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Amateurish speed of light question.

 


ocalhoun
Okay, suppose we have a pair of spacecraft. Each is accelerated towards the other one until they both are at 90% of the speed of light (relative to their respective launching sites).

Then, there is another pair, exactly the same, except they both are accelerated to 60% of the speed of light (relative to their respective launch sites).

At this moment, each pair of ships is exactly 1 million miles away from the other ship in the respective pair. (The two pairs are parallel; they won't hit a ship from the other pair.)

So, given that the relative speed between the two ships in a pair cannot be at or over the speed of light, which pair of ships will collide first? Or will they hit at the same time?
Bikerman
The quick and ready answer is that you need to do the sums from each independent frame of reference. You cannot assume that things are perceived to be simultaneous from the different frames - that is dependant on the Lorentz calculations for each frame in question.

The more complete answer is that velocity does not add as a normal 'linear sum'. The 90%c addition (presuming a common observer) would be higher than the 60%c addition - I can't be bothered to do the sums but you can do so yourself with a bit of simple algebra substitution:
http://en.wikipedia.org/wiki/Velocity-addition_formula
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