What Angular Velocity is Required for Relativistic Effects?

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this isn't a homework question, incidentally

All the foormulas for time dilation, relaitivsitc momentum, do they apply for non linear motion (circular/elliptical?) SO then that leads me to the question :
what kind of angular velocity would a planet require such that a stationary observer watching this planet from some distance, would observe relativistic effects (time dilation et al) such taht the deviation is significant. Could we handle this without resorting to vector calculus and the like?
I guess significant would mean something that deviates maybe more than 5% from the classical mechanical handling of the problem at hand.
 
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AFAIK, the force equation for the circular motion holds correct in SR as well. but, if you're planning to observe a speedy planet, it'd have a GREAT mass, and you'd probably need GR as well. And worse, you need to deal some sort of messy tensor calculus to get along with calculations.
However, to observe effects of SR, you don't need to look at planets, magnetism is a well-known relativistic effect!
 

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