Can I apply the formula t= gamma * t' if the path is Circular?
Why would you want to do that ?
That formula is important for GPS location. But there is another term, due to the centripetal acceleration, that also depends on the observer's location.
Are you trying to talk about gravitational time dilation in the context of a centrifugal acceleration field? Sounds like hogwash.
Yes. In special relativity the only thing that matters is the instantaneous speed, and that's constant here.
You can prove it by integrating the interval along the circular path of you want.
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