Gravity and Gravitation

The Greek philosopher Aristotle (384–322 B.C.) 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 centertrending 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 the 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 the common-sense fact that heavier objects fall faster than light ones of the same mass: drop a feather and a pebble of equal mass 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 medium rock? This is an easy experiment to perform, and the results have profound implications. As early as the sixth century A.D. 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 feet 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:

That is, if one drops an object, after 1 second it has fallen approximately 5m; after 2 seconds, 20m; 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.