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So, the ship is always traveling at the same speed v, therefore each time I can go to a certain inertial reference frame and say dt' = dt*(gamma), and gamma always stays the same. so if I integrate it I get that the total time in one system is gamma times the time in the other one.

However, for the ship to travel at constant speed in a circle, it must have a constant acceleration, and I'd expect it have some influence on the calculation (for example, by the previous one I get that the time for the circling ship is the same as I'd get for a ship going in a constand velocity)

But I don't see what's wrong at the first calculation, or how to add the effect of acceleration if it's speed is not changing.

thanks

ibc