World Science Scholars
3.9 The Speed of Light
Problem
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## 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:

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