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Chapter 14: Problem 40

On average, how long does it take particles in the solar wind to reach Earth from the Sun if they are traveling at an average speed of \(400 \mathrm{km} / \mathrm{s} ?\)

Short Answer

Expert verified
The particles take approximately 104 hours to reach Earth from the Sun.

Step by step solution

01

Define the Given Values

Identify the values given in the problem. Here, the average speed of the particles is given as \(400 \mathrm{km} / \mathrm{s}\). We'll also need the average distance from the Sun to Earth, which is approximately \(1.496 \times 10^8 \) km.
02

Use the Formula for Time

To find the time, use the formula: \[ t = \frac{d}{v} \] where \( t \) is the time, \( d \) is the distance, and \( v \) is the speed.
03

Plug in the Values

Substitute the known values into the formula: \[ t = \frac{1.496 \times 10^8 \text{ km}}{400 \text{ km/s}} \]
04

Calculate the Time

Perform the division: \[ t = \frac{1.496 \times 10^8}{400} = 3.74 \times 10^5 \text{ seconds} \]
05

Convert Time to Appropriate Units

Convert the time from seconds into hours for a more comprehensible answer: \[ t = \frac{3.74 \times 10^5}{3600} \approx 104 \text{ hours} \]

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Key Concepts

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

solar wind
Solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. These particles are primarily electrons and protons that travel through space at high speeds.
Since the Sun continuously emits this stream, the solar wind plays a crucial role in shaping the magnetic field of our planet and affects space weather. Understanding solar wind is essential, as it can disrupt satellite operations and even power grids on Earth.
The speed of solar wind can vary, but for our exercise, we are considering an average speed of 400 km/s.
distance from Sun to Earth
The average distance from the Sun to Earth, also known as an Astronomical Unit (AU), is approximately 1.496 × 10^8 kilometers.
This distance varies slightly due to the elliptical shape of Earth's orbit around the Sun. However, for most calculations, this average value is used.
Knowing this distance is essential for calculating the travel time of solar wind particles from the Sun to Earth, as it serves as the 'd' in our time calculation formula.
speed calculation
To find how long it takes solar wind particles to travel from the Sun to Earth, we need to calculate the average speed, which is given as 400 km/s in this case.
The formula to calculate the time (t) is:
\[ t = \frac{d}{v} \]
where 'd' is the distance, and 'v' is the speed.
By substituting the given values, we can find the time it takes for the particles to travel the given distance.
time conversion
After calculating the time in seconds using the formula, it often helps to convert this time into more familiar units, like hours.
This makes the answer easier to relate to and understand.
For our problem, after finding that the travel time is 3.74 × 10^5 seconds, we convert this time into hours by dividing by 3600 (the number of seconds in an hour):
\[ t = \frac{3.74 \times 10^5}{3600} \approx 104 \text{ hours} \]
astrophysics
Astrophysics is the branch of astronomy that deals with the physics of celestial objects and phenomena. It encompasses a broad range of studies, including the behavior of solar wind, planetary motions, and the mechanics of stars and galaxies.
Calculating the travel time of solar wind particles to Earth involves principles from astrophysics, such as understanding distances in space, the speed of particles, and converting units of time.
By learning these core concepts, students gain a deeper appreciation of the universe's mechanics and the continuous dynamic interactions between various celestial elements.

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Most popular questions from this chapter

The solar corona has a temperature of 1 million to 2 million \(K\) the photosphere has a temperature of only about \(6000 \mathrm{K}\) Why isn't the corona much, much brighter than the photosphere? a. The magnetic field traps the light. b. The corona emits only X-rays. c. The photosphere is closer to us. d. The corona has a much lower density.

a. Go to the Space Weather website (http://spaceweather com \(.\) Are there any solar flares today? What is the sunspot number? Is it about what you would expect for this year? (Click on "What is the sunspot number?" to see a current graph.) Are there any coronal holes today? b. Citizen science: Go to the website for Sunspotter (http:// www.sunspotter.org/), a Zooniverse project that evaluates the complexity of sunspots and how they change over time. Zooniverse projects offer an opportunity for people to contribute to science by analyzing pieces of data. Create ar account for Zooniverse if you don't already have one (you will use it again in this course). Log in and click on "Science" and skim through the sections. What are the goals o this project? Why is it useful to have multiple people looking at these data? Click on "Classify" and analyze some sunspots. Save a screen shot for your homework. c. Citizen science: Go to the Solar Stormwatch website (http://solarstormwatch.com), a Zooniverse project from the Royal Observatory in Greenwich, England. Create an account for Zooniverse if you don't already have one (you will use it again in this course). Log in and click on "Spot and Track Storms" and go through the Spot and Track training exercises. You are now ready to look at some real data. Click on an image to do the classification. Save a screen shot for your homework.

Energy is produced primarily in the center of the Sun because a. the strong nuclear force is too weak elsewhere. b. that's where neutrinos are created. c. that's where most of the helium is. d. the outer parts have lower temperatures and densities.

The solar wind pushes on the magnetosphere of Earth, changing its shape, because a. the solar wind is so dense. b. the magnetosphere is so weak. c. the solar wind contains charged particles. d. the solar wind is so fast.

Place in order the following steps in the fusion of hydrogen into helium. If two or more steps happen simultaneously, use an equals sign ( =). a. A positron is emitted. b. One gamma ray is emitted. c. Two hydrogen nuclei are emitted. d. Two \(^{3}\) He collide and become \(^{4}\) He. e. Two hydrogen nuclei collide and become \(^{2} \mathrm{H}\). f. Two gamma rays are emitted. g. A neutrino is emitted. h. One deuterium nucleus and one hydrogen nucleus collide and become \(^{3}\) He.
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