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Chapter 4: Problem 12

If two objects are tidally locked to each other a. the tides always stay on the same place on each object. b. the objects always remain in the same place in each other's sky. c. the objects are falling together. d. both a and b

Short Answer

Expert verified
d. both a and b

Step by step solution

01

- Understand Tidal Locking

Tidal locking is a situation where an object's orbital period matches its rotational period. This usually happens when one side of the object always faces the other, as is the case with Earth's moon.
02

- Analyze Statements

a. If two objects are tidally locked, the gravitational forces cause the same side of each object to face the other, hence the tides would be in the same place.b. Tidal locking also means that the objects keep the same relative position, so each object would stay in the same place in the other's sky.c. While tidal locking involves gravitational forces, it does not mean the objects are falling together but rather synchronizing their orbits and rotations.
03

- Choose the Correct Answer

Given the analysis of the statements:- Statement a is true because the tidal forces keep the same side facing each other.- Statement b is also true as the objects would remain fixed in each other鈥檚 sky.- Statement c is incorrect.
04

- Final Answer

Both statements a and b are true. Therefore, the correct answer is d.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Orbital Period
The orbital period is the time an object takes to complete one full orbit around another object. Consider the Moon orbiting the Earth. It takes approximately 27.3 days to make one complete trip around our planet.

Several factors influence the orbital period, including:
  • The mass of both objects.
  • The distance between the two objects.
  • Gravitational forces acting on the objects.
For objects that are tidally locked, the object鈥檚 orbital period is equal to its rotational period. This synchronized movement means that one hemisphere of the tidally locked body always faces the other object.
Rotational Period
The rotational period refers to the time an object takes to complete a full rotation on its axis. For example, Earth's rotational period is about 24 hours, while the Moon's rotational period is about 27.3 days, matching its orbital period around Earth.

Important aspects of rotational periods include:
  • The rotational speed of the object.
  • The object鈥檚 size and shape.
  • Gravitational forces exerted by nearby objects.

For tidal locking, the rotational period of each object matches its orbital period. This synchronized rotation means that the same side of the objects always faces each other, creating a stable configuration.
Gravitational Forces
Gravitational forces are the forces of attraction between two masses. They play a key role in the motion of objects in space. The force of gravity depends on:
  • The mass of each object.
  • The distance between the objects.

Tidal locking results from the gravitational interaction between two objects. Over time, these forces cause the objects鈥� rotational periods to slow down and match their orbital periods. This gradual process involves energy dissipation due to the deformation caused by tidal forces.

In summary, gravitational forces cause the synchronization of both the orbital and rotational periods in tidal locking scenarios, ensuring that the same side of one object always faces the other.

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Most popular questions from this chapter

Self-gravity is a. the gravitational pull of a person. b. the force that holds objects like people and lamps together. c. the gravitational interaction of all the parts of a body. d. the force that holds objects on Earth.

a. Watch the first 12 minutes of the episode "Gravity" in the Universe series (http://www.history.com/shows/theuniverse/videos/the-universe-gravity) to see several illustrated examples of gravity. Why does the tennis ball appear to float when dropped at the top of the roller coaster? How was Newton able to imagine a satellite orbiting Earth centuries before it was possible? Why is it the speed of the cannonball that determines whether it goes into orbit? What was the technical difficulty in launching a satellite? b. In the same video as in part (a), watch the trip on the zero-G plane, at \(23-29\) minutes. How does the plane simulate zero-G? Why does it last for only \(20-30\) seconds? How is this similar to the roller coaster in part (a)?

Earth's average radius is \(6,370 \mathrm{km}\) and its mass is \(5.97 \times 10^{24} \mathrm{kg}\) Show that the acceleration of gravity at the surface of Earth is \(9.81 \mathrm{m} / \mathrm{s}^{2}\).

Compared to your mass on Earth, on the Moon your mass would be a. lower because the Moon is smaller than Earth. b. lower because the Moon has less mass than Earth. c. higher because of the combination of the Moon's mass and size. d. the same, mass doesn't change.

If you went to Mars, your weight would be a. higher because you are closer to the center of the planet. b. lower because Mars has two small moons instead of one big moon, so there's less tidal force. c. lower because Mars has lower mass and a smaller radius that together produce a lower gravitational force. d. the same as on Earth.
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