Chapter 12: Problem 3

Suppose you were traveling toward the Sun at a constant velocity of \(0.25 c\). With what speed does the light streaming out from the Sun go past you? Explain your reasoning.

Short Answer

Expert verified

Answer: The speed of light streaming from the Sun remains constant at \(c = 3.00 \times 10^8 \, m/s\) even when the observer is moving towards the Sun at a constant velocity of 0.25c, due to the principle of constancy of the speed of light.

Step by step solution

Understand the principle of constancy of the speed of light

According to Einstein's theory of relativity, the speed of light in vacuum is constant for all observers, regardless of their motion relative to the light source. This principle is called the "principle of constancy of the speed of light" and is a key point in understanding the problem. In this case, the speed of light in vacuum is denoted by \(c\) and is approximately \(3.00 \times 10^8 \, m/s\).

Determine the observer's speed

We are given that the observer is traveling toward the Sun at a constant speed of \(0.25 c\), which means their speed is \(0.25 \times 3.00 \times 10^8 \, m/s = 7.5 \times 10^7 \, m/s\).

Apply the principle of constancy of the speed of light

Since the speed of light is constant for all observers, the light streaming from the Sun will still go past the observer at the same speed of light in vacuum, which is \(c = 3.00 \times 10^8 \, m/s\).

Conclude the solution

Regardless of the observer's motion towards or away from the Sun, the speed of the light streaming from the Sun will still go past the observer with the same speed of light in vacuum, which is \(c = 3.00 \times 10^8 \, m/s\). This is due to the principle of constancy of the speed of light, which states that the speed of light in vacuum is constant for all observers, regardless of their motion relative to the source of the light.

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Suppose you were traveling toward the Sun at a constant velocity of \(0.25 c\). With what speed does the light streaming out from the Sun go past you? Explain your reasoning.

Short Answer

Step by step solution

Understand the principle of constancy of the speed of light

Determine the observer's speed

Apply the principle of constancy of the speed of light

Conclude the solution

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