Galileo’s measurements were used by Newton as the basis of his laws of motion. In Galileo’s experiments, as a body rolled down the slope it was always acted on by the same force (its weight), and the effect was to make it constantly speed up. This showed that the real effect of a force is always to change the speed of a body, rather than just to set it moving, as was previously thought. It also meant that whenever a body is not acted on by any force, it will keep on moving in a straight line at the same speed. This idea was first stated explicitly in Newton’s Principia Mathematica, published in 1687, and is known as Newton’s first law. What happens to a body when a force does act on it is given by Newton’s second law. This states that the body will accelerate, or change its speed, at a rate that is proportional to the force. (For example, the acceleration is twice as great if the force is twice as great.) The acceleration is also smaller the greater the mass (or quantity of matter) of the body. (The same force acting on a body of twice the mass will produce half the acceleration.) A familiar example is provided by a car: the more powerful the engine, the greater the acceleration, but the heavier the car, the smaller the acceleration for the same engine. In addition to his laws of motion, Newton discovered a law to describe the force of gravity, which states that every body attracts every other body with a force that is proportional to the mass of each body. Thus the force between two bodies would be twice as strong if one of the bodies (say, body A) had its mass doubled. This is what you might expect because one could think of the new body A as being made of two bodies with the original mass. Each would attract body B with the original force. Thus the total force between A and B would be twice the original force. And if, say, one of the bodies had twice the mass, and the other had three times the mass, then the force would be six times as strong. One can now see why all bodies fall at the same rate: a body of twice the weight will have twice the force of gravity pulling it down, but it will also have twice the mass. According to Newton’s second law, these two effects will exactly cancel each other, so the acceleration will be the same in all cases.
Newton’s law of gravity also tells us that the farther apart the bodies, the smaller the force. Newton’s law of gravity says that the gravitational attraction of a star is exactly one quarter that of a similar star at half the distance. This law predicts the orbits of the earth, the moon, and the planets with great accuracy. If the law were that the gravitational attraction of a star went down faster or increased more rapidly with distance, the orbits of the planets would not be elliptical, they would either spiral in to the sun or escape from the sun.
The big difference between the ideas of Aristotle and those of Galileo and Newton is that Aristotle believed in a preferred state of rest, which any body would take up if it were not driven by some force Or impulse. In particular, he thought that the earth was at rest. But it follows from Newton’s laws that there is no unique standard of rest. One could equally well say that body A was at rest and body B was moving at constant speed with respect to body A, or that body B was at rest and body A was moving. For example, if one sets aside for a moment the rotation of the earth and its orbit round the sun, one could say that the earth was at rest and that a train on it was traveling north at ninety miles per hour or that the train was at rest and the earth was moving south at ninety miles per hour. If one carried out experiments with moving bodies on the train, all Newton’s laws would still hold. For instance, playing Ping-Pong on the train, one would find that the ball obeyed Newton’s laws just like a ball on a table by the track. So there is no way to tell whether it is the train or the earth that is moving.