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3.9 The Speed of Light
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Compared with Exercises, Problems often require more calculation and a deeper understanding of key concepts. They are essential to acquiring a working knowledge of the subject. Most problems are also broken down into multiple parts. When presented with a question, you must select the best answer, and then click on the Check button. Next, you’ll see whether you’ve answered correctly or incorrectly, along with a corresponding explanation. Click on the Finish Quiz button to see your overall results. Problems are not graded, and you can always click on the Restart Quiz or the View Questions buttons before clicking on the arrow to advance to the next course element.

3.9 The Speed of Light

Imagine that light did not have a constant speed, but behaved in the manner expected from experience. Namely, if the source of the light is rushing toward you, the light will approach you faster; if the source is rushing away from you, the light will approach you slower. This is incorrect, of course, but it’s worth investigating the consequences of a non-constant speed of light because the failure to observe those consequences is evidence that the speed of light is constant. With that backdrop, consider a binary star system situated a very large distance LL from Earth. Let the angular velocity of the smaller star be ω\omega, as it orbits the larger star in a circle of radius rr. We want to find the value of ω\omega for which the light emitted by the smaller star, when it’s traveling directly away from Earth, arrives at Earth at the same moment as light emitted a little later, when the star is traveling directly toward Earth. Let’s work this out in stages:

  1. 1. Question

    Recall from basic physics that if the angular velocity of the smaller star is ω\omega then its linear speed vv is given by v=ωrv = \omega r. In terms of vv, what is the time t1t_1 that it will take light emitted by the smaller star to reach Earth, if that light is emitted when the smaller star's orbit has it moving directly away from Earth? (Again, assume—incorrectly—that light behaves as you would expect from everyday experience, with its base speed cc being increased or decreased by the motion of the source.)

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  2. 2. Question

    In terms of vv, what is the time t2t_2 that it will take light emitted by the smaller star to reach Earth if that light is emitted when the smaller star's orbit has it moving directly toward Earth? (Again, assume—incorrectly—that light behaves as you would expect from everyday experience, with its base speed cc being increased or decreased by the motion of the source.)

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  3. 3. Question

    In terms of vv, what is the time t3t_3 that it takes the smaller star to move from the position relevant to part (A) to the position relevant to part (B)—that is, how long does it take the star to complete one half of a full orbit around the larger star?

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  4. 4. Question

    What value of ω=v/r\omega = v/r will result in the light emitted when the smaller star is traveling directly away from Earth reaching us at the same moment as the light emitted later, when the smaller star's orbit has it moving directly toward earth?

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