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Answer Key
Chapter 7 continued
Analyze
1. See Data Table.
2. See Data Table.
3. See Data Table. Sample Calculation for
Pluto: e 4/16 0.25
4. See Data Table.
5. Both foci are at the center.
6. It is very close to being a circle.
7. The comet. It looks more flattened out then
the other orbits.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Conclude and Apply
1. Yes, the planets and comet travel in elliptical
orbits.
2. Since the eccentricity of Earth is so small,
Kepler might not have concluded that planets have elliptical orbits.
3. It travels fastest at perihelion. According to
Kepler’s second law, equal areas are swept
out in equal time. Since there is less area
available at perihelion, the planet must
move faster.
vP
A
10.0
1.7
4. P
6 .0
1
vA
5. vA minimum velocity
3.7 km/s
vP 1.7 vA
1.7 3.7 km/s
6.3 km/s
Going Further
1. Collect data using dates of location of a
planet. Use areas and dates to confirm the
second law.
2. In order to show the third law, a computer
model would have a planet actually moving
so that periods and distances could be
measured.
Real-World Physics
Students can research elliptical orbits of satellites.
Encourage the students to pick one or two satellites and, if possible, plot orbit data to determine
the path that each satellite takes.
Physics: Principles and Problems
Study Guide
Vocabulary Review
1.
2.
3.
4.
5.
inertial mass
Kepler’s second law
gravitational mass
gravitational field
Newton’s law of universal gravitation
Section 7-1
Planetary Motion and Gravitation
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Copernicus
Brahe
Brahe
Kepler
Newton
Kepler
Newton
Kepler
third
first
first
third
second
t2 t1 t4 t3
planet B’s average distance from the Sun
It is least at point 3 and greatest at point 1.
1
The magnitude of the force at point 3 is F
36
TB2rA3
rB 3 TA2
2F
1
F
4
6F
4F
4F
the planet’s mean distance from the Sun as
well as the mass of the Sun
冪莦
Chapters 6–10 Resources
185
Answer Key
25. It was a thin rod with small lead spheres at
each end. The rod was suspended by a thin
wire attached at its center so that the rod
could spin freely. He then placed two larger
lead spheres in fixed positions near the
smaller spheres. The gravitational attraction
between the lead spheres allowed Cavendish
to obtain a value for the universal gravitational constant.
m1m2
26. F G (6.671011 N·m2/kg2)
r2
(1.00 kg)(1.00 kg)
6.671011 N. This
(1.00 m)2
number is significant because it is equal to
the value of the universal gravitational constant. Thus, the constant is defined as the
value of the gravitational force between two
1.00 kg masses placed exactly one meter
apart.
horizontal, vertical
9.80 m/s2
horizontal
air resistance
orbit
the radius of the satellite’s orbit.
the same
true
would change
inverse-square relationship
true
N/kg
toward Earth’s center
Gravitational mass determines the force of
attraction between two masses and inertial
mass determines an object’s resistance to
any type of force
15. No; the inertial mass is a function of an
object’s resistance to an exterior force, not to
its position relative to other objects.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
186 Chapters 6–10 Resources
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
c
e
d
f
b
a
gravitational
force; space
space
mass
general relativity
Section 7-1 Quiz
Planetary Motion and Gravitation
1. 1st: The paths of the planets are ellipses with
the Sun at one focus.
2nd: An imaginary line from the Sun to a
planet sweeps out equal areas in equal time
intervals.
3rd: The square of the periods of two planets
is equal to the cube of their respective mean
TA 2
rA 3
distances from the Sun, or TB
rB
冢 冣 冢 冣
M
冣 (224.7 d)
冪冢莦莦
rV 莦
2. TM TV
r
3
57910 km
87.8 days
冪莦冢莦
1082106 km 冣莦
6
3
mSmN
3. F G (6.671011 N·m2/kg2)
r2
(1.991030 kg)(1.031026 kg)
(4.501012 m)2
6.771020 N
4. Cavendish used a small rod suspended at its
midpoint by a thin wire. The rod had small
lead spheres at either end. He then placed
larger lead spheres in fixed positions near the
rod. He then used the angle through which
the rod turned to calculate the attractive
force between the spheres and then to calculate the universal gravitational constant.
Physics: Principles and Problems
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Section 7-2
Using the Law of Universal
Gravitation
Chapter 7 continued