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Chapter 14: Problem 50

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
It takes approximately 103.9 hours for particles in the solar wind to reach Earth from the Sun.

Step by step solution

01

Identify the Given Values

The problem states that the average speed of the particles in the solar wind is \(400 \, \text{km/s}\).
02

Determine the Distance from the Sun to Earth

The average distance from the Sun to Earth is approximately \(1.496 \times 10^8 \, \text{km}\).
03

Apply the Formula for Time

The formula to calculate time is given by \( t = \frac{d}{v} \)where \( t \) is the time, \( d \) is the distance, and \( v \) is the velocity.
04

Substitute the Values into the Formula

Substitute \( d = 1.496 \times 10^8 \, \text{km} \) and \( v = 400 \, \text{km/s} \) into the formula:\[ t = \frac{1.496 \times 10^8}{400} \]
05

Calculate the Time

Perform the division:\[ t = \frac{1.496 \times 10^8}{400} = 3.74 \times 10^5 \, \text{s} \]
06

Convert Time into Hours

Convert the time from seconds to hours by dividing by the number of seconds in an hour (3600 seconds/hour):\[ t_{\text{hours}} = \frac{3.74 \times 10^5}{3600} \approx 103.9 \text{ hours} \]

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Key Concepts

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

solar wind
Solar wind consists of charged particles, primarily electrons and protons, emitted from the upper atmosphere of the Sun. These particles travel through space and can affect the entire solar system. They can cause auroras and can interrupt satellite communications when they interact with Earth's magnetic field. Understanding solar wind helps us learn more about space weather and its impact on space technology and astronauts.
average speed
The average speed of particles in the solar wind is approximately 400 km/s, although this speed can vary based on solar activity. Average speed is the total distance traveled divided by the total time taken. In the context of solar wind, this means how far the particles travel from the Sun to the Earth within a certain period. Knowing the average speed is essential for calculating travel times and understanding the dynamics of these particles in space.
distance from Sun to Earth
The average distance from the Sun to Earth, known as an Astronomical Unit (AU), is roughly 1.496 × 10^8 km. This distance plays a crucial role in space science, providing a standard measurement for distances within our solar system. It helps in calculating travel times of solar wind and understanding the scale of space phenomena. For instance, knowing this distance lets us determine how long it takes solar wind particles to reach Earth.
time calculation
Time calculation involves determining how long it takes for an object to travel from one point to another at a given speed. The formula for time is:\( t = \frac{d}{v} \)where \( t \) is time, \( d \) is distance, and \( v \) is velocity. In the exercise, we use this formula to find out how long it takes for solar wind particles to travel from the Sun to the Earth. By substituting the given distance and average speed, we get the time in seconds and then convert it to hours.
unit conversion
Unit conversion is essential in physics and everyday life for ensuring consistent and accurate measurements. In our exercise, we start with the time in seconds and convert it to hours for easier understanding.The conversion factor from seconds to hours is 3600 seconds per hour.To convert the calculated time:\[ t_{\text{hours}} = \frac{time_{\text{seconds}}}{3600} \]In our example, 374000 seconds converts to approximately 103.9 hours. This step is crucial for practical applications and better comprehension of the time involved in such large-scale phenomena.

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Most popular questions from this chapter

Gas is not an efficient conductor of thermal energy because the particles a. are too slow. b. are too far apart. c. are too heavy. d. don't interact with light.

(a) Go to the National Ignition Facility (NIF) website (https://lasers.llnl.gov/about/nif). Under "Programs," click on "Internal Fusion Energy" and then "How to Make a Star."How are lasers used in experiments to develop controlled nuclear fusion on Earth? How does the fusion reaction here differ from that in the Sun? (b) An alternative approach is to fuse \(^{3} \mathrm{He}+^{3} \mathrm{He}\) instead of the hydrogen isotopes. But on Earth, \(^{3} \mathrm{He}\) is found in limited supply. \(^{3}\) He is in much greater abundance on the Moon, so some people propose setting up mining colonies on the Moon to extract \(^{3}\) He for fusion reactions on Earth. Do a search on "helium 3 moon." Which countries are talking about going to the Moon for this purpose? What is the timeline for when this might happen? What are the difficulties?

Two of the three atoms in a molecule of water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) are hydrogen. Why are Earth's oceans not fusing hydrogen into helium and setting Earth ablaze?

Engineers and physicists dream of solving the world's energy supply problem by constructing power plants that would convert globally plentiful hydrogen into helium. The Sun seems to have solved this problem. On Earth, what is a major obstacle to this potentially environmentally clean solution?

Verify the claim made at the start of this chapter that the Sun produces more energy per second than all the electric power plants on Earth could generate in a half-million years. Estimate or look up how many power plants there are on the planet, and how much energy an average power plant produces. Be sure to account for different kinds of power-for example, coal, nuclear, wind.
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