What Is Physics?
One of the long-standing goals of physics is to understand the gravitational
force—the force that holds you to Earth, holds the Moon in orbit around Earth,
and holds Earth in orbit around the Sun. It also reaches out through the whole of
our Milky Way galaxy, holding together the billions and billions of stars in the
Galaxy and the countless molecules and dust particles between stars. We are
located somewhat near the edge of this disk-shaped collection of stars and other
matter, 2.6 ϫ 10
4
light-years (2.5 ϫ 10
20
m) from the galactic center, around
which we slowly revolve.
The gravitational force also reaches across intergalactic space, holding
together the Local Group of galaxies, which includes, in addition to the Milky
Way, the Andromeda Galaxy (Fig. 13-1) at a distance of 2.3 ϫ 10
6
light-years
away from Earth, plus several closer dwarf galaxies, such as the Large Magellanic
Cloud. The Local Group is part of the Local Supercluster of galaxies that is being
drawn by the gravitational force toward an exceptionally massive region of space
called the Great Attractor. This region appears to be about 3.0 ϫ 10
8
light-years
from Earth, on the opposite side of the Milky Way. And the gravitational force is
even more far-reaching because it attempts to hold together the entire universe,
which is expanding.
C
H
A
P
T
E
R
1
3
Gravitation
13-1 NEWTON’S LAW OF GRAVITATION
After reading this module, you should be able to . . .
13.01 Apply Newton’s law of gravitation to relate the gravitational force between two particles to their masses and
their separation.
13.02 Identify that a uniform spherical shell of matter attracts
a particle that is outside the shell as if all the shell’s mass
were concentrated as a particle at its center.
13.03 Draw a free-body diagram to indicate the gravitational
force on a particle due to another particle or a uniform,
spherical distribution of matter.
Key Ideas
Learning Objectives
354
● Any particle in the universe attracts any other particle with a
gravitational force whose magnitude is
(Newton’s law of gravitation),
where m 1 and m 2 are the masses of the particles, r is their
separation, and G (ϭ 6.67 ϫ 10
Ϫ11
N иm
2
/kg
2
) is the gravitational constant.
F ϭ G
m 1 m 2
r
2
● The gravitational force between extended bodies is found
by adding (integrating) the individual forces on individual particles within the bodies. However, if either of the bodies is a
uniform spherical shell or a spherically symmetric solid, the
net gravitational force it exerts on an external object may be
computed as if all the mass of the shell or body were located
at its center.
One of the long-standing goals of physics is to understand the gravitational
force—the force that holds you to Earth, holds the Moon in orbit around Earth,
and holds Earth in orbit around the Sun. It also reaches out through the whole of
our Milky Way galaxy, holding together the billions and billions of stars in the
Galaxy and the countless molecules and dust particles between stars. We are
located somewhat near the edge of this disk-shaped collection of stars and other
matter, 2.6 ϫ 10
4
light-years (2.5 ϫ 10
20
m) from the galactic center, around
which we slowly revolve.
The gravitational force also reaches across intergalactic space, holding
together the Local Group of galaxies, which includes, in addition to the Milky
Way, the Andromeda Galaxy (Fig. 13-1) at a distance of 2.3 ϫ 10
6
light-years
away from Earth, plus several closer dwarf galaxies, such as the Large Magellanic
Cloud. The Local Group is part of the Local Supercluster of galaxies that is being
drawn by the gravitational force toward an exceptionally massive region of space
called the Great Attractor. This region appears to be about 3.0 ϫ 10
8
light-years
from Earth, on the opposite side of the Milky Way. And the gravitational force is
even more far-reaching because it attempts to hold together the entire universe,
which is expanding.
C
H
A
P
T
E
R
1
3
Gravitation
13-1 NEWTON’S LAW OF GRAVITATION
After reading this module, you should be able to . . .
13.01 Apply Newton’s law of gravitation to relate the gravitational force between two particles to their masses and
their separation.
13.02 Identify that a uniform spherical shell of matter attracts
a particle that is outside the shell as if all the shell’s mass
were concentrated as a particle at its center.
13.03 Draw a free-body diagram to indicate the gravitational
force on a particle due to another particle or a uniform,
spherical distribution of matter.
Key Ideas
Learning Objectives
354
● Any particle in the universe attracts any other particle with a
gravitational force whose magnitude is
(Newton’s law of gravitation),
where m 1 and m 2 are the masses of the particles, r is their
separation, and G (ϭ 6.67 ϫ 10
Ϫ11
N иm
2
/kg
2
) is the gravitational constant.
F ϭ G
m 1 m 2
r
2
● The gravitational force between extended bodies is found
by adding (integrating) the individual forces on individual particles within the bodies. However, if either of the bodies is a
uniform spherical shell or a spherically symmetric solid, the
net gravitational force it exerts on an external object may be
computed as if all the mass of the shell or body were located
at its center.