In the case where the object is moving slowly or not near a VERY large gravity field Newtonain mechanics and relativity give EXACTLY the same results.
Am I wrong in stating that they DO NOT give the exactly same results, only that the differences are too minute for our ability to measure them?
Do you mean to state that if a ball going exactly 30 miles an hour from my perspective, passes another ball going in the opposite direction of the first at exactly 30 miles an hour from my perspective, that an observer on one ball (with a perfect measuring device) will measure the speed of the other ball at 60 mph EXACTLY?