A Brief History of Time - Stephen Hawking | Page 8

motion of bodies date back to Galileo and Ne\
wton. Before them people believed
Aristotle, who said that the natural state of a body was to be at rest a\
nd that it moved only if driven by a force or
impulse. It followed that a heavy body should fall faster than a light o\
ne, because it would have a greater pull
toward the earth.
The Aristotelian tradition also held that one could work out all the law\
s that govern the universe by pure
thought: it was not necessary to check by observation. So no one until G\
alileo bothered to see whether bodies
of different weight did in fact fall at different speeds. It is said tha\
t 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 bec\
ause the Speeds are smaller. Galileo’s
measurements indicated that each body increased its speed at the same ra\
te, 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 secon\
d 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 resist\
ance. 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 perfor\
med the feather and lead weight
experiment and found that indeed they did hit the ground at the same tim\
e.
Galileo’s measurements were used by Newton as the basis of his laws o\
f motion. In Galileo’s experiments, as a
body rolled down the slope it was always acted on by the same force (it\
s weight), and the effect was to make it
constantly speed up. This showed that the real effect of a force is alwa\
ys to change the speed of a body, rather
than just to set it moving, as was previously thought. It also meant tha\
t 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 t\
o a body when a
force does act on it is given by Newton’s second law. This states tha\
t the body will accelerate, or change its
speed, at a rate that is proportional to the force. (For example, the a\
cceleration 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 acce\
leration.) A familiar example is
provided by a car: the more powerful the engine, the greater the acceler\
ation, 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 eve\
ry 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 b\
ody 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 w\
ould 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 Newt\
on’s second law, these two effects will
exactly cancel each other, so the acceleration will be the same in all c\
ases.
Newton’s law of gravity also tells us that the farther apart the bodi\
es, 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 p\
lanets with great accuracy. If the law
were that