CHAPTER 5 | GRAVITY 77
He began by studying the motions of falling bodies, but he
quickly discovered that the velocities were so great and the times
so short that he could not measure them accurately. Consequently,
he began using polished bronze balls rolling down gently sloping
inclines. In that instance, the velocities are lower, and the times
are longer. Using an ingenious water clock, he was able to mea-
sure the time the balls took to roll given distances down the
incline, and he correctly recognized that these times are propor-
tional to the times he would have measured using falling bodies.
Galileo found that falling bodies do not fall at constant
rates, as Aristotle had said, but are accelerated. Th at is, they move
faster with each passing second. Near Earth’s surface, a falling
object will have a velocity of 9.8 m/s (32 ft/s) at the end of 1
second, 19.6 m/s (64 ft/s) after 2 seconds, 29.4 m/s (96 ft/s) after
3 seconds, and so on. Each passing second adds 9.8 m/s (32 ft/s)
to the object’s velocity (■ Figure 5-3). In modern terms, this
steady increase in the velocity of a falling body by 9.8 m/s each
second (usually written 9.8 m/s^2 ) is called the acceleration of
gravity at Earth’s surface.
Galileo also discovered that the acceleration does not depend
on the weight of the object. Th is, too, is contrary to the teachings
of Aristotle, who believed that heavy objects, containing more
earth and water, fell with higher velocity. Galileo found that the
acceleration of a falling body is the same whether it is heavy or
light. According to some accounts, he demonstrated this by
dropping balls of iron and wood from the top of the Leaning
Tower of Pisa to show that they would fall together and hit the
ground at the same time (■ Figure 5-4a). In fact, he probably
didn’t perform this experiment. It would not have been conclu-
sive anyway because of air resistance. More than 300 years later,
Apollo 15 astronaut David Scott, standing on the airless moon,
demonstrated the truth of Galileo’s discovery by simultaneously
dropping a feather and a steel geologist’s hammer. Th ey fell at the
same rate and hit the lunar surface at the same time
(Figure 5-4b).
Having described natural motion, Galileo turned his atten-
tion to violent motion—that is, motion directed other than
toward an object’s proper place in the cosmos. Aristotle said that
such motion must be sustained by a cause. We would say “a
cause” today. Galileo pointed out that an object rolling down an
incline is accelerated and that an object rolling up the same
incline is decelerated. If the incline were perfectly horizontal and
frictionless, he reasoned, there could be no acceleration or decel-
eration to change the object’s velocity, and, in the absence of
friction, the object would continue to move forever. In his own
words, “any velocity once imparted to a moving body will be
rigidly maintained as long as the external causes of acceleration
or retardation are removed.” Motion need not be sustained by a
cause, said Galileo. Once begun, motion continues until some-
thing changes it. In fact, Galileo’s statement is a perfectly valid
summary of the law of inertia, which became Newton’s fi rst law
of motion.
have to understand motion before he could truly understand the
Copernican system.
In addition to writing about a geocentric universe, Aristotle
also wrote about the nature of motion, and those ideas still held
sway in Galileo’s time. Aristotle said that the world is made up of
four classical elements: earth, water, air, and fi re, each located in
its proper place. Th e proper place for earth (meaning soil and
rock) is the center of the universe, and the proper place of water
is just above earth. Air and then fi re form higher layers, and
above them lies the realm of the planets and stars. (You can see
the four layers of the classical elements in the diagram at the top
of page 56.) Th e four elements were believed to have a natural
tendency to move toward their proper place in the cosmos.
Th ings made up mostly of air or fi re—smoke, for instance—tend
to move upward. Th ings composed mostly of earth and water—
wood, rock, fl esh, bone, and so on—tend to move downward.
According to Aristotle, objects fall downward because they are
moving toward their proper place.*
Aristotle called these motions natural motions to distin-
guish them from the violent motions that are produced when,
for instance, you push on an object and make it move other than
toward its proper place. According to Aristotle, such motions
stop as soon as the force is removed. To explain how an arrow
could continue to move upward even after it had left the bow-
string, he said currents in the air around the arrow carried it
forward even though the bowstring was no longer pushing it.
In Galileo’s time and for the two preceding millennia, schol-
ars had tended to resolve problems by referring to authority. To
analyze the fl ight of a cannonball, for instance, they would turn
to the writings of Aristotle and other classical philosophers and
try to deduce what those philosophers would have said on the
subject. Th is generated a great deal of discussion but little real
progress. Galileo broke with this tradition when he conducted
his own experiments.
■ Figure 5-2
Although Galileo is often associ-
ated with the telescope, as on this
Italian stamp, he also made sys-
tematic studies of the motion of
falling bodies and made discover-
ies that led to the law of inertia.
*Th is is one reason why Aristotle had to have a geocentric universe. If Earth’s
center had not also been the center of the cosmos, his explanation of gravity
would not have worked.