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# Test Prep

### Multiple Choice

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

1.
A planet of mass m circles a sun of mass M. Which distance changes throughout the planet’s orbit?
1. $f 1 f 2 ¯$
2. $m M¯$
3. $M f 2 ¯$
4. $M f 1 ¯$
2.
The focal point of the elliptical orbit of a moon is $50 , 000 km$ from the center of the orbit. If the eccentricity of the orbit is $0.25$, what is the length of the semi-major axis?
1. $12 , 500 km$
2. $100 , 000 km$
3. $200 , 000 km$
4. $400 , 000 km$
3.

An artificial satellite orbits the Earth at a distance of 1.45×104 km from Earth’s center. The moon orbits the Earth at a distance of 3.84×105 km once every 27.3 days. How long does it take the satellite to orbit the Earth?

1. 0.200 days
2. 3.07 days
3. 243 days
4. 3721 days
4.
Earth is $1.496 × 10 8 km$ from the Sun, and Venus is $1.08 × 10 8 km$ from the Sun. One day on Venus is 243 Earth days long. What best represents the number of Venusian days in a Venusian year?
1. 0.78 days
2. 0.92 days
3. 1.08 days
4. 1.21 days

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

5.

What did the Cavendish experiment measure?

1. The mass of Earth
2. The gravitational constant
3. Acceleration due to gravity
4. The eccentricity of Earth’s orbit
6.
You have a mass of $55 kg$ and you have just landed on one of the moons of Jupiter where you have a weight of $67.9 N$. What is the acceleration due to gravity, $g$, on the moon you are visiting?
1. $.810 m/s 2$
2. $1.23 m/s 2$
3. $539 m/s 2$
4. $3735 m/s 2$
7.
A person is in an elevator that suddenly begins to descend. The person knows, intuitively, that the feeling of suddenly becoming lighter is because the elevator is accelerating downward. What other change would produce the same feeling? How does this demonstrate Einstein’s postulate on which he based the theory of general relativity?
1. It would feel the same if the force of gravity suddenly became weaker. This illustrates Einstein’s postulates that gravity and acceleration are indistinguishable.
2. It would feel the same if the force of gravity suddenly became stronger. This illustrates Einstein’s postulates that gravity and acceleration are indistinguishable.
3. It would feel the same if the force of gravity suddenly became weaker. This illustrates Einstein’s postulates that gravity and acceleration are distinguishable.
4. It would feel the same if the force of gravity suddenly became stronger. This illustrates Einstein’s postulates that gravity and acceleration are distinguishable.

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

8.
Explain how the masses of a satellite and its parent body must compare in order to apply Kepler’s laws of planetary motion.
1. The mass of the parent body must be much less than that of the satellite.
2. The mass of the parent body must be much greater than that of the satellite.
3. The mass of the parent body must be equal to the mass of the satellite.
4. There is no specific relationship between the masses for applying Kepler’s laws of planetary motion.
9.
Hyperion is a moon of the planet Saturn. Its orbit has an eccentricity of $0.123$ and a semi-major axis of $1.48 × 10 6 km$. How far is the center of the orbit from the center of Saturn?
1. $1.82 × 10 5 km$
2. $3.64 × 10 5 km$
3. $1.20 × 10 7 km$
4. $2.41 × 10 7 km$
10.
The orbits of satellites are elliptical. Define an ellipse.
1. An ellipse is an open curve wherein the sum of the distance from the foci to any point on the curve is constant.
2. An ellipse is a closed curve wherein the sum of the distance from the foci to any point on the curve is constant.
3. An ellipse is an open curve wherein the distances from the two foci to any point on the curve are equal.
4. An ellipse is a closed curve wherein the distances from the two foci to any point on the curve are equal.
11.
Mars has two moons, Deimos and Phobos. The orbit of Deimos has a period of $1.26 days$ and an average radius of $2.35 × 10 3 km$. The average radius of the orbit of Phobos is $9.374 × 10 3 km$. According to Kepler’s third law of planetary motion, what is the period of Phobos?
1. $0.16 d$
2. $0.50 d$
3. $3.17 d$
4. $10.0 d$

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

12.

Newton’s third law of motion says that, for every action force, there is a reaction force equal in magnitude but that acts in the opposite direction. Apply this law to gravitational forces acting between the Washington Monument and Earth.

1. The monument is attracted to Earth with a force equal to its weight, and Earth is attracted to the monument with a force equal to Earth’s weight. The situation can be represented with two force vectors of unequal magnitude and pointing in the same direction.
2. The monument is attracted to Earth with a force equal to its weight, and Earth is attracted to the monument with a force equal to Earth’s weight. The situation can be represented with two force vectors of unequal magnitude but pointing in opposite directions.
3. The monument is attracted to Earth with a force equal to its weight, and Earth is attracted to the monument with an equal force. The situation can be represented with two force vectors of equal magnitude and pointing in the same direction.
4. The monument is attracted to Earth with a force equal to its weight, and Earth is attracted to the monument with an equal force. The situation can be represented with two force vectors of equal magnitude but pointing in opposite directions.
13.

True or false—Gravitational force is the attraction of the mass of one object to the mass of another. Light, either as a particle or a wave, has no rest mass. Despite this fact gravity bends a beam of light.

1. True
2. False
14.
The average radius of Earth is $6.37 × 10 6 m$. What is Earth’s mass?
1. $9.35 × 10 17 kg$
2. $5.96 × 10 24 kg$
3. $3.79 × 10 31 kg$
4. $2.42 × 10 38 kg$
15.
What is the gravitational force between two $60.0 kg$ people sitting $100 m$ apart?
1. $2.4 × 10 − 11 N$
2. $2.4 × 10 − 9 N$
3. $3.6 × 10 − 1 N$
4. $3.6 × 10 1 N$

### Extended Response

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

16.

The orbit of Halley’s Comet has an eccentricity of 0.967 and stretches to the edge of the solar system.

Part A. Describe the shape of the comet’s orbit.
Part B. Compare the distance traveled per day when it is near the sun to the distance traveled per day when it is at the edge of the solar system.
Part C. Describe variations in the comet’s speed as it completes an orbit. Explain the variations in terms of Kepler’s second law of planetary motion.

1. Part A. The orbit is circular, with the sun at the center. Part B. The comet travels much farther when it is near the sun than when it is at the edge of the solar system. Part C. The comet decelerates as it approaches the sun and accelerates as it leaves the sun.
2. Part A. The orbit is circular, with the sun at the center. Part B. The comet travels much farther when it is near the sun than when it is at the edge of the solar system. Part C. The comet accelerates as it approaches the sun and decelerates as it leaves the sun.
3. Part A. The orbit is very elongated, with the sun near one end. Part B. The comet travels much farther when it is near the sun than when it is at the edge of the solar system. Part C. The comet decelerates as it approaches the sun and accelerates as it moves away from the sun.
4. Part A. The orbit is very elongated, with the sun near one end. Part B. The comet travels much farther when it is near the sun than when it is at the edge of the solar system. Part C. The comet accelerates as it approaches the sun and decelerates as it moves away from the sun.
17.

For convenience, astronomers often use astronomical units (AU) to measure distances within the solar system. One AU equals the average distance from Earth to the sun. Halley’s Comet returns once every 75.3 years. What is the average radius of the orbit of Halley’s Comet in AU?

1. 0.002 AU
2. 0.056 AU
3. 17.8 AU
4. 653 AU

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

18.
It took scientists a long time to arrive at the understanding of gravity as explained by Galileo and Newton. They were hindered by two ideas that seemed like common sense but were serious misconceptions. First was the fact that heavier things fall faster than light things. Second, it was believed impossible that forces could act at a distance. Explain why these ideas persisted and why they prevented advances.
1. Heavier things fall faster than light things if they have less surface area and greater mass density. In the Renaissance and before, forces that acted at a distance were considered impossible, so people were skeptical about scientific theories that invoked such forces.
2. Heavier things fall faster than light things because they have greater surface area and less mass density. In the Renaissance and before, forces that act at a distance were considered impossible, so people were skeptical about scientific theories that invoked such forces.
3. Heavier things fall faster than light things because they have less surface area and greater mass density. In the Renaissance and before, forces that act at a distance were considered impossible, so people were quick to accept scientific theories that invoked such forces.
4. Heavier things fall faster than light things because they have larger surface area and less mass density. In the Renaissance and before, forces that act at a distance were considered impossible because of people’s faith in scientific theories.
19.

The masses of Earth and the moon are 5.97×1024 kg and 7.35×1022 kg, respectively. The distance from Earth to the moon is 3.80×105 km. At what point between the Earth and the moon are the opposing gravitational forces equal? (Use subscripts e and m to represent Earth and moon.)

1. 3.42×105 km from the center of Earth
2. 3.80×105 km from the center of Earth
3. 3.42×106 km from the center of Earth
4. 3.10×107 km from the center of Earth