**Assignment 7.0
– Vocabulary**

Define each of the following terms.

1. Kepler’s First Law

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2. Kepler’s Second Law

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3. Kepler’s Third Law

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4. Gravitational Force

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5. Law of Universal Gravitation

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6. Gravitational Field

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7. Inertial Mass

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8. Gravitational Mass

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**Assignment 7.1
– Planetary Motion & Gravitation**

__Short Answer__: Answer each question in the
space provided. Write or print clearly. IF I CAN’T READ IT, IT’S WRONG.

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1. Earth moves more slowly in its orbit during summer in the northern hemisphere than it does during winter. Is it closer to the Sun in summer or in winter?

2. Is the area swept out per unit of time by Earth moving around the Sun equal to the area swept out per unit of time by Mars moving around the sun?

3. Why did Newton think that force must act on the Moon?

4. What happens to the gravitational force between two masses when the distance between the masses is doubled?

5. The force of gravity acting on an object near Earth’s surface is proportional to the mass of the object. If this is true, why does a tennis ball not fall faster than a golf ball?

6. The Moon and Earth are attracted to each other by gravitational force. Does the more massive Earth attract the Moon with a greater force than the Moon attracts Earth? Explain.

__Problems:__ Solve each of the following
problems. Show all work. Circle your answer expressed with the correct number of
significant figures and units.

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7. Jupiter is 5.2 times farther from the Sun the Earth is. Find Jupiter’s orbital period in Earth years.

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8. The figure to the right shows a Cavendish apparatus like the one used to find G. It has a large lead sphere that is 5.9 kg in mass and small one with a mass of 0.047 kg. Their centers are separated by 0.055 m. Find the force of attraction between them.

9. Use Table 7-1 on page 173 to compute the gravitational force that the sun exerts on Jupiter.

10. Tom has a mass of 70.0 kg and Sally has a mass of 50.0 kg. Tom and Sally are standing 20.0 m apart on the dance floor. Sally looks up and sees Tom. She feels an attraction. If the attraction is gravitational, find its size.

11.
Assume that you have a mass of 50.0 kg. Earth has a mass of 5.97 x 10^{24}
kg and a radius of 6.38 x 10^{6} m.

A) What is the force of gravitational attraction between you and Earth?

B) What is your weight?

12. Uranus requires 84 years to circle the Sun. Find Uranus’s orbital radius as a multiple of Earth’s orbital radius.

13. Venus has a period of revolution of 225 Earth days. Find the distance between the Sun and Venus as a multiple of Earth’s orbital radius.

14. If a small planet, D, were located 8.0 times as far from the Sun as Earth is, how many years would it take the planet to orbit the Sun?

15.
Mimas, one of Saturn’s moon, has an orbital radius of 1.87 x 10^{8}
m and an orbital period of about 23.0 h. Use Newton’s version of Kepler’s third
law to find Saturn’s mass.

**16.
**The Moon is 3.9 x 10^{8º }m away from Earth and has a period
of 27.33 days. Use Newton’s version of Kepler’s third law to find the mass of
Earth.

**Assignment 7.2
– Using the Law of Universal Gravitation**

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__Short Answer__: Answer each question in the
space provided. Write or print clearly. IF I CAN’T READ IT, IT’S WRONG.

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1. A satellite is orbiting Earth. On which of the following does it speed depend?

A) mass of the satellite

B) distance from Earth

C) mass of Earth

2. What provides the force that causes the centripetal acceleration of a satellite in orbit?

3. During space flight, astronauts often refer to forces as multiples of the force of gravity on Earth’s surface. What does a force of 5-g mean to an astronaut?

4. If Earth were twice as massive but remained the same size:

A) What would happen to the value of g?

B) What would happen to the value of G?

5. If the space shuttle goes into a higher orbit what happens to the shuttle’s period?

6. A satellite is one Earth radius above the surface of Earth. How does the acceleration due to gravity at that location compare to the acceleration at the surface of Earth?

7. If a mass in Earth’s gravitational field is doubled, what will happen to the force exerted by the field upon this mass?

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__Problems:__ Solve each of the following
problems. Show all work. Circle your answer expressed with the correct number of
significant figures and units.

8. A geosynchronous satellite is one that appears to remain over one spot on Earth as shown in the figure to the right.

A) Calculate its speed in orbit

B) Calulate is period.

9. A 1.25 kg book in space has a weight of 8.35 N. What is the value of the gravitational field at this point?

10. How high does a rocket have to go above Earth’s surface before its weight is half of what it is on Earth?

11.
Two satellites of equal mass are put into orbit 30.0 m apart. The
gravitational force between them is 2.0 x 10^{-7} N.

A) What is the mass of each satellite?

B) What is the initial acceleration given to each satellite by gravitational force?

12. Find the value of g, acceleration due to gravity, in the following situations.

A) Earth’s mass is triple its actual value, but its radius remains the same.

B) Earth’s radius is triple, but its mass remains the same.

C) Both the mass and radius of Earth are doubled.