CHAPTER 5CHAPTERCHAPTER 5 5 ||| GRAVITYGRAVITYGRAVITY 9595
Summary
▶ (^) Aristotle argued that the universe was composed of four elements:
earth at the center, with water, air, and fi re in layers above. Natural
motion (p. 77) occurred when a displaced object returned to its
natural place. Violent motion (p. 77) was motion other than natural
motion and had to be sustained by a force.
▶ (^) Galileo found that a falling object is accelerated; that is, it falls faster
and faster with each passing second. The rate at which it accelerates,
termed the acceleration of gravity (p. 77), is 9.8 m/s^2 (32 ft/s^2 ) at
Earth’s surface and does not depend on the weight of the object,
contrary to what Aristotle said.
▶ (^) According to tradition, Galileo demonstrated this by dropping balls of
iron and wood from the Leaning Tower of Pisa to show that they would
fall together. Air resistance would have ruined the experiment, but a
feather and a hammer dropped on the airless moon by an astronaut did
fall together.
▶ (^) Galileo stated the law of inertia: In the absence of friction, a moving
body on a horizontal plane will continue moving forever.
▶ (^) The fi rst of Newton’s three laws of motion was based on Galileo’s law of
inertia: A body continues at rest or in uniform motion in a straight line
unless it is acted on by some force.
▶ (^) Momentum (p. 79) is the tendency of a moving body to continue
moving.
▶ (^) Mass (p. 79) is the amount of matter in a body.
▶ (^) Newton’s second law says that an acceleration (p. 79) (a change in
velocity) must be caused by a force. A velocity (p. 79) is a directed
speed, so a change in speed or direction is an acceleration.
▶ (^) Newton’s third law says that forces occur in pairs acting in opposite
directions.
▶ (^) Newton realized that the curved path of the moon meant that it was
being accelerated toward Earth and away from a straight-line path.
That required the presence of a force—gravity.
What Are We? Falling
Everything in the universe is falling. The
moon is falling around Earth. Earth is falling
along its orbit around the sun, and the sun
and every other star in our galaxy are falling
along their orbits around the center of our
galaxy. Stars in other galaxies are falling
around the center of those galaxies, and
every galaxy in the universe is falling as it
feels the gravitational tugs of every bit of
matter that exists.
Newton’s explanation of gravity as a force
between two unconnected masses was action
at a distance, and it offended many of the
scientists of his time. They thought Newton’s
gravity seemed like magic. Einstein explained
that gravity is a curvature of space-time and
that every mass accelerates according to the
curvature it feels around it. That’s not action
at a distance, and it can give you a new
insight into how the universe works.
The mass of every atom in the universe
contributes to the curvature, creating a
universe fi lled with three-dimensional hills
and valleys of curved space-time. You and
your world, your sun, your galaxy, and every
other object in the universe are falling
through space guided by the curvature of
space-time.
SCIENTIFIC ARGUMENT
What does the equivalence principle tell you?
The equivalence principle says that there is no observation you
can make inside a closed spaceship to distinguish between uniform
acceleration and gravitation. Of course, you could open a window
and look outside, but then you would no longer be in a closed
spaceship. As long as you make no outside observations, you can’t
tell whether your spaceship is fi ring its rockets and accelerating
through space or resting on the surface of a planet where gravity
gives you weight.
Einstein took the equivalence principle to mean that gravity
and acceleration through space-time are somehow related. The
general theory of relativity gives that relationship mathematical
form and shows that gravity is really a distortion in space-time
that physicists refer to as curvature. Consequently, you can say
“mass tells space-time how to curve, and space-time tells mass
how to accelerate.” The equivalence principle led Einstein to an
explanation for gravity.
Einstein began his work by thinking carefully about common
things such as what you feel when you are moving uniformly or
accelerating. This led him to deep insights now called postulates.
Special relativity sprang from two postulates. Why does the second
postulate have to be true if the fi rst postulate is true?