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The Greek philosopher Aristotle (384–322 BC) posed, following earlier traditions, that the material world consisted of four elements: Earth, water, air, and fire. For example, a rock was mostly Earth with a little water, air, and fire, a cloud was mostly air and water with a little Earth and fire. Each element had a natural or proper place in the universe to which it spontaneously inclined; Earth belonged at the very center, water in a layer covering the Earth, air above the water, and fire above the air. Each element had a natural tendency to return to its proper place, so that, for example, rocks fell toward the center and fire rose above the air. This was one of the earliest explanations of gravity: that it was the natural tendency for the heavier elements, Earth and water, to return to their proper positions near the center of the universe.
Aristotle’s theory was for centuries taken as implying that objects with different weights should fall at different speeds; that is, a heavier object should fall faster because it contains more of the center-trending elements, Earth and water. However, this is not correct. Objects with different weights fall, in fact, at the same rate. (This statement still only an approximation, however, for it assumes that the Earth is perfectly stationary, which it is not. When an object is dropped the Earth accelerates “upward” under the influence of their mutual gravitation, just as the object “falls,” and they meet somewhere in the middle. For a heavier object, this meeting does take place slightly sooner than for a light object, and thus, heavier objects actually do fall slightly faster than light ones. In practice, however, the Earth’s movement is not measurable for “dropped” objects of less than planetary size, and so it is accurate to state that all small objects fall at the same rate, regardless of their mass.)
Aristotle’s model of the universe also included the moon, sun, the visible planets, and the fixed stars. Aristotle assumed that these were outside the layer of fire and were made of a fifth element, the ether or quintessence (the term is derived from the Latin expression quinta essentia, or fifth essence, used by Aristotle’s medieval translators). The celestial bodies circled Earth attached to nested ethereal spheres centered on Earth. No forces were required to maintain these motions, since everything was considered perfect and unchanging, having been set in motion by a Prime Mover — God.
Aristotle’s ideas were accepted in Europe and the Near East for centuries, until the Polish astronomer Nicolaus Copernicus (1473–1543) developed a heliocentric (sun-centered) model to replace the geocentric (Earth-centered) one that had been the dominant cosmological concept ever since Aristotle’s time. (Non-European astronomers unfamiliar with Aristotle, such as the Chinese and Aztecs, had developed geocentric models of their own; no heliocentric model existed prior to Copernicus.) Copernicus’s model placed the sun in the center of the universe, with all of the planets orbiting the sun in perfect circles. This development was such a dramatic change from the previous model that it is now called the Copernican Revolution. It was an ingenious intellectual construct, but it still did not explain why the planets circled the sun, in the sense of what caused them to do so.
While many scientists were trying to explain these celestial motions, others were trying to understand terrestrial mechanics. It seemed to be a commonsense fact that heavier objects fall faster than light ones: drop a feather and a rock and see which hits the ground first. The fault in this experiment is that air resistance affects the rate at which objects fall. What about another experiment, one in which air resistance plays a smaller role: observing the difference between dropping a large rock and a small rock? This is an easy experiment to perform, and the results have profound implications. As early as the sixth century AD, Johannes Philiponos (c. 490–566) claimed that the difference in landing times was small for objects of different weight but similar shape. Galileo’s friend, Italian physicist Giambattista Benedetti (1530–1590), in 1553, and Dutch physicist Simon Stevin (1548–1620), in 1586, also considered the falling-rock problem and concluded that rate of fall was independent of weight. However, the individual most closely associated with the falling-body problem is Italian physicist Galileo Galilei (1564–1642), who systematically observed the motions of falling bodies. (It is unlikely that he actually dropped weights off the Leaning Tower of Pisa, but he did write that such an experiment might be performed.)
Because objects speed up (accelerate) quickly while falling, and Galileo was restricted to naked-eye observation by the technology of his day, he studied the slower motions of pendulums and of bodies rolling and sliding down incline. From his results, Galileo formulated his law of falling bodies. This states that, disregarding air resistance, bodies in free fall speed up with a constant acceleration (rate of change of velocity) that is independent of their weight or composition. The acceleration due to gravity near Earth’s surface is given the symbol g and has a value of about 32 ft per second per second (9.8 m/s2) This means that 1 second after a release a falling object is moving at about 10 m/s; after 2 seconds, 20 m/s; after 10 seconds, 100 m/s. That is, after falling for 10 seconds, it is dropping fast enough to cross the length of a football field in less than one second. Writing v for the velocity of the falling body and t for the time since commencement of free fall, we have v = gt.
Galileo also determined a formula to describe the distance d that a body falls in a given time: d = ½gt2
That is, if one drops an object, after 1 second it has fallen approximately 5 m; after 2 seconds, 20 m; and after 10 seconds, 500 meters.
Galileo did an excellent job of describing the effect of gravity on objects on Earth, but it wasn’t until English physicist Isaac Newton (1642–1727) studied the problem that it was understood just how universal gravity is. An old story says that Newton suddenly understood gravity when an apple fell out of a tree and hit him on the head; this story may not be exactly true, but Newton did say that a falling apple helped him develop his theory of gravity.
Newton’s universal law of gravitation states that all objects in the universe attract all other objects. Thus the sun attracts Earth, Earth attracts the sun, Earth attracts a book, a book attracts Earth, the book attracts the desk, and so on. The gravitational pull between small objects, such as molecules and books, is generally negligible; the gravitational pull exerted by larger objects, such as stars and planets, organizes the universe. It is gravity that keeps us on the Earth, the moon in orbit around the Earth, and the Earth in orbit around the sun.
Newton’s law of gravitation also states that the strength of the force of attraction depends on the masses of the two objects. The mass of an object is a measure of how much material it has, but it is not the same as its weight, which is a measure of how much force a given mass experiences in a given gravitational field; a given rock, say, will have the same mass anywhere in the universe but will weigh more on Earth than on the moon.
We do not feel the gravitational forces from objects other than the Earth because they are weak. For example, the gravitational force of attraction between two friends weighing 100 lb (45.5 kg) standing 3 ft (1 m) apart is only about 3 × 10−8 N = 0.00000003 lb, which is about the weight of a bacterium. (Note: the pound is a measure of weight — the gravitational force experienced by an object — while the kilogram is a measure of mass. Strictly speaking, then, pounds and kilograms cannot be substituted for each other as in the previous sentence. However, near Earth’s surface weight and mass can be approximately equated because Earth’s gravitational field is approximately constant; treating pounds and kilograms as proportional units is therefore standard practice under this condition.)
The gravitational force between two objects becomes weaker if the two objects are moved apart and stronger if they are brought closer together; that is, the force depends on the distance between the objects. If we take two objects and double the distance between them, the force of attraction decreases to one fourth of its former value. If we triple the distance, the force decreases to one ninth of its former value. The force depends on the inverse square of the distance.
All these statements are derived from one simple equation: for two objects having masses m1 and m1 respectively, the magnitude of the force of gravity acting on each object is given by: F = Gm1m2/r2, where r is the distance between the objects’ centers and G is the gravitational constant (6.673 × 10−11N m2/kg2.) Note that the gravitational constant is an extremely small number; this explains why we only feel gravity when we are near a large mass (e.g., the Earth).
Newton also explained how bodies respond to forces (including gravitational forces) that act on them. His second law of motion states that a net force (i.e., force not canceled by a contrary force) causes a body to accelerate. The amount of this acceleration is inversely proportional to the mass of the object. This means that under the influence of a given force, more massive objects accelerate more slowly than less massive objects. Alternatively, to experience the same acceleration, more massive objects require more force. Consider the gravitational force exerted by the Earth on two rocks, the first with a mass of 2 lb (1 kg) and a second with a mass of 22 lb (10 kg). Since the mass of the second is 10 times the mass of the first, the gravitational force on the second will be 10 times the force on the first. But a 22-lb (10-kg) mass requires 10 times more force to accelerate it, so both masses accelerate Earthward at the same rate. Ignoring the Earth’s own acceleration toward the rocks (which is extremely small), it follows that equal falling rates for small objects are a natural consequence of Newton’s law of gravity and second law of motion.
What if one throws a ball horizontally? If one throws it slowly, it will hit the ground a short distance away. If one throws it faster, it will land farther away. Since the Earth is round, the Earth will curve slightly away from the ball before it lands; the farther the throw, the greater the amount of curve. If one could throw or launch the ball at 18,000 mi/h (28,800 km/h), the Earth would curve away from the ball by the same amount that the ball falls. The ball would never get any closer to the ground, and would be in orbit around the Earth. Gravity still accelerates the ball at 9.8 m/s2 toward the Earth’s center, but the ball never approaches the ground. (This is exactly what the moon is doing.) In addition, the orbits of the Earth and other planets around the sun and all the motions of the stars and galaxies follow Newton’s laws. This is why Newton’s law of gravitation is termed “universal;” it describes the effect of gravity on all objects in the universe.
Newton published his laws of motion and gravity in 1687, in his seminal Philosophiae Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy, or Principia for short). When we need to solve problems relating to gravity, Newton’s laws usually suffice. There are, however, some phenomena that they cannot describe. For example, the motions of the planet Mercury are not exactly described by Newton’s laws. Newton’s theory of gravity, therefore, needed modifications that would require another genius, Albert Einstein, and his theory of general relativity.
German physicist Albert Einstein (1879–1955) realized that Newton’s theory of gravity had problems. He knew, for example, that Mercury’s orbit showed unexplained deviations from that predicted by Newton’s laws. However, he was worried about a much more serious problem. As the force between two objects depends on the distance between them, if one object moves closer, the other object will feel a change in the gravitational force. According to Newton, this change would be immediate, or instantaneous, even if the objects were millions of miles apart. Einstein saw this as a serious flaw in Newtonian gravity. Einstein assumed that nothing could travel instantaneously, not even a change in force. Specifically, nothing can travel faster than light in a vacuum, which has a speed of approximately 186,000 mi/s (300,000 km/s). In order to fix this problem, Einstein had not only to revise Newtonian gravity, but to change the way we think about space, time, and the structure of the universe. He stated this new way of thinking mathematically in his general theory of relativity.
Einstein said that a mass bends space, like a heavy ball making a dent on a rubber sheet. Further, Einstein contended that space and time are intimately related to each other, and that we do not live in three spatial dimensions and time (all four quite independent of each other), but rather in a four-dimensional space-time continuum, a seamless blending of the four. It is thus not “space,” naively conceived, but space-time that warps in reaction to a mass. This, in turn, explains why objects attract each other. Consider the sun sitting in space-time, imagined as a ball sitting on a rubber sheet. It curves the space-time around it into a bowl shape. The planets orbit around the sun because they are rolling across through this distorted space-time, which curves their motions like those of a ball rolling around inside a shallow bowl. Gravity, from this point of view, is the way objects affect the motions of other objects by affecting the shape of space-time.
Einstein’s general relativity makes predictions that Newton’s theory of gravitation does not. Since particles of light (photons) have no mass, Newtonian theory predicts that they will not be affected by gravity. However, if gravity is due to the curvature of space-time, then light should be affected in the same way as matter. This proposition was tested as follows: During the day, the sun is too bright to see any stars. However, during a total solar eclipse the sun’s disk is blocked by the moon, and it is possible to see stars that appear in the sky near to the sun. During the total solar eclipse of 1919, astronomers measured the positions of several stars that were close to the sun in the sky. It was determined that the measured positions were altered as predicted by general relativity; the sun’s gravity bent the starlight so that the stars appeared to shift their locations when they were near the sun in the sky. The detection of the bending of starlight by the sun was one of the great early experimental verifications of general relativity; many others have been conducted since.
Another surprising prediction made by general relativity is that waves can travel in gravitational forces just as waves travel through air or other media. These gravitational waves are formed when masses move back and forth in space-time, much as sound waves are created by the oscillations of a speaker cone. In 1974, two stars were discovered orbiting around each other, and scientists found out that the stars were losing energy at the exact rate required to generate the predicted gravity waves; that is, they were steadily radiating energy away in the form gravitational waves. Scientists have already verified that changes in gravitation do propagate at the speed of light, as predicted by Einstein’s theory but not by Newton’s.
In October 2017, American physicists Rainer Weiss, Barry C. Barish, and Kip S. Thorne were awarded the 2017 Nobel Prize in physics for their detection of gravitational waves that, according to the Novel Committee provided ‘an entirely new way of observing the most violent events in space and testing the limits of our knowledge.’ Barish led the LIGO project while Weiss and Thorne made key advances in the methodology needed to detect the small disturbances caused by passing gravitational waves.
Of all the predictions of general relativity, the strangest is the existence of black holes. When a very massive star runs out of fuel, the gravitational self-attraction of the star makes it shrink. If the star is massive enough, it will collapse it to a point having finite mass but infinite density. Space-time will be so distorted in the vicinity of this “singularity,” as it is termed, that not even light will be able to escape; hence the term “black hole.” Astronomers have been searching for objects in the sky that might be black holes, but since they do not give off light directly, they must be detected indirectly. When material falls into a black hole, it must heat up so much that it glows in x rays. Astronomers look for strong x-ray sources in the sky because these sources may be likely candidates to be black holes. Numerous black holes have been detected by these means, and it is now believed that many or most galaxies contain a supermassive black hole at their center, having a mass millions or billions of times greater than that of the sun.
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