Page 10 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 2
CHAPTER 2

SPACE AND TIME

Our present ideas about the motion of bodies date back to Galileo and Newton. Before them people believed
Aristotle, who said that the natural state of a body was to be at rest and that it moved only if driven by a force or
impulse. It followed that a heavy body should fall faster than a light one, because it would have a greater pull
toward the earth.

The Aristotelian tradition also held that one could work out all the laws that govern the universe by pure
thought: it was not necessary to check by observation. So no one until Galileo bothered to see whether bodies
of different weight did in fact fall at different speeds. It is said that Galileo demonstrated that Aristotle’s belief
was false by dropping weights from the leaning tower of Pisa. The story is almost certainly untrue, but Galileo
did do something equivalent: he rolled balls of different weights down a smooth slope. The situation is similar to
that of heavy bodies falling vertically, but it is easier to observe because the Speeds are smaller. Galileo’s
measurements indicated that each body increased its speed at the same rate, no matter what its weight. For
example, if you let go of a ball on a slope that drops by one meter for every ten meters you go along, the ball
will be traveling down the slope at a speed of about one meter per second after one second, two meters per
second after two seconds, and so on, however heavy the ball. Of course a lead weight would fall faster than a
feather, but that is only because a feather is slowed down by air resistance. If one drops two bodies that don’t
have much air resistance, such as two different lead weights, they fall at the same rate. On the moon, where
there is no air to slow things down, the astronaut David R. Scott performed the feather and lead weight
experiment and found that indeed they did hit the ground at the same time.

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

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