# Chapter Review

### Concept Items

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

- The foci of a circle are at the same point and are located at the center of the circle.
- The foci of a circle are at the same point and are located at the circumference of the circle.
- The foci of a circle are at the same point and are located outside of the circle.
- The foci of a circle are at the same point and are located anywhere on the diameter, except on its midpoint.

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.

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

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

- True
- False

- 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.
- The string, pins, and pencil method works because the area of the triangle remains constant as you are drawing the ellipse.
- The string, pins, and pencil method works because the perimeter of the triangle remains constant as you are drawing the ellipse.
- The string, pins, and pencil method works because the volume of the triangle remains constant as you are drawing the ellipse.

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

- 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.
- 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.
- 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.
- 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.

- $1.35\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $3.49\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $3.49\times {10}^{6}\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $1.35\times {10}^{6}\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$

Saturn’s moon Titan has an orbital period of 15.9 days. If Saturn has a mass of 5.68×10^{23} kg, what is the average distance from Titan to the center of Saturn?

- 1.22×10
^{6}m - 4.26×10
^{7}m - 5.25×10
^{4}km - 4.26×10
^{10}km

- The weight is two times the gravitational force between the object and Earth.
- The weight is half the gravitational force between the object and Earth.
- 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.
- The weight is directly proportional to the square of the gravitational force between the object and Earth.

- It can be explained by using the concept of atmospheric refraction.
- It can be explained by using the concept of the special theory of relativity.
- It can be explained by using the concept of the general theory of relativity.
- It can be explained by using the concept of light scattering in the atmosphere.

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?

- 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. - 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. - 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. - 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

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

Compare the areas *A*_{1}, *A*_{2}, and *A*_{3} in terms of size.

*A*_{1}≠*A*_{2}≠*A*_{3}*A*_{1}=*A*_{2}=*A*_{3}*A*_{1}=*A*_{2}>*A*_{3}*A*_{1}>*A*_{2}=*A*_{3}

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?

- 400, 000 km
- 450, 000, km
- 800, 000 km
- 850,000 km

*f*

_{1}represents the parent body, which set of statements holds true?

- Area
*X*> Area*Y*; The speed is greater for area*X.* - Area
*X*> Area*Y*; The speed is greater for area*Y*. - Area
*X*= Area*Y*; The speed is greater for area*X*. - Area
*X*= Area*Y*; The speed is greater for area*Y*.

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

Rhea, with a radius of 7.63×10^{5} m, is the second-largest moon of the planet Saturn. If the mass of Rhea is 2.31×10^{21} kg, what is the acceleration due to gravity on the surface of this moon?

- 2.65×10
^{−1}m/s - 2.02×10
^{5}m/s - 2.65×10
^{−1}m/s^{2} - 2.02×10
^{5}m/s^{2}

Earth has a mass of 5.971×10^{24} kg and a radius of 6.371×10^{6} m. Use the data to check the value of the gravitational constant.

- $6.66\times {10}^{-11}\frac{\text{N}\xb7\text{m}}{\text{k}{\text{g}}^{2}},$ it matches the value of the gravitational constant G.
- $1.05\times {10}^{-17}\frac{\text{N}\xb7\text{m}}{\text{k}{\text{g}}^{2}},$ it matches the value of the gravitational constant G.
- $6.66\times {10}^{-11}\frac{\text{N}\xb7{\text{m}}^{2}}{\text{k}{\text{g}}^{2}},$ it matches the value of the gravitational constant G.
- $1.05\times {10}^{-17}\frac{\text{N}\xb7{\text{m}}^{2}}{\text{k}{\text{g}}^{2}},$ it matches the value of the gravitational constant G.

The orbit of the planet Mercury has a period of 88.0 days and an average radius of 5.791×10^{10} m. What is the mass of the sun?

- 3.43×10
^{19}kg - 1.99×10
^{30}kg - 2.56×10
^{29}kg - 1.48×10
^{40}kg

### Problems

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

The closest Earth comes to the sun is 1.47×10^{8} km, and Earth’s farthest distance from the sun is 1.52×10^{8} km. What is the area inside Earth’s orbit?

- 2.23×10
^{16}km^{2} - 6.79×10
^{16}km^{2} - 7.02×10
^{16}km^{2} - 7.26×10
^{16}km^{2}

Earth is 1.496×10^{8} km from the sun, and Neptune is 4.490×10^{9} km from the sun. What best represents the number of Earth years it takes for Neptune to complete one orbit around the sun?

- 10 years
- 30 years
- 160 years
- 900 years

### Performance Task

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

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: $F=C/{d}^{2}$.

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.

- What will be the independent variable?
- What will be the dependent variable?
- How will you measure each of these variables?
- 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.
- Which plot would be a straight line if the inverse square law were upheld?