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NoteCompared 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 $L$ from Earth. Let the angular velocity of the smaller star be $\omega$, as it orbits the larger star in a circle of radius $r$. We want to find the value of $\omega$ 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: