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object too. In fact, he knew that since the moon was constantly changing direction, a force had to be acting on it. It was this speculation, triggered by a simple everyday event, that led to the healing of the artificial distinction between the earthly and the heavenly, and that finally gave humanity both a new way to approach the world (science) and a new metaphor (the clockwork universe).
    Newton knew that a dropped apple would fall straight down to Earth under the influence of terrestrial gravity. Throw an apple straight out and it follows a curved path as gravity pulls it down. Throw the apple harder and it lands farther away. Throw it very hard indeed and it could even circle Earth. Once it makes one circuit, it will continue around and make another (ignoring air resistance), and will in fact continue to do so forever. But of course this is just what the moon (or any satellite) does. The force that constantly acts on the moon—that keeps pulling it into a curved path instead of the straight line the first law says it should follow—is gravity, the same gravity that pulls down on the apple. With this insight, Newton abolished the centuries-old split between Earth and the heavens and showed that both were fit subjects for scientific study.
    He went even further, deducing the exact mathematical formula for the gravitational force. Only three physical quantitiesdetermine gravitational force: the masses of the two objects and the distance between them. He stated his result in what we know as Newton’s law of universal gravitation:
    Between any two objects there is an attractive force proportional to the product of the two masses divided by the square of the distance between them
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    This law has many interesting consequences. Obviously any large mass will exert a large gravitational force, but no special distinction is made between large masses and small ones. Earth pulls on the apple, but the apple also exerts a force on Earth. In fact, the two forces are the same size. We speak of apples falling to the ground because they are much less massive than Earth and so undergo a much greater acceleration due to the force exerted by the apple. As the apple falls 15 feet to the ground, Earth “falls” a distance about the diameter of an atomic nucleus toward the apple.
    The law of gravity tells us that every object in the universe is exerting a gravitational force on you right now. Earth exerts the biggest, but the person next to you exerts a force as well, as do the most distant star and galaxy. In practice, however, the massive sun and nearby moon are the only heavenly bodies that can exert a bigger force on you than familiar nearby objects like buildings. This simple fact is one of several reasons why scientists have a hard time taking astrology seriously.
The Clockwork Universe
    With the law of universal gravitation, Newton closed the circle on his work. He had the force—gravity—that operated everywhere, and he had the rules—the laws of motion—that governedthe operation of all forces. Suddenly scientists saw the universe in a new way, ordered and predictable as never before. With Newton’s equations and the language of mathematics, scientists could describe and predict the behavior of all kinds of systems. In the centuries following Newton’s work, philosophers compared his vision of the universe to a clock. The visible phenomena in the world, like the hands of a clock, move in response to the actions of invisible gears—the natural laws. In the solar system the motions of the planets are governed by the law of universal gravitation and the laws of motion. The planets tick along, as regular as a clock. For the Newtonians, in fact, the universe resembled a clock in other ways: once set in motion by God, the universe followed an inevitable course. The future was completely and comfortably predictable.
    This is a wonderful vision, but like all scientific ideas it had to be tested. The most dramatic test of Newton’s