Sections
Chapter Review

# Chapter Review

### Concept Items

#### 7.1Kepler's Laws of Planetary Motion

1.
A circle is a special case of an ellipse. Explain how a circle is different from other ellipses.
1. The foci of a circle are at the same point and are located at the center of the circle.
2. The foci of a circle are at the same point and are located at the circumference of the circle.
3. The foci of a circle are at the same point and are located outside of the circle.
4. The foci of a circle are at the same point and are located anywhere on the diameter, except on its midpoint.
2.

Comets have very elongated elliptical orbits with the sun at one focus. Using Kepler's Law, explain why a comet travels much faster near the sun than it does at the other end of the orbit.

1. Because the satellite sweeps out equal areas in equal times
2. Because the satellite sweeps out unequal areas in equal times
3. Because the satellite is at the other focus of the ellipse
4. Because the square of the period of the satellite is proportional to the cube of its average distance from the sun
3.

True or False—A planet-satellite system must be isolated from other massive objects to follow Kepler’s laws of planetary motion.

1. True
2. False
4.
Explain why the string, pins, and pencil method works for drawing an ellipse.
1. The string, pins, and pencil method works because the length of the two sides of the triangle remains constant as you are drawing the ellipse.
2. The string, pins, and pencil method works because the area of the triangle remains constant as you are drawing the ellipse.
3. The string, pins, and pencil method works because the perimeter of the triangle remains constant as you are drawing the ellipse.
4. The string, pins, and pencil method works because the volume of the triangle remains constant as you are drawing the ellipse.

#### 7.2Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity

5.
Describe the postulate on which Einstein based the theory of general relativity and describe an everyday experience that illustrates this postulate.
1. Gravity and velocity have the same effect and cannot be distinguished from each other. An acceptable illustration of this is any description of the feeling of constant velocity in a situation where no outside frame of reference is considered.
2. Gravity and velocity have different effects and can be distinguished from each other. An acceptable illustration of this is any description of the feeling of constant velocity in a situation where no outside frame of reference is considered.
3. Gravity and acceleration have the same effect and cannot be distinguished from each other. An acceptable illustration of this is any description of the feeling of acceleration in a situation where no outside frame of reference is considered.
4. Gravity and acceleration have different effects and can be distinguished from each other. An acceptable illustration of this is any description of the feeling of acceleration in a situation where no outside frame of reference is considered.
6.
Titan, with a radius of $2.58×106m$, is the largest moon of the planet Saturn. If the mass of Titan is $1.35×1023kg$, what is the acceleration due to gravity on the surface of this moon?
1. $1.35m/s2$
2. $3.49m/s2$
3. $3.49×106m/s2$
4. $1.35×106m/s2$
7.

Saturn’s moon Titan has an orbital period of 15.9 days. If Saturn has a mass of 5.68×1023 kg, what is the average distance from Titan to the center of Saturn?

1. 1.22×106 m
2. 4.26×107 m
3. 5.25×104 km
4. 4.26×1010 km
8.
Explain why doubling the mass of an object doubles its weight, but doubling its distance from the center of Earth reduces its weight fourfold.
1. The weight is two times the gravitational force between the object and Earth.
2. The weight is half the gravitational force between the object and Earth.
3. The weight is equal to the gravitational force between the object and Earth, and the gravitational force is inversely proportional to the distance squared between the object and Earth.
4. The weight is directly proportional to the square of the gravitational force between the object and Earth.
9.
Explain why a star on the other side of the Sun might appear to be in a location that is not its true location.
1. It can be explained by using the concept of atmospheric refraction.
2. It can be explained by using the concept of the special theory of relativity.
3. It can be explained by using the concept of the general theory of relativity.
4. It can be explained by using the concept of light scattering in the atmosphere.
10.The Cavendish experiment marked a milestone in the study of gravity.
Part A. What important value did the experiment determine?
Part B. Why was this so difficult in terms of the masses used in the apparatus and the strength of the gravitational force?
1. Part A. The experiment measured the acceleration due to gravity, g. Part B. Gravity is a very weak force but despite this limitation, Cavendish was able to measure the attraction between very massive objects.
2. Part A. The experiment measured the gravitational constant, G. Part B. Gravity is a very weak force but, despite this limitation, Cavendish was able to measure the attraction between very massive objects.
3. Part A. The experiment measured the acceleration due to gravity, g. Part B. Gravity is a very weak force but despite this limitation, Cavendish was able to measure the attraction between less massive objects.
4. Part A. The experiment measured the gravitational constant, G. Part B. Gravity is a very weak force but despite this limitation, Cavendish was able to measure the attraction between less massive objects.

### Critical Thinking Items

#### 7.1Kepler's Laws of Planetary Motion

11. In the figure, the time it takes for the planet to go from A to B, C to D, and E to F is the same.
Figure 7.15

Compare the areas A1, A2, and A3 in terms of size.

1. A1A2A3
2. A1 = A2 = A3
3. A1 = A2 > A3
4. A1 > A2 = A3
12.

A moon orbits a planet in an elliptical orbit. The foci of the ellipse are 50, 000 km apart. The closest approach of the moon to the planet is 400, 000 km. What is the length of the major axis of the orbit?

1. 400, 000 km
2. 450, 000, km
3. 800, 000 km
4. 850,000 km
13. In this figure, if f1 represents the parent body, which set of statements holds true?
Figure 7.16
1. Area X > Area Y; The speed is greater for area X.
2. Area X > Area Y; The speed is greater for area Y.
3. Area X = Area Y; The speed is greater for area X.
4. Area X = Area Y; The speed is greater for area Y.

#### 7.2Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity

14.

Rhea, with a radius of 7.63×105 m, is the second-largest moon of the planet Saturn. If the mass of Rhea is 2.31×1021 kg, what is the acceleration due to gravity on the surface of this moon?

1. 2.65×10−1 m/s
2. 2.02×105 m/s
3. 2.65×10−1 m/s2
4. 2.02×105 m/s2
15.

Earth has a mass of 5.971×1024 kg and a radius of 6.371×106 m. Use the data to check the value of the gravitational constant.

1. it matches the value of the gravitational constant G.
2. it matches the value of the gravitational constant G.
3. it matches the value of the gravitational constant G.
4. it matches the value of the gravitational constant G.
16.

The orbit of the planet Mercury has a period of 88.0 days and an average radius of 5.791×1010 m. What is the mass of the sun?

1. 3.43×1019 kg
2. 1.99×1030 kg
3. 2.56×1029 kg
4. 1.48×1040 kg

### Problems

#### 7.1Kepler's Laws of Planetary Motion

17.

The closest Earth comes to the sun is 1.47×108 km, and Earth’s farthest distance from the sun is 1.52×108 km. What is the area inside Earth’s orbit?

1. 2.23×1016 km2
2. 6.79×1016 km2
3. 7.02×1016 km2
4. 7.26×1016 km2
18.

Earth is 1.496×108 km from the sun, and Neptune is 4.490×109 km from the sun. What best represents the number of Earth years it takes for Neptune to complete one orbit around the sun?

1. 10 years
2. 30 years
3. 160 years
4. 900 years

#### 7.2Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity

19.

Design an experiment to test whether magnetic force is inversely proportional to the square of distance. Gravitational, magnetic, and electrical fields all act at a distance, but do they all follow the inverse square law? One difference in the forces related to these fields is that gravity is only attractive, but the other two can repel as well. In general, the inverse square law says that force F equals a constant C divided by the distance between objects, d, squared: $F=C/d2F=C/d2$.

Incorporate these materials into your design:

• Two strong, permanent bar magnets
• A spring scale that can measure small forces
• A short ruler calibrated in millimeters

Use the magnets to study the relationship between attractive force and distance.

1. What will be the independent variable?
2. What will be the dependent variable?
3. How will you measure each of these variables?
4. If you plot the independent variable versus the dependent variable and the inverse square law is upheld, will the plot be a straight line? Explain.
5. Which plot would be a straight line if the inverse square law were upheld?