonian logic to compute the orbit of the comet that bears his name, and he predicted its return in 1758. The “recovery” of Halley's Comet on Christmas Eve of that year was celebrated around the world as a triumph for the Newtonian system. Summary

Since before recorded history, people have observed regularities in the heavens and have built monuments such as Stonehenge to help order their lives. Models such as the Earth-centered system of Ptolemy and the Sun-centered system of Copernicus attempted to explain these regular motions of stars and planets. New, more precise astronomical data by Tycho Brahe led mathematician Johannes Kepler to propose his laws of planetary motion, which state that planets orbit the Sun in elliptical orbits, not circular orbits as had been previously assumed.

Meanwhile, Galileo Galilei and other scientists investigated the science of mechanics—the way things move near Earth's surface. These investigators recognized two fundamentally different kinds of motion: uniform motion, which involves a constant speed and direction (velocity), and acceleration, which entails a change in either speed or direction of travel. Galileo's experiments revealed that all objects fall the same way, at the constant acceleration of 9.8 meters/second2. Isaac Newton combined the work of Kepler, Galileo, and others in his sweeping laws of motion and the law of universal gravitation. Newton realized that nothing accelerates without a force acting on it, and that the amount of acceleration is proportional to the force applied, but inversely proportional to the mass. He also pointed out that forces always act in pairs.

This understanding of forces and motions led Newton to describe gravity, the most obvious force in our daily lives. An object's weight is the force it exerts due to gravity. He demonstrated that the same force that pulls a falling apple to Earth causes the Moon to curve around Earth in its elliptical orbit. Indeed, the force of gravity operates everywhere, with pairs of forces between every pair of masses in the universe.