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Chapter 3: Problem 21

The speed of a planet in its orbit varies in its journey around the Sun. At what point in its orbit is the planet moving the fastest? At what point is it moving the slowest?

Short Answer

Expert verified
The planet is moving fastest at perihelion and slowest at aphelion.

Step by step solution

01

Understand Kepler's Laws of Planetary Motion

Kepler's Second Law states that a planet sweeps out equal areas in equal times. This means that when a planet is closer to the Sun, it moves faster, and when it is farther from the Sun, it moves slower.
02

Identify Perihelion and Aphelion

The point where the planet is closest to the Sun is called perihelion, and the point where it is farthest from the Sun is called aphelion.
03

Relate Speed to Distance from the Sun

According to Kepler's Second Law, the speed of the planet is greatest at perihelion (closest to the Sun) and least at aphelion (farthest from the Sun).

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Key Concepts

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

Kepler's Second Law
Kepler's Second Law, also known as the Law of Equal Areas, is an essential principle in understanding the behavior of planets in their orbits. It states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
This implies that a planet moves faster when it is closer to the Sun and slower when it is farther away. Kepler's Second Law helps us understand the changing speeds of a planet as it follows its elliptical orbit around the Sun. It's a critical concept in celestial mechanics and is fundamental in the study of planetary motion.
Perihelion
The term 'perihelion' refers to the point in the orbit of a planet where it is closest to the Sun. At this position, the gravitational pull from the Sun is strongest. Because of this strong gravitational force, the planet's speed increases. According to Kepler's Second Law, a planet moves faster at perihelion to sweep out equal areas in equal times.
This increased speed compensates for the shorter distance from the Sun, allowing the planet to cover the same area it would when it is further away. Hence, perihelion plays a crucial role in understanding the dynamics of planetary motion and their varying speeds.
Aphelion
The term 'aphelion' is used to describe the point in a planet's orbit where it is farthest from the Sun. At this point, the gravitational pull from the Sun is weaker compared to other parts of the orbit. This reduced gravitational pull means the planet moves more slowly at aphelion.
According to Kepler's Second Law, the slower speed enables the planet to cover the same area over equal time intervals as it would when closer to the Sun. Understanding aphelion helps explain why planets do not have a constant speed in their orbits and why they move slower when they are farther from the Sun.
Planetary Speed
The speed of a planet in its orbit is not constant; it varies depending on its distance from the Sun. Thanks to Kepler's Second Law, we know that when a planet is closer to the Sun (at perihelion), it moves faster. Conversely, when it is farther from the Sun (at aphelion), it moves slower.
This variation in speed ensures that the planet sweeps out equal areas in equal times, maintaining a balance in its orbital motion. Understanding planetary speed is key to predicting planetary positions and is essential in astronomy and space navigation. Kepler's insights into planetary speed remain a cornerstone in the study of our solar system.

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Most popular questions from this chapter

Planets with high eccentricity may be unlikely candidates for life because a. the speed varies too much. b. the period varies too much. c. the temperature varies too much. d. the orbit varies too much.

Suppose you are pushing a small refrigerator of mass \(50 \mathrm{kg}\) on wheels. You push with a force of \(100 \mathrm{N}\) a. What is the refrigerator's acceleration? b. Assume the refrigerator starts at rest. How long will the refrigerator accelerate at this rate before it gets away from you (that is, before it is moving faster than you can run-of the order \(10 \mathrm{m} / \mathrm{s}\) )?

Galileo observed that Venus had phases that correlated with its size in his telescope. From this information, you may conclude that Venus a. is the center of the Solar System. b. orbits the Sun. c. orbits Earth. d. orbits the Moon.

During the latter half of the 19 th century, a few astronomers thought there might be a planet circling the Sun inside Mercury's orbit. They even gave it a name: Vulcan. We now know that Vulcan does not exist. If a planet with an orbit one-fourth the size of Mercury's actually existed, what would be its orbital period relative to that of Mercury?

When riding in a car, we can sense changes in speed or direction through the forces that the car applies on us. Do we wear seat belts in cars and airplanes to protect us from speed or from acceleration? Explain your answer.
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