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Suppose somewhere in the abyss of space, person X is in a free-float frame. X observes spaceship Y travelling in a uniform circular path centered at X. X measures Y's constant speed to be V and Y's paths's radius to be R. If the pilot of Y starts a stopwatch, and stops it just as Y completes one revolution around X, what time will the stop watch record?

One approach might be to assume Y's path to be a regular $n$-gon, and calculate the time recorded assuming Y is in free float when in travelling in each of the $n$-sides, then calculating the limit as $n$ approaches infinity. Unless I am missing something, (which I more likely than not am), this is in effect the same as "uncoiling" Y's path into a straight line of length $2*\pi*R$

Any ideas?

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    $\begingroup$ Related, possible duplicate: physics.stackexchange.com/q/632229/123208 $\endgroup$
    – PM 2Ring
    Commented Nov 23, 2023 at 10:20
  • $\begingroup$ I don't see the link between the uncoiling analogy and the calculation of Y's round trip time. $\endgroup$
    – LPZ
    Commented Nov 23, 2023 at 13:50

1 Answer 1

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One approach might be to assume Y's path to be a regular n-gon, and calculate the time recorded assuming Y is in free float when in travelling in each of the n-sides, then calculating the limit as n approaches infinity.

Yes. And then you will notice that the answer is the same for any n.

And the angles between n-sides do not matter. So one could assume Y's path to be a line too.

I don't know what complicating factors you thought that there would be. Maybe acceleration? Acceleration of a clock has no effect on that clock.

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