Chapter 12: Gravity
Ch12-1 Newton’s Law of Universal Gravitation
Fg = Gm1m2/r2
G = 6.67 x 10-11 Nm2/kg2
Figure 12-2
Dependence of the Gravitational Force
on Separation Distance, r
CT1: Suppose Earth had no atmosphere and a ball were
fired from the top of Mt. Everest in a direction tangent
to the ground. If the initial speed were high enough
to cause the ball to travel in a circular trajectory
around Earth, the ball’s acceleration would
A. be much less than g (because the ball doesn’t fall to
the ground).
B. be approximately g.
C. depend on the ball’s speed.
P12.8 (p.389)
Not to scale!
FSM
1.5 x 1011 m
F
1.5 x 1011 m

3.84 x 108 m
FEM
CT2: It is best to say that the Moon orbits
the
A. Earth.
B. Sun.
Chapter 12: Gravity
Ch12-2 Gravitational Attraction of Spherical
Bodies
CT3: Two satellites A and B of the same mass
are going around Earth in concentric orbits.
The distance of satellite B from Earth’s
center is twice that of satellite A. What is the
ratio of the centripetal force acting on B to
that acting on A? (FB/FA)
A. 2
B. 1/4
C. 1/2
D. 1/2
E. 4
CT4: In addition to using kinematics, the big
picture principle in P12.20 (p.390) will be
A. Newton’s laws.
B. conservation of energy.
C. conservation of momentum.
D. the work-kinetic energy theorem.
Chapter 12: Gravity
Ch12-3 Kepler’s Laws
2a
Kepler’s First Law: The
planets orbit the Sun in
ellipses with the Sun at
one of the foci.
Semi-major axis = a.
2a
2a = 2r
Kepler’s Second Law: The orbits sweep out
equal areas in equal times.
greater v
smaller v
L = mvr is constant. Angular momentum is conserved
because the central force of the Sun produces
net = 0.
Kepler’s Third Law: T  a3/2, where a is the semimajor axis of the ellipse. For a circle, a = r.
CT5: In addition to using kinematics, the big
picture principle in P12.28 (p.390) will be
A. Newton’s laws.
B. conservation of energy.
C. conservation of momentum.
D. the work-kinetic energy theorem.
CT6: For P12.31 (p.390), the period depends on
A. the mass of the Earth.
B. the mass of the satellite.
C. both the mass of the Earth and the satellite.
D. neither the mass of the Earth nor the mass of
the satellite.
Chapter 12: Gravity
Ch12-4 and 5 Potential Energy and Energy
Conservation
Ug = -GMm/r for two masses M and m
separated by r
E = K + Ug is conserved when only the
gravitational force is acting because the
universal gravitational force is a conservative
force
CT7: In addition to using kinematics, the big
picture principle in P12.41 (p.391) will be
A. Newton’s laws.
B. conservation of energy.
C. conservation of momentum.
D. the work-kinetic energy theorem.
P12.66 (p.392)
CT8: In addition to using kinematics, the big
picture principle in P12.67 (p.392) will be
A. Newton’s laws.
B. conservation of energy.
C. conservation of momentum.
D. the work-kinetic energy theorem.
CT9:
System A has masses m and m separated by r;
system B has masses m and 2m separated by 2r;
system C has masses 2m and 3m separated by 2r;
and system D has masses 4m and 5m separated by 3r.
Which system has the smallest attraction between
the two masses?
A. A
B. B
C. C
D. D
CT10:
System A has masses m and m separated by r;
system B has masses m and 2m separated by 2r;
system C has masses 2m and 3m separated by 2r;
and system D has masses 4m and 5m separated by 3r.
Which system has the next smallest attraction
between the two masses?
A. A
B. B
C. C
D. D
CT11:
System A has masses m and m separated by r;
system B has masses m and 2m separated by 2r;
system C has masses 2m and 3m separated by 2r;
and system D has masses 4m and 5m separated by 3r.
Which system has the greatest attraction between
the two masses?
A. A
B. B
C. C
D. D