Gravitation
| I | INTRODUCTION |
Gravitation, the force of attraction between all
objects that tends to pull them toward one another. It is a universal force,
affecting the largest and smallest objects, all forms of matter, and energy.
Gravitation governs the motion of astronomical bodies. It keeps the moon in
orbit around the earth and keeps the earth and the other planets of the solar
system in orbit around the sun. On a larger scale, it governs the motion of
stars and slows the outward expansion of the entire universe because of the
inward attraction of galaxies to other galaxies. Typically the term
gravitation refers to the force in general, and the term gravity
refers to the earth's gravitational pull.
Gravitation is one of the four fundamental
forces of nature, along with electromagnetism and the weak and strong nuclear
forces, which hold together the particles that make up atoms. Gravitation is by
far the weakest of these forces and, as a result, is not important in the
interactions of atoms and nuclear particles or even of moderate-sized objects,
such as people or cars. Gravitation is important only when very large objects,
such as planets, are involved. This is true for several reasons. First, the
force of gravitation reaches great distances, while nuclear forces operate only
over extremely short distances and decrease in strength very rapidly as distance
increases. Second, gravitation is always attractive. In contrast,
electromagnetic forces between particles can be repulsive or attractive
depending on whether the particles both have a positive or negative electrical
charge, or they have opposite electrical charges (see Electricity). These
attractive and repulsive forces tend to cancel each other out, leaving only a
weak net force. Gravitation has no repulsive force and, therefore, no such
cancellation or weakening.
The gravitational attraction of objects for one
another is the easiest fundamental force to observe and was the first
fundamental force to be described with a complete mathematical theory by the
English physicist and mathematician Sir Isaac Newton. A more accurate theory
called general relativity was formulated early in the 20th century by the
German-born American physicist Albert Einstein. Scientists recognize that even
this theory is not correct for describing how gravitation works in certain
circumstances, and they continue to search for an improved theory.
| II | EARTH'S GRAVITATION |
Gravitation plays a crucial role in most
processes on the earth. The ocean tides are caused by the gravitational
attraction of the moon and the sun on the earth and its oceans. Gravitation
drives weather patterns by making cold air sink and displace less dense warm
air, forcing the warm air to rise. The gravitational pull of the earth on all
objects holds the objects to the surface of the earth. Without it, the spin of
the earth would send them floating off into space.
The gravitational attraction of every bit of
matter in the earth for every other bit of matter amounts to an inward pull that
holds the earth together against the pressure forces tending to push it outward.
Similarly, the inward pull of gravitation holds stars together. When a star's
fuel nears depletion, the processes producing the outward pressure weaken and
the inward pull of gravitation eventually compresses the star to a very compact
size (see Star, Black Hole).
| A | Acceleration |
If an object held near the surface of the
earth is released, it will fall and accelerate, or pick up speed, as it
descends. This acceleration is caused by gravity, the force of attraction
between the object and the earth. The force of gravity on an object is also
called the object's weight. This force depends on the object's mass, or the
amount of matter in the object. The weight of an object is equal to the mass of
the object multiplied by the acceleration due to gravity.
A bowling ball that weighs 16 lb is
actually being pulled toward the earth with a force of 16 lb. In the metric
system, the bowling ball is pulled toward the earth with a force of 71 newtons
(a metric unit of force abbreviated N). The bowling ball also pulls on the earth
with a force of 16 lb (71 N), but the earth is so massive that it does not move
appreciably. In order to hold the bowling ball up and keep it from falling, a
person must exert an upward force of 16 lb (71 N) on the ball. This upward force
acts to oppose the 16 lb (71 N) downward weight force, leaving a total force of
zero. The total force on an object determines the object's acceleration.
If the pull of gravity is the only force
acting on an object, then all objects, regardless of their weight, size, or
shape, will accelerate in the same manner. At the same place on the earth, the
16 lb (71 N) bowling ball and a 500 lb (2200 N) boulder will fall with the same
rate of acceleration. As each second passes, each object will increase its
downward speed by about 9.8 m/sec (32 ft/sec), resulting in an acceleration of
9.8 m/sec/sec (32 ft/sec/sec). In principle, a rock and a feather both would
fall with this acceleration if there were no other forces acting. In practice,
however, air friction exerts a greater upward force on the falling feather than
on the rock and makes the feather fall more slowly than the rock.
The mass of an object does not change as it
is moved from place to place, but the acceleration due to gravity, and therefore
the object's weight, will change because the strength of the earth's
gravitational pull is not the same everywhere. The earth's pull and the
acceleration due to gravity decrease as an object moves farther away from the
center of the earth. At an altitude of 4000 miles (6400 km) above the earth's
surface, for instance, the bowling ball that weighed 16 lb (71 N) at the surface
would weigh only about 4 lb (18 N). Because of the reduced weight force, the
rate of acceleration of the bowling ball at that altitude would be only one
quarter of the acceleration rate at the surface of the earth. The pull of
gravity on an object also changes slightly with latitude. Because the earth is
not perfectly spherical, but bulges at the equator, the pull of gravity is about
0.5 percent stronger at the earth's poles than at the equator.
| III | EARLY IDEAS ABOUT GRAVITATION |
The ancient Greek philosophers developed
several theories about the force that caused objects to fall toward the earth.
In the 4th century bc, the Greek
philosopher Aristotle proposed that all things were made from some combination
of the four elements, earth, air, fire, and water. Objects that were similar in
nature attracted one another, and as a result, objects with more earth in them
were attracted to the earth. Fire, by contrast, was dissimilar and therefore
tended to rise from the earth. Aristotle also developed a cosmology, that is, a
theory describing the universe, that was geocentric, or earth-centered, with the
moon, sun, planets, and stars moving around the earth on spheres. The Greek
philosophers, however, did not propose a connection between the force behind
planetary motion and the force that made objects fall toward the earth.
At the beginning of the 17th century, the
Italian physicist and astronomer Galileo discovered that all objects fall toward
the earth with the same acceleration, regardless of their weight, size, or
shape, when gravity is the only force acting on them. Galileo also had a theory
about the universe, which he based on the ideas of the Polish astronomer
Nicolaus Copernicus. In the mid-16th century, Copernicus had proposed a
heliocentric, or sun-centered system, in which the planets moved in circles
around the sun, and Galileo agreed with this cosmology. However, Galileo
believed that the planets moved in circles because this motion was the natural
path of a body with no forces acting on it. Like the Greek philosophers, he saw
no connection between the force behind planetary motion and gravitation on
earth.
In the late 16th and early 17th centuries
the heliocentric model of the universe gained support from observations by the
Danish astronomer Tycho Brahe, and his student, the German astronomer Johannes
Kepler. These observations, made without telescopes, were accurate enough to
determine that the planets did not move in circles, as Copernicus had suggested.
Kepler calculated that the orbits had to be ellipses (slightly elongated
circles). The invention of the telescope made even more precise observations
possible, and Galileo was one of the first to use a telescope to study
astronomy. In 1609 Galileo observed that moons orbited the planet Jupiter, a
fact that could not reasonably fit into an earth-centered model of the
heavens.
The new heliocentric theory changed
scientists' views about the earth's place in the universe and opened the way for
new ideas about the forces behind planetary motion. However, it was not until
the late 17th century that Isaac Newton developed a theory of gravitation that
encompassed both the attraction of objects on the earth and planetary
motion.
| IV | NEWTON'S THEORY OF GRAVITATION |
To develop his theory of gravitation, Newton
first had to develop the science of forces and motion called mechanics. Newton
proposed that the natural motion of an object is motion at a constant speed on a
straight line, and that it takes a force to slow down, speed up, or change the
path of an object. Newton also invented calculus, a new branch of mathematics
that became an important tool in the calculations of his theory of
gravitation.
Newton proposed his law of gravitation in
1687 and stated that every particle in the universe attracts every other
particle in the universe with a force that depends on the product of the two
particles' masses divided by the square of the distance between them. The
gravitational force between two objects can be expressed by the following
equation: F= GMm/d2 where F is the gravitational force,
G is a constant known as the universal constant of gravitation, M
and m are the masses of each object, and d is the distance between
them. Newton considered a particle to be an object with a mass that was
concentrated in a small point. If the mass of one or both particles increases,
then the attraction between the two particles increases. For instance, if the
mass of one particle is doubled, the force of attraction between the two
particles is doubled. If the distance between the particles increases, then the
attraction decreases as the square of the distance between them. Doubling the
distance between two particles, for instance, will make the force of attraction
one quarter as great as it was.
According to Newton, the force acts along a
line between the two particles. In the case of two spheres, it acts along the
line between their centers. The attraction between objects with irregular shapes
is more complicated. Every bit of matter in the irregular object attracts every
bit of matter in the other object. A simpler description is possible near the
surface of the earth where the pull of gravity is approximately uniform in
strength and direction. In this case there is a point in an object (even an
irregular object) called the center of gravity, at which all the force of
gravity can be considered to be acting.
Newton's law affects all objects in the
universe, from raindrops in the sky to the planets in the solar system. It is
therefore known as the universal law of gravitation. In order to know the
strength of gravitational forces in general, however, it became necessary to
find the value of G, the universal constant of gravitation. Scientists needed to
perform an experiment, but gravitational forces are very weak between objects
found in a common laboratory and thus hard to observe. In 1798 the English
chemist and physicist Henry Cavendish finally measured G with a very sensitive
experiment in which he nearly eliminated the effects of friction and other
forces. The value he found was 6.754 x 10-11
N-m2/kg2—close to the currently accepted value of 6.670 x
10-11 N-m2/kg2 (a decimal point followed by 10
zeros and then the number 6670). This value is so small that the force of
gravitation between two objects with a mass of 1 metric ton each, 1 meter from
each other, is about 67 millionths of a newton, or about 15 millionths of a
pound.
Gravitation may also be described in a
completely different way. A massive object, such as the earth, may be thought of
as producing a condition in space around it called a gravitational field. This
field causes objects in space to experience a force. The gravitational field
around the earth, for instance, produces a downward force on objects near the
earth surface. The field viewpoint is an alternative to the viewpoint that
objects can affect each other across distance. This way of thinking about
interactions has proved to be very important in the development of modern
physics.
| A | Planetary Motion |
Newton's law of gravitation was the first
theory to accurately describe the motion of objects on the earth as well as the
planetary motion that astronomers had long observed. According to Newton's
theory, the gravitational attraction between the planets and the sun holds the
planets in elliptical orbits around the sun. The earth's moon and moons of other
planets are held in orbit by the attraction between the moons and the planets.
Newton's law led to many new discoveries, the most important of which was the
discovery of the planet Neptune. Scientists had noted unexplainable variations
in the motion of the planet Uranus for many years. Using Newton's law of
gravitation, the French astronomer Urbain Leverrier and the British astronomer
John Couch each independently predicted the existence of a more distant planet
that was perturbing the orbit of Uranus. Neptune was discovered in 1864, in an
orbit close to its predicted position.
| B | Problems with Newton's Theory |
Scientists used Newton's theory of
gravitation successfully for many years. Several problems began to arise,
however, involving motion that did not follow the law of gravitation or
Newtonian mechanics. One problem was the observed and unexplainable deviations
in the orbit of Mercury (which could not be caused by the gravitational pull of
another orbiting body).
Another problem with Newton's theory
involved reference frames, that is, the conditions under which an observer
measures the motion of an object. According to Newtonian mechanics, two
observers making measurements of the speed of an object will measure different
speeds if the observers are moving relative to each other. A person on the
ground observing a ball that is on a train passing by will measure the speed of
the ball as the same as the speed of the train. A person on the train observing
the ball, however, will measure the ball's speed as zero. According to the
traditional ideas about space and time, then, there could not be a constant,
fundamental speed in the physical world because all speed is relative. However,
near the end of the 19th century the Scottish physicist James Clerk Maxwell
proposed a complete theory of electric and magnetic forces that contained just
such a constant, which he called c. This constant speed was 300,000 km/sec
(186,000 mi/sec) and was the speed of electromagnetic waves, including light
waves. This feature of Maxwell's theory caused a crisis in physics because it
indicated that speed was not always relative.
Albert Einstein resolved this crisis in
1905 with his special theory of relativity. An important feature of Einstein's
new theory was that no particle, and even no information, could travel faster
than the fundamental speed c. In Newton's gravitation theory, however,
information about gravitation moved at infinite speed. If a star exploded into
two parts, for example, the change in gravitational pull would be felt
immediately by a planet in a distant orbit around the exploded star. According
to Einstein's theory, such forces were not possible.
Though Newton's theory contained several
flaws, it is still very practical for use in everyday life. Even today, it is
sufficiently accurate for dealing with earth-based gravitational effects such as
in geology (the study of the formation of the earth and the processes
acting on it), and for most scientific work in astronomy. Only when examining
exotic phenomena such as black holes (points in space with a
gravitational force so strong that not even light can escape them) or in
explaining the big bang (the origin of the universe) is Newton's theory
inaccurate or inapplicable.
| V | EINSTEIN'S THEORY OF RELATIVITY |
In 1915 Einstein formulated a new theory of
gravitation that reconciled the force of gravitation with the requirements of
his theory of special relativity. He proposed that gravitational effects move at
the speed of c. He called this theory general relativity to distinguish
it from special relativity, which only holds when there is no force of
gravitation. General relativity produces predictions very close to those of
Newton's theory in most familiar situations, such as the moon orbiting the
earth. Einstein's theory differed from Newton's theory, however, in that it
described gravitation as a curvature of space and time.
In Einstein's general theory of relativity,
he proposed that space and time may be united into a single, four-dimensional
geometry consisting of 3 space dimensions and 1 time dimension. In this
geometry, called spacetime, the motions of particles from point to point as time
progresses are represented by curves called world lines. If there is no gravity
acting, the most natural lines in this geometry are straight lines, and they
represent particles that are moving always in the same direction with the same
speed—that is, particles that have no force acting on them. If a particle is
acted on by a force, then its world line will not be straight. Einstein also
proposed that the effect of gravitation should not be represented as the
deviation of a world line from straightness, as it would be for an electrical
force. If gravitation is present, it should not be considered a force. Rather,
gravitation changes the most natural world lines and thereby curves the geometry
of spacetime. In a curved geometry, such as the two-dimensional surface of the
earth, there are no straight lines. Instead, there are special curves called
geodesics, an example of which are great circles around the earth. These special
curves are at each point as straight as possible, and they are the most natural
lines in a curved geometry. The effect of gravitation would be to influence the
geodesics in spacetime. Near sources of gravitation the space is strongly curved
and the geodesics behave less and less like those in flat, uncurved spacetime.
In the solar system, for example, the effect of the sun and the earth is to
cause the moon to move on a geodesic that winds around the geodesic of the earth
12 times a year.
| A | Testing Einstein's Theory |
Einstein's theory required verification,
but the level of precision in measurement needed to distinguish between
Einstein's theory and Newton's theory was difficult to achieve in the early 20th
century and remains so today. There were two predictions, however, that could be
tested. One involved deviations in the orbit of Mercury. Astronomers had
observed that the ellipse of Mercury's orbit itself rotated—that is, the point
nearest the sun, called the perihelion, slowly advanced around the sun. The rate
of advancement predicted by Newton's theory differed slightly from what
astronomers had measured, but Einstein's theory predicted the correct rate.
The second test involved measuring the
bending of light as it passed around the sun. Both Newton's and Einstein's
theories predicted that light would be deflected by gravitation. But the amount
of deflection predicted by the two theories differed. The light to be measured
in such a test originates in distant stars. However, under ordinary conditions
the sun's brightness prevents scientists from observing the light from these
stars. This problem disappears during an eclipse, when the moon blocks the sun's
light. In 1919 a special British expedition took photographs during an eclipse.
Scientists measured the deflection of starlight as it passed by the sun and
arrived at numbers that agreed with Einstein's prediction. Subsequent eclipse
observations also have confirmed Einstein's theory.
Other physicists have proposed relativistic
theories of gravitation to compete with Einstein's. In these competing theories,
almost all of which are geometrical like Einstein's, gravitational effects move
at the speed c. They differ mostly in the mathematical details. Even using the
technology of the late 20th century, scientists still find it very difficult to
test these theories with experiments and observations. But Einstein's theory has
passed all tests that have been made so far.
| B | Applications of Einstein's Theory |
Einstein's general relativity theory
predicts special gravitational conditions. The Big Bang theory, which describes
the origin and early expansion of the universe, is one conclusion based on
Einstein's theory that has been verified in several independent ways.
Another conclusion suggested by general
relativity, as well as other relativistic theories of gravitation, is that
gravitational effects move in waves. Astronomers have observed a loss of energy
in a pair of neutron stars (stars composed of densely packed neutrons) that are
orbiting each other. The astronomers theorize that energy-carrying gravitational
waves are radiating from the pair, depleting the stars of their energy. Very
violent astrophysical events, such as the explosion of stars or the collision of
neutron stars, can produce gravitational waves strong enough that they may
eventually be directly detectable with extremely precise instruments.
Astrophysicists are designing such instruments with the hope that they will be
able to detect gravitational waves by the beginning of the 21st century.
Another gravitational effect predicted by
general relativity is the existence of black holes. The idea of a star with a
gravitational force so strong that light cannot escape from its surface can be
traced to Newtonian theory. Einstein modified this idea in his general theory of
relativity. Because light cannot escape from a black hole, for any object—a
particle, spacecraft, or wave—to escape, it would have to move past light. But
light moves outward at the speed c. According to relativity, c is the highest
attainable speed, so nothing can pass it. The black holes that Einstein
envisioned, then, allow no escape whatsoever. An extension of this argument
shows that when gravitation is this strong, nothing can even stay in the same
place, but must move inward. Even the surface of a star must move inward, and
must continue the collapse that created the strong gravitational force. What
remains then is not a star, but a region of space from which emerges a
tremendous gravitational force.
| VI | OTHER MODERN THEORIES |
Einstein's theory of gravitation
revolutionized 20th-century physics. Another important revolution that took
place was quantum theory. Quantum theory states that physical interactions, or
the exchange of energy, cannot be made arbitrarily small. There is a minimal
interaction that comes in a packet called the quantum of an interaction. For
electromagnetism the quantum is called the photon. Like the other interactions,
gravitation also must be quantized. Physicists call a quantum of gravitational
energy a graviton. In principle, gravitational waves arriving at the earth would
consist of gravitons. In practice, gravitational waves would consist of
apparently continuous streams of gravitons, and individual gravitons could not
be detected.
Einstein's theory did not include quantum
effects. For most of the 20th century, theoretical physicists have been
unsuccessful in their attempts to formulate a theory that resembles Einstein's
theory but also includes gravitons. Despite the lack of a complete quantum
theory, it is possible to make some partial predictions about quantized
gravitation. In the 1970s, British physicist Stephen Hawking showed that quantum
mechanical processes in the strong gravitational pull just outside of black
holes would create particles and quanta that move away from the black hole,
thereby robbing it of energy.
| A | Theory of Everything |
An important trend in modern theoretical
physics is to find a theory of everything (TOE), in which all four of the
fundamental forces are seen to be really different aspects of the same single
universal force. Physicists already have unified electromagnetism and the weak
nuclear force and have made progress in joining these two forces with the strong
nuclear force (see Grand Unification Theories). However, relativistic
gravitation, with its geometric and mathematically complex character, poses the
most difficult challenge. Einstein spent most of his later years searching for
an all-encompassing theory by trying to make electromagnetism geometrical like
gravitation. The modern approach is to try to make gravitation fit the pattern
of the other fundamental forces. Much of this work involves looking for
mathematical patterns. A TOE is difficult to test using experiments because the
effects of a TOE would be important only in the rarest circumstances.
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