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“A BOOK NOBODY UNDERSTANDS” (6)

The first of the Principia’s three books deals with problems of motion involving no friction or resistance. Book II is concerned with the motions of fluids and the effect of friction on the motions of solid bodies in fluids. Important though these books are, it is Book III, entitled System of the World, that most concerns us.

According to Newton’s first law, “Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.” As we have seen, Galileo was actually the first to formulate this principle. Taking up where the Italian left off, Newton recast and incorporated it into his own system of mechanics, or the behavior of matter. If no outside force acts on a body, it will continue to move at a constant speed in the same direction. If left alone, a planet will orbit the sun eternally.

Yet the planets, as Newton had demonstrated mathematically, circle the sun, tracing out elliptical orbits. Why is it that they do not move off into space in a straight line, as would be expected according to his first law? This is where Newton’s second law comes into play: “The change of motion [of a body] is proportional to the motive force impressed; and is made in the direction of the straight line in which that force is impressed.” Stated in less rigorous terms, this law tells us that the orbiting planet is pulled at a right angle toward the sun. Its natural tendency to move outward into space, or what Christiaan Huygens called its “centrifugal” force, is perfectly balanced by the sun’s inward pull, or what Newton termed “centripetal” force. One of the best ways to illustrate this principle is to whirl an object on a rope or a string over one’s head. The object can be likened to a planet, the anchoring hand to the sun, while the string acts as the “force” that keeps the object from flying off into the blue.

But what of the string itself ? No such visible tether binds a planet to the sun. Enter Newton’s third law, which was uniquely his own: “To every action there is always opposed an equal reaction: or, the mutual action of two bodies upon each other are always equal, and directed to contrary parts.” Hence, if one body acts upon another at a distance, the second also acts on the first with an equal and opposite force. The moon pulls the Earth with the same force with which the Earth pulls the moon. This is no less true of the Earth and an apple, except that in this instance the force exerted causes the apple to visibly change its position, while the Earth, because of its far greater size, seems totally unaffected. With these three laws of motion, Newton founded the branch of modern physics we call dynamics.

The genius of Newton’s achievement becomes even clearer when we focus on the third law. Gravity acting at a distance could no longer be thought of as something peculiar to the sun and the planets; it applies to every object in existence, no matter how large or how small. As a universal property of all bodies, its force is dependent solely on the amount of matter each body contains. Or, as Newton announced in Proposition VII of Book III: “Every particle of matter attracts every other particle with a force proportional to the product of the masses and inversely proportional to the square of the distances between them.” With this elegant principle, he had made the universe a “democracy” by treating all objects as equals. Everything—from the smallest of atoms to the largest of planets— obeys the same unchanging law, as profound a thought as has ever crossed a human mind.

Taken From : Isaac Newton