# Special Relaticity and Uniform Circular Motion, a (Seemingly) Elementary Problem?

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?

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

## 1 Answer

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.