GRAVITY AND GRAVITATION

CONCEPT

Gravity is, quite simply, the force that holds together the universe. People are accustomed to thinking of it purely in terms of the gravitational pull Earth exerts on smaller bodies—a stone, a human being, even the Moon—or perhaps in terms of the Sun's gravitational pull on Earth. In fact, everything exerts a gravitational attraction toward everything else, an attraction commensurate with the two body's relative mass, and inversely related to the distance between them. The earliest awareness of gravity emerged in response to a simple question: why do objects fall when released from any restraining force? The answers, which began taking shape in the sixteenth century, were far from obvious. In modern times, understanding of gravitational force has expanded manyfold: gravity is clearly a law throughout the universe—yet some of the more complicated questions regarding gravitational force are far from settled.

HOW IT WORKS

ARISTOTLE'S MODEL

Greek philosophers of the period from the sixth to the fourth century B.C. grappled with a variety of questions concerning the fundamental nature of physical reality, and the forces that bind that reality into a whole. Among the most advanced thinkers of that period was Democritus (c. 460-370 B.C.), who put forth a hypothesis many thousands of years ahead of its time: that all of matter interacts at the atomic level.

Aristotle (384-322 B.C.), however, rejected the explanation offered by Democritus, an unfortunate circumstance given the fact that the great philosopher exerted an incalculable influence on the development of scientific thought. Aristotle's contributions to the advancement of the sciences were many and varied, yet his influence in physics was at least as harmful as it was beneficial. Furthermore, the fact that intellectual progress began slowing after several fruitful centuries of development in Greece only compounded the error. By the time civilization had reached the Middle Ages (c. 500 A.D.) the Aristotelian model of physical reality had been firmly established, and an entire millennium passed before it was successfully challenged.

Wrong though it was in virtually all particulars, the Aristotelian system offered a comforting symmetry amid the troubled centuries of the early medieval period. It must have been reassuring indeed to believe that the physical universe was as simple as the world of human affairs was complex. According to this neat model, all materials on Earth consisted of four elements: earth, water, air, and fire.

Each element had its natural place. Hence, earth was always the lowest, and in some places, earth was covered by water. Water must then be higher, but clearly air was higher still, since it covered earth and water. Highest of all was fire, whose natural place was in the skies above the air. Reflecting these concentric circles were the orbits of the Sun, the Moon, and the five known planets. Their orbital paths, in the Aristotelian model of the universe—a model developed to a great degree by the astronomer Ptolemy (c. 100-170)—were actually spheres that revolved around Earth with clockwork precision.

On Earth, according to the Aristotelian model, objects tended to fall toward the ground in accordance with the admixtures of differing

elements they contained. A rock, for instance, was mostly earth, and hence it sought its own level, the lowest of all four elements. For the same reason, a burning fire rose, seeking the heights that were fire's natural domain. It followed from this that an object falls faster or slower, depending on the relative mixtures of elements in it: or, to use more modern terms, the heavier the object, the faster it falls.

GALILEO TAKES UP THE COPERNICAN CHALLENGE

Over the centuries, a small but significant body of scientists and philosophers—each working independent from the other but building on the ideas of his predecessors—slowly began chipping away at the Aristotelian framework. The pivotal challenge came in the early part of the century, and the thinker who put it forward was not a physicist but an astronomer: Nicolaus Copernicus (1473-1543.)

Based on his study of the planets, Copernicus offered an entirely new model of the universe, one that placed the Sun and not Earth at its center. He was not the first to offer such an idea: half a century after Aristotle's death, Aristarchus (fl. 270 B.C.) had a similar idea, but Ptolemy rejected his heliocentric (Sun-centered) model in favor of the geocentric or Earth-centered one. In subsequent centuries, no less a political authority than the Catholic Church gave its approval to the Ptolemaic system. This system seemed to fit well with a literal interpretation of biblical passages concerning God's relationship with man, and man's relationship to the cosmos; hence, the heliocentric model of Copernicus constituted an offense to morality.

For this reason, Copernicus was hesitant to defend his ideas publicly, yet these concepts found their way into the consciousness of European thinkers, causing a paradigm shift so fundamental that it has been dubbed "the Copernican Revolution." Still, Copernicus offered no explanation as to why the planets behaved as they did: hence, the true leader of the Copernican Revolution was not Copernicus himself but Galileo Galilei (1564-1642.)

Initially, Galileo set out to study and defend the ideas of Copernicus through astronomy, but soon the Church forced him to recant. It is said that after issuing a statement in which he refuted the proposition that Earth moves—a direct attack on the static harmony of the Aristotelian/Ptolemaic model—he protested in private:" E pur si muove!" (But it does move!) Placed under house arrest by authorities from Rome, he turned his attention to an effort that, ironically, struck the fatal blow against the old model of the cosmos: a proof of the Copernican system according to the laws of physics.

GRAVITATIONAL ACCELERATION.

In the process of defending Copernicus, Galileo actually inaugurated the modern history of physics as a science (as opposed to what it had been during the Middle Ages: a nest of suppositions masquerading as knowledge). Specifically, Galileo set out to test the hypothesis that objects fall as they do, not because of their weight, but as a consequence of gravitational force. If this were so, the acceleration of falling bodies would have to be the same, regardless of weight. Of course, it was clear that a stone fell faster than a feather, but Galileo reasoned that this was a result of factors other than weight, and later investigations confirmed that air resistance and friction, not weight, are responsible for this difference.

On the other hand, if one drops two objects that have similar air resistance but differing weight—say, a large stone and a smaller one—they fall at almost exactly the same rate. To test this directly, however, would have been difficult for Galileo: stones fall so fast that, even if dropped from a great height, they would hit the ground too soon for their rate of fall to be tested with the instruments then available.

Instead, Galileo used the motion of a pendulum, and the behavior of objects rolling or sliding down inclined planes, as his models. On the basis of his observations, he concluded that all bodies are subject to a uniform rate of gravitational acceleration, later calibrated at 32 ft (9.8 m) per second. What this means is that for every 32 ft an object falls, it is accelerating at a rate of 32 ft per second as well; hence, after 2 seconds, it falls at the rate of 64 ft (19.6 m) per second; after 3 seconds, at 96 ft (29.4 m) per second, and so on.

NEWTON DISCOVERS THE PRINCIPLE OF GRAVITY

Building on the work of his distinguished fore-bear, Sir Isaac Newton (1642-1727)—who, incidentally, was born the same year Galileo died—developed a paradigm for gravitation that, even today, explains the behavior of objects in virtually all situations throughout the universe. Indeed, the Newtonian model reigned until the early

twentieth century, when Albert Einstein (1879-1955) challenged it on certain specifics.

Even so, Einstein's relativity did not disprove the Newtonian system as Copernicus and Galileo disproved Aristotle's and Ptolemy's theories; rather, it showed the limitations of Newtonian mechanics for describing the behavior of certain objects and phenomena. However, in the ordinary world of day-to-day experience—the world in which stones drop and heavy objects are hard to lift—the Newtonian system still offers the key to how and why things work as they do. This is particularly the case with regard to gravity and gravitation.

Like Galileo, Newton began in part with the aim of testing hypotheses put forth by an astronomer—in this case Johannes Kepler (1571-1630). In the early years of the seventeenth century, Kepler published his three laws of planetary motion, which together identified the elliptical (oval-shaped) path of the planets around the Sun. Kepler had discovered a mathematical relationship that connected the distances of the planets from the Sun to the period of their revolution around it. Like Galileo with Copernicus, Newton sought to generalize these principles to explain, not only how the planets moved, but also why they did.

Almost everyone has heard the story of Newton and the apple—specifically, that while he was sitting under an apple tree, a falling apple struck him on the head, spurring in him a great intuitive leap that led him to form his theory of gravitation. One contemporary biographer, William Stukely, wrote that he and Newton were sitting in a garden under some apple trees when Newton told him that "…he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasion'd by the fall of an apple, as he sat in a contemplative mood. Why should that apple always descend perpendicularly to the ground, he thought to himself. Why should it not go sideways or upwards, but constantly to the earth's centre?"

The tale of Newton and the apple has become a celebrated myth, rather like that of George Washington and the cherry tree. It is an embellishment of actual events: Newton never said that an apple hit him on the head, just that he was thinking about the way that apples fell. Yet the story has become symbolic of the creative intellectual process that occurs when a thinker makes a vast intuitive leap in a matter of moments. Of course, Newton had spent many years contemplating these ideas, and their development required great effort. What is important is that he brought together the best work of his predecessors, yet transcended all that had gone before—and in the process, forged a model that explained a great deal about how the universe functions.

The result was his Philosophiae Naturalis Principia Mathematica, or "Mathematical Principles of Natural Philosophy." Published in 1687, the book—usually referred to simply as the Principia—was one of the most influential works ever written. In it, Newton presented his three laws of motion, as well as his law of universal gravitation.

The latter stated that every object in the universe attracts every other one with a force proportional to the masses of each, and inversely proportional to the square of the distance between them. This statement requires some clarification with regard to its particulars, after which it will be reintroduced as a mathematical formula.

MASS AND FORCE.

The three laws of motion are a subject unto themselves, covered elsewhere in this volume. However, in order to understand gravitation, it is necessary to understand at least a few rudimentary concepts relating to them. The first law identifies inertia as the tendency of an object in motion to remain in motion, and of an object at rest to remain at rest. Inertia is measured by mass, which—as the second law states—is a component of force.

Specifically, the second law of motion states that force is equal to mass multiplied by acceleration. This means that there is an inverse relationship between mass and acceleration: if force remains constant and one of these factors increases, the other must decrease—a situation that will be discussed in some depth below.

Also, as a result of Newton's second law, it is possible to define weight scientifically. People typically assume that mass and weight are the same, and indeed they are on Earth—or at least, they are close enough to be treated as comparable factors. Thus, tables of weights and measures show that a kilogram, the metric unit of mass, is equal to 2.2 pounds, the latter being the principal unit of weight in the British system.

In fact, this is—if not a case of comparing to apples to oranges—certainly an instance of comparing apples to apple pies. In this instance, the kilogram is the "apple" (a fitting Newtonian metaphor!) and the pound the "apple pie." Just as an apple pie contains apples, but other things as well, the pound as a unit of force contains an additional factor, acceleration, not included in the kilo.

BRITISH VS. SI UNITS.

Physicists universally prefer the metric system, which is known in the scientific community as SI (an abbreviation of the French Système International d'Unités—that is, "International System of Units"). Not only is SI much more convenient to use, due to the fact that it is based on units of 10; but in discussing gravitation, the unequal relationship between kilograms and pounds makes conversion to British units a tedious and ultimately useless task.

Though Americans prefer the British system to SI, and are much more familiar with pounds than with kilos, the British unit of mass—called the slug—is hardly a household word. By contrast, scientists make regular use of the SI unit of force—named, appropriately enough, the newton. In the metric system, a newton (N) is the amount of force required to accelerate 1 kilogram of mass by 1 meter per second squared (m/s²) Due to the simplicity of using SI over the British system, certain aspects of the discussion below will be presented purely in terms of SI. Where appropriate, however, conversion to British units will be offered.

CALCULATING GRAVITATIONAL FORCE.

The law of universal gravitation can be stated as a formula for calculating the gravitational attraction between two objects of a certain mass, m₁ AND M₂: F_grav = G · (m₁M₂)/R². F_grav is gravitational force, and r² the square of the distance between m₁ and m₂.

As for G, in Newton's time the value of this number was unknown. Newton was aware simply that it represented a very small quantity: without it, (m₁m₂)/r² could be quite sizeable for objects of relatively great mass separated by a relatively small distance. When multiplied by this very small number, however, the gravitational attraction would be revealed to be very small as well. Only in 1798, more than a century after Newton's writing, did English physicist Henry Cavendish (1731-1810) calculate the value of G.

As to how Cavendish derived the figure, that is an exceedingly complex subject far beyond the scope of the present discussion. Even to identify G as a number is a challenging task. First of all, it is a unit of force multiplied by squared area, then divided by squared mass: in other words, it is expressed in terms of (N · m²)/kg², where N stands for newtons, m for meters, and kg for kilograms. Nor is the coefficient, or numerical value, of G a whole number such as 1. A figure as large as 1, in fact, is astronomically huge compared to G, whose coefficient is 6.67 · 10⁻¹¹—in other words, 0.0000000000667.

REAL-LIFE APPLICATIONS

WEIGHT VS. MASS

Before discussing the significance of the gravitational constant, however, at this point it is appropriate to address a few issues that were raised earlier—issues involving mass and weight. In many ways, understanding these properties from the framework of physics requires setting aside everyday notions.

First of all, why the distinction between weight and mass? People are so accustomed to converting pounds to kilos on Earth that the difference is difficult to comprehend, but if one considers the relation of mass and weight in outer space, the distinction becomes much clearer. Mass is the same throughout the universe, making it a much more fundamental characteristic—and hence, physicists typically speak in terms of mass rather than weight.

Weight, on the other hand, differs according to the gravitational pull of the nearest large body. On Earth, a person weighs a certain amount, but on the Moon, this weight is much less, because the Moon possesses less mass than Earth. Therefore, in accordance with Newton's formula for universal gravitation, it exerts less gravitational pull. By contrast, if one were on Jupiter, it would be almost impossible even to stand up, because the pull of gravity on that planet—with its greater mass—would be vastly greater than on Earth.

It should be noted that mass is not at all a function of size: Jupiter does have a greater mass than Earth, but not because it is bigger. Mass, as noted earlier, is purely a measure of inertia: the more resistant an object is to a change in its velocity, the greater its mass. This in itself yields some results that seem difficult to understand as long as one remains wedded to the concept—true enough on Earth—that weight and mass are identical.

A person might weigh less on the Moon, but it would be just as difficult to move that person from a resting position as it would be to do so on Earth. This is because the person's mass, and hence his or her resistance to inertia, has not changed. Again, this is a mentally challenging concept: is not lifting a person, which implies upward acceleration, not an attempt to counteract their inertia when standing still? Does it not follow that their mass has changed? Understanding the distinction requires a greater clarification of the relationship between mass, gravity, and weight.

F = ma.

Newton's second law of motion, stated earlier, shows that force is equal to mass multiplied by acceleration, or in shorthand form, F = ma. To reiterate a point already made, if one assumes that force is constant, then mass and acceleration must have an inverse relationship. This can be illustrated by performing a simple experiment.

Suppose one were to apply a certain amount of force to an empty shopping cart. Assuming the floor had just enough friction to allow movement, it would be easy for almost anyone to accelerate the shopping cart. Now assume that the shopping cart were filled with heavy lead balls, so that it weighed, say, 1,102 lb (500 kg). If one applied the same force, it would not move.

What has changed, clearly, is the mass of the shopping cart. Because force remained constant, the rate of acceleration would become very small—in this case, almost infinitesimal. In the first case, with an empty shopping cart, the mass was relatively small, so acceleration was relatively high.

Now to return to the subject of lifting someone on the Moon. It is true that in order to lift that person, one would have to overcome inertia, and, in that sense, it would be as difficult as it is on Earth. But the other component of force, acceleration, has diminished greatly.

Weight is, again, a unit of force, but in calculating weight it is useful to make a slight change to the formula F = ma. By definition, the acceleration factor in weight is the downward acceleration due to gravity, usually rendered as g. So one's weight is equal to mg—but on the Moon, g is much smaller than it is on Earth, and hence, the same amount of force yields much greater results.

These facts shed new light on a question that bedeviled physicists at least from the time of Aristotle, until Galileo began clarifying the issue some 2,000 years later: why shouldn't an object of greater mass fall at a different rate than one of smaller mass? There are two answers to that question, one general and one specific. The general answer—that Earth exerts more gravitational pull on an object of greater mass—requires a deeper examination of Newton's gravitational formula. But the more specific answer, relating purely to conditions on Earth, is easily addressed by considering the effect of air resistance.

GRAVITY AND AIR RESISTANCE

One of Galileo's many achievements lay in using an idealized model of reality, one that does not take into account the many complex factors that affect the behavior of objects in the real world.

This permitted physicists to study processes that apparently defy common sense. For instance, in the real world, an apple does drop at a greater rate of speed than does a feather. However, in a vacuum, they will drop at the same rate. Since Galileo's time, it has become commonplace for physicists to discuss specific processes such as gravity with the assumption that all non-pertinent factors (in this case, air resistance or friction) are nonexistent or irrelevant. This greatly simplified the means of testing hypotheses.

Idealization of reality makes it possible to set aside the things people think they know about the real world, where events are complicated due to friction. The latter may be defined as a force that resists motion when the surface of one object comes into contact with the surface of another. If two balls are released in an environment free from friction—one of them simply dropped while the other is rolled down a curved surface or inclined plane—they will reach the bottom at the same time. This seems to go against everything that is known, but that is only because what people "know" is complicated by variables that have nothing to do with gravity.

The same is true for the behavior of falling objects with regard to air resistance. If air resistance were not a factor, one could fire a cannonball over horizontal space and then, when the ball reached the highest point in its trajectory, release another ball from the same height—and again, they would hit the ground at the same time. This is the case, even though the cannonball that was fired from the cannon has to cover a great deal of horizontal space, whereas the dropped ball does not. The fact is that the rate of acceleration due to gravity will be identical for the two balls, and the fact that the ball fired from a cannon also covers a horizontal distance during that same period is irrelevant.

TERMINAL VELOCITY.

In the real world, air resistance creates a powerful drag force on falling objects. The faster the rate of fall, the greater the drag force, until the air resistance forces a leveling in the rate of fall. At this point, the object is said to have reached terminal velocity, meaning that its rate of fall will not increase thereafter. Galileo's idealized model, on the other hand, treated objects as though they were falling in a vacuum—space entirely devoid of matter, including air. In such a situation, the rate of acceleration would continue to grow indefinitely.

By means of a graph, one can compare the behavior of an object falling through air with that of an object falling in a vacuum. If the x axis measures time and the y axis downward speed, the rate of an object falling in a vacuum describes a 60°-angle. In other words, the speed of its descent is increasing at a much faster rate than is the rate of time of its descent—as indeed should be the case, in accordance with gravitational acceleration. The behavior of an object falling through air, on the other hand, describes a curve. Up to a point, the object falls at the same rate as it would in a vacuum, but soon velocity begins to increase at a much slower rate than time. Eventually, the curve levels off at the point where the object experiences terminal velocity.

Air resistance and friction have been mentioned separately as though they were two different forces, but in fact air resistance is simply a prominent form of friction. Hence air resistance exerts an upward force to counter the downward force of mass multiplied by gravity—that is, weight. Since g is a constant (32 ft or 9.8 m/sec²), the greater the weight of the falling object, the longer it takes for air resistance to bring it to terminal velocity.

A feather quickly reaches terminal velocity, whereas it takes much longer for a cannonball to do the same. As a result, a heavier object does take less time to fall, even from a great height, than does a light one—but this is only because of friction, and not because of "elements" seeking their "natural level." Incidentally, if raindrops (which of course fall from a very great height) did not reach terminal velocity, they would cause serious injury by the time they hit the ground.

APPLYING THE GRAVITATIONAL FORMULA

Using Newton's gravitational formula, it is relatively easy to calculate the pull of gravity between two objects. It is also easy to see why the attraction is insignificant unless at least one of the objects has enormous mass. In addition, application of the formula makes it clear why G (the gravitational constant, as opposed to g, the rate of acceleration due to gravity) is such a tiny number.

If two people each have a mass of 45.5 kg (100 lb) and stand 1 m (3.28 ft) apart, m₁m₂ is equal to 2,070 kg (4,555 lb) and r² is equal to 1 m² . Applied to the gravitational formula, this figure is rendered as 2,070 kg²/1 m². This number is then multiplied by gravitational constant, which again is equal to 6.67 · 10⁻¹¹ (N · m²)/kg². The result is a net gravitational force of 0.000000138 N (0.00000003 lb)—about the weight of a single-cell organism!

EARTH, GRAVITY, AND WEIGHT.

Though it is certainly interesting to calculate the gravitational force between any two people, computations of gravity are only significant for objects of truly great mass. For instance, there is the Earth, which has a mass of 5.98 · 10²⁴ kg—that is, 5.98 septillion (1 followed by 24 zeroes) kilograms. And, of course, Earth's mass is relatively minor compared to that of several planets, not to mention the Sun. Yet Earth exerts enough gravitational pull to keep everything on it—living creatures, manmade structures, mountains and other natural features—stable and in place.

One can calculate Earth's gravitational force on any one person—if one wants to take the time to do so using Newton's formula. In fact, it is much simpler than that: gravitational force is equal to weight, or m · g. Thus if a woman weighs 100 lb (445 N), this amount is also equal to the gravitational force exerted on her. By dividing 445 N by the acceleration of gravity—9.8 m/sec²—it is easy to obtain her mass: 45.4 kg.

The use of the mg formula for gravitation helps, once again, to explain why heavier objects do not fall faster than lighter ones. The figure for g is a constant, but for the sake of argument, let us assume that it actually becomes larger for objects with a greater mass. This in turn would mean that the gravitational force, or weight, would be bigger than it is—thus creating an irreconcilable logic loop.

Furthermore, one can compare results of two gravitation equations, one measuring the gravitational force between Earth and a large stone, the other measuring the force between Earth and a small stone. (The distance between Earth and each stone is assumed to be the same.) The result will yield a higher quantity for the force exerted on the larger stone—but only because its mass is greater. Clearly, then, the increase of force results only from an increase in mass, not acceleration.

GRAVITY AND CURVED SPACE

As should be clear from Newton's gravitational formula, the force of gravity works both ways: not only does a stone fall toward Earth, but Earth actually falls toward it. The mass of Earth is so great compared to that of the stone that the movement of Earth is imperceptible—but it does happen. Furthermore, because Earth is round, when one hurls a projectile at a great distance, Earth curves away from the projectile; but eventually gravity itself forces the projectile to the ground.

However, if one were to fire a rocket at 17,700 MPH (28,500 km/h), at every instant of time the projectile is falling toward Earth with the force of gravity—but the curved Earth would be falling away from it at the same moment as well. Hence, the projectile would remain in constant motion around the planet—that is, it would be in orbit.

The same is true of an artificial satellite's orbit around Earth: even as the satellite falls toward Earth, Earth falls away from it. This same relationship exists between Earth and its great natural satellite, the Moon. Likewise, with the Sun and its many satellites, including Earth: Earth plunges toward the Sun with every instant of its movement, but at every instant, the Sun falls away.

WHY IS EARTH ROUND?

Note that in the above discussion, it was assumed that Earth and the Sun are round. Everyone knows that to be the case, but why? The answer is "Because they have to be"—that is, gravity will not allow them to be otherwise. In fact, the larger the mass of an object, the greater its tendency toward roundness: specifically, the gravitational pull of its interior forces the surface to assume a relatively uniform shape. There is a relatively small vertical differential for Earth's surface: between the lowest point and the highest point is just 12.28 mi (19.6 km)—not a great distance, considering that Earth's radius is about 4,000 mi (6,400 km).

It is true that Earth bulges near the equator, but this is only because it is spinning rapidly on its axis, and thus responding to the centripetal force of its motion, which produces a centrifugal component. If Earth were standing still, it would be much nearer to the shape of a sphere. On the other hand, an object of less mass is more likely to retain a shape that is far less than spherical. This can be shown by reference to the Martian moons Phobos and Deimos, both of which are oblong—and both of which are tiny, in terms of size and mass, compared to Earth's Moon.

Mars itself has a radius half that of Earth, yet its mass is only about 10% of Earth's. In light of what has been said about mass, shape, and gravity, it should not surprising to learn that Mars is also home to the tallest mountain in the solar system. Standing 15 mi (24 km) high, the volcano Olympus Mons is not only much taller than Earth's tallest peak, Mount Everest (29,028 ft [8,848 m]); it is 22% taller than the distance from the top of Mount Everest to the lowest spot on Earth, the Mariana Trench in the Pacific Ocean (−35,797 ft [−10,911 m])

A spherical object behaves with regard to gravitation as though its mass were concentrated near its center. And indeed, 33% of Earth's mass is at is core (as opposed to the crust or mantle), even though the core accounts for only about 20% of the planet's volume. Geologists believe that the composition of Earth's core must be molten iron, which creates the planet's vast electromagnetic field.

THE FRONTIERS OF GRAVITY.

The subject of curvature with regard to gravity can be both a threshold or—as it is here—a point of closure. Investigating questions over perceived anomalies in Newton's description of the behavior of large objects in space led Einstein to his General Theory of Relativity, which posited a curved four-dimensional space-time. This led to entirely new notions concerning gravity, mass, and light. But relativity, as well as its relation to gravity, is another subject entirely. Einstein offered a new understanding of gravity, and indeed of physics itself, that has changed the way thinkers both inside and outside the sciences perceive the universe. Here on Earth, however, gravity behaves much as Newton described it more than three centuries ago.

Meanwhile, research in gravity continues to expand, as a visit to the Web site <www.Gravity.org> reveals. Spurred by studies in relativity, a branch of science called relativistic astrophysics has developed as a synthesis of astronomy and physics that incorporates ideas put forth by Einstein and others. The <www.Gravity.org> site presents studies—most of them too abstruse for a reader who is not a professional scientist—across a broad spectrum of disciplines. Among these is bioscience, a realm in which researchers are investigating the biological effects—such as mineral loss and motion sickness—of exposure to low gravity. The results of such studies will ultimately protect the health of the astronauts who participate in future missions to outer space.

WHERE TO LEARN MORE

Ardley, Neil. The Science Book of Gravity. San Diego, CA: Harcourt Brace Jovanovich, 1992.

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Bendick, Jeanne. Motion and Gravity. New York: F. Watts, 1972.

Dalton, Cindy Devine. Gravity. Vero Beach, FL: Rourke, 2001.

David, Leonard. "Artificial Gravity and Space Travel." Bio-Science, March 1992, pp. 155-159.

Exploring Gravity—Curtin University, Australia (Web site). <http://www.curtin.edu.au/curtin/dept/physsci/gravity/> (March 18, 2001).

The Gravity Society (Web site). <http://www.gravity.org>(March 18, 2001).

Nardo, Don. Gravity: The Universal Force. San Diego, CA: Lucent Books, 1990.

Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981.

Stringer, John. The Science of Gravity. Austin, TX: Raintree Steck-Vaughn, 2000.

KEY TERMS

FORCE:

The product of mass multiplied by acceleration.

FRICTION:

The force that resists motion when the surface of one object comes into contact with the surface of another.

INERTIA:

The tendency of an object in motion to remain in motion, and of an object at rest to remain at rest.

INVERSE RELATIONSHIP:

A situation involving two variables, in which one of the two increases in direct proportion to the decrease in the other.

LAW OF UNIVERSAL GRAVITATION:

A principle, put forth by Sir Isaac Newton (1642-1727), which states that every object in the universe attracts every other one with a force proportional to the masses of each, and inversely proportional to the square of the distance between them.

MASS:

A measure of inertia, indicating the resistance of an object to a change in itsmotion.

TERMINAL VELOCITY:

A term describing the rate of fall for an object experiencing the drag force of air resistance. In a vacuum, the object would continue to accelerate with the force of gravity, but in most real-world situations, air resistance creates a powerful drag force that causes a leveling in the object's rate off all.

VACUUM:

Space entirely devoid of matter, including air.

WEIGHT:

A measure of the gravitational force on an object; the product of mass multiplied by the acceleration due to gravity.