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Chapter 3: Problem 16

At what point in a planet's elliptical orbit does it move fastest? At what point does it move slowest? At what point does it sweep out an area at the fastest rate?

Short Answer

Expert verified
Answer: A planet moves fastest at perihelion (closest to the Sun), slowest at aphelion (farthest from the Sun), and the rate of sweeping out an area remains constant throughout the orbit.

Step by step solution

01

Identify the Fastest Moving Point

According to Kepler's second law, when the planet is closest to the Sun, it will have to move faster in order to sweep out the same area as when it's farther away. So, the planet moves fastest when it is closest to the Sun, which is at the point called perihelion for its orbit.
02

Identify the Slowest Moving Point

Similarly, using Kepler's second law, we can conclude that the planet moves slowest when it is farthest from the Sun since it needs to travel slower to sweep out the same area during equal intervals of time. This point is called the aphelion.
03

Identify the Fastest Area Sweep Rate Point

Since Kepler's second law informs that the rate of sweeping the area is constant throughout the orbit, there isn't a specific point where the area sweep rate is fastest. It remains constant at every point along the elliptical orbit. So, the final answer is: - The planet moves fastest at perihelion (closest to the Sun). - The planet moves slowest at aphelion (farthest from the Sun). - The rate of sweeping out an area remains constant throughout the orbit.

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Most popular questions from this chapter

How is an astronomical unit (AU) defined? Give an example of a situation in which this unit of measure would be convenient to use.

The orbit of a spacecraft about the Sun has a perihelion distance of \(0.1 \mathrm{AU}\) and an aphelion distance of \(0.4 \mathrm{AU}\). What is the semimajor axis of the spacecraft's orbit? What is its orbital period?

When the Voyager 2 spacecraft sent back pictures of Neptune during its flyby of that planet in 1989 , the spacecraft's radio signals traveled for 4 hours at the speed of light to reach Earth. How far away was the spacecraft? Give your answer in kilometers, using powers-of-ten notation. (Hint: See the preceding question.)

Write the following numbers using powers-of-ten notation: (a) ten million, (b) sixty thousand, (c) four one-thousandths, (d) thirty-eight billion, (e) your age in months.

How did the models of Aristarchus and Copernicus explain the retrograde motion of the planets?
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