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Editor's note: This article originally appeared in the March 1961 issue of Scientific American.
In the days when civilized men believed that the world was flat they had no reason to think about gravity. There was up and down. All material things tended naturally to move downward, or to fall, and no one thought to ask why. The notion of absolute up and down directions persisted into the Middle Ages, when it was still invoked to prove that the earth could not be round.
The first ray of light to pierce the mist of scholastic ideas about falling bodies issued from the work of Galileo Galilei. Since free fall was too fast to measure directly, Galileo decided to dilute the motion by studying bodies placed on an inclined plane. He argued—and at the time it was a novel argument—that since a ball resting on a horizontal surface does not move at all, and since a ball falling parallel to a vertical surface moves as fast as it would if the surface were not there, a ball on an inclined surface should roll with an intermediate speed depending on the angle of inclination. Letting balls roll down planes tilted at various angles, he observed their rates of travel and the distances covered in different time intervals, which he measured with a water clock. The experiments showed that at any angle the speed increases in direct proportion to time (counted from the moment of release) and that the distance covered increases in proportion to the square of the time. Galileo also observed that a massive iron ball and a much lighter wooden ball roll down side by side if released simultaneously from the same height on the same inclined plane.
As another way to dilute free fall he employed simple pendulums-weights suspended by thin strings. Here the steepness of the arc along which the weight travels is adjusted by changing the length of the string. Pendulums of the same length proved to have the same period of oscillation even when the weight was varied, a result in agreement with the outcome of the inclined-plane experiments. From all these observations Galileo was Ied to infer that in free fall all material bodies, light or heavy, also move in exactly the same way. This idea directly contradicted the opinion of the then prevailing Aristotelian school of philosophy, which held that heavier bodies fall faster than light ones. According to the celebrated legend, which may or may not be true, Galileo climbed the leaning tower of Pisa and dropped a light and a heavy ball, which hit tile ground Simultaneously, to the consternation of contemporary philosophers.
Newton's Law of Gravity
These studies laid the foundation for the science of mechanics. The main structure was erected by Isaac Newton, who was born the year Galileo died. With his laws of motion Newton introduced the notions of force and of inertial mass. When a force is applied to material bodies, it changes their speed or direction of motion or both. Their inertial mass opposes these changes. Newton stated that the rate of change of velocity (acceleration) of an object is directly proportional to the force acting on it and inversely proportional to its mass. Doubling the force doubles the acceleration; doubling the mass cuts the acceleration in half; if both force and mass are doubled, the acceleration is unchanged. In the light of this law Galileo's conclusion about free-falling bodies implies a fact that is usually taken for granted, but which is actually very curious; namely, the weight of a body (that is, the gravitational pull of the earth upon it) is strictly proportional to its inertial mass. Otherwise an iron and a wooden ball of the same size would not fall at the same rate. If the two objects have the same acceleration when they are dropped, the inertial mass opposing a change of motion in the iron ball must be greater than that in the wooden ball in exactly the same proportion that the downward force on the iron ball is greater. This proportionality is far from trivial; in fact, it holds true only for gravity and not for other familiar forces such as those of electricity and magnetism. Thus while an electron and a proton would fall with equal acceleration in a gravitational field, when these particles are placed in an electric field the electron is accelerated 1,836 times' faster.