# How does an IFR observer measure the speeds of two craft going oppisite directions approaching "C"?

Asked by

mr_g (

8)
June 2nd, 2012

Take the example that an observer (“Rick”) is standing on earth. Now obviously from Einstein we know a ship cannot travel faster than the speed of light. So lets have two ships travelling 0.95c in either direction away from each other.

So how can the person on earth measure their relative speeds? Wouldn’t the earth observer see them travelling 1.9c away from each other?

Obviously in either ships (say ship “A”) reference frame, the length dilation affects the measured velocity of the other ship (Ship “B”), such that the measured velocity of the other ship (Ship “B”) is less than the speed of light.

But to the observer on earth, how would they calculate the relative velocities of each ship? Surely what he measures is greater than C.

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## 8 Answers

Response moderated (Unhelpful)

What the observer measures is two objects moving relative to them at 0.95C.

Response moderated (Unhelpful)

The observer sees both spacecraft moving independently.

I’m not sure there’s a problem measuring the relative speed of two craft at greater than c (1.9 c in this case). That is, I don’t think it violates the principles of relativity. So long as no object is moving at c or greater with respect to the observer, and so long as the two pilots measure each other’s speed to be less than c relative to themselves, I think it’s okay that they approach, pass, and move apart at 1.9 c.

One ship will be seen as traveling at 0.95c

and

One ship will be seen as traveling at -0.95c

The space between them will get bigger faster than the speed of light but this is allowed as space isnâ€™t something that moves.

@DrBill is correct. From Ship A, Ship B will appear to be moving towards him, provided Ship A is cloaked. Otherwise, Ship B will appear invisible.

Of course, I could be wrong about this, since I haven’t actually done this.

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