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I am currently taking the online course on Relativity and Astrophysics provided by Cornell on EdX.

There, how the apparent velocity of an object moving at a fraction of c might sometimes be greater than c was shown. But the thought experiment only described a situation where the moving object was approaching the observer. And the fact that V(app) for an object moving away from the observer in some fraction of light will always be greater than -c/2 was only stated. I tried to think of a situation where I would be able to visualize this but I couldn't. So, can anyone please describe a thought experiment where it can be seen that V(app) for an object moving away at a fraction of speed of light will be greater than -c/2?

If you want to see the exact thought experiment used in the course. This is the hand out. If you can use the same situation as in the handout, it would be even better. Gracias.

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  • $\begingroup$ That means the apparent speed of the craft (ignoring direction) is always less than $\frac c2$. Is that the confusion, or are you asking why the speed is less than that? $\endgroup$
    – BowlOfRed
    Commented May 16, 2018 at 16:44

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Imagine you have a craft receding from you at basically $c$. At observer time $t$ after launch, the craft shines a light. We know where the craft is at that point in the observer frame, it's $ct$ distance away. The light returns to the observer, and provides evidence of the craft at that distance. But the light takes another time $t$ to return to the observer.

So the image of the craft at $x=ct$ is received at $t=2t$. The apparent speed of the craft based on that image is $\frac{x}{t}$ therefore $\frac{ct}{2t}$ or $\frac c2$

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  • $\begingroup$ Thanks. So, how this adds up in my mind is: the rocket takes t time to gain the distance ct. For us, the observer, time t has elapsed when the rocket travels the distance ct. When the rocket shines the light at time t, when it is ct distance away, the light takes t time to travel to us. This means that we see the rocket at ct distance after 2t time has elapsed. So the apparent speed is c/2. Thank you very much. $\endgroup$
    – Breamhall
    Commented May 17, 2018 at 7:08

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