# B Calculate the speed of a relativistic rocket by observation...

#### Azaravicius Hi, here are image of situation. We have observer in point A. He have clock and know distance L between points B and C. He is observing rocket travel from point B to point C at speed near light speed. Can he calculate the speed of rocket using v = L / TimeA?

In rocket at point B here are passenger with clock. He knows distance L between points B and C. After arrival in point C he calculates time it took to travel from point B to point C for him. Can he calculate the speed of rocket using v = L / TimeB?

From relativity we know that time in rocket will be slower nor for point A. And if rocket speed are 100 km/h?

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#### Ibix

Science Advisor
Hi, here are image of situation. We have observer in point A. He have clock and know distance L between points B and C. He is observing rocket travel from point B to point C at speed near light speed. Can he calculate the speed of rocket using v = L / TimeA?
Yes.

In rocket at point B here are passenger with clock. He knows distance L between points B and C. After arrival in point C he calculates time it took to travel from point B to point C for him. Can he calculate the speed of rocket using v = L / TimeB?
No. In his rest frame he knows his speed - zero. He can calculate the velocity of the dots you labelled B and C (perhaps they are space stations or marker bouys or something) using measurements in his frame. He will come up with the same answer as A, although with the opposite sign because the dots are moving left to right while he is moving right to left.

From relativity we know that time in rocket will be slower nor for point A. And if rocket speed are 100 km/h?
Relativistic calculations work at all speeds. It's just that at 100km/h the difference from the Newtonian form is so small that it's not worth the more complex maths.

#### Vitro

Hi, here are image of situation. We have observer in point A. He have clock and know distance L between points B and C. He is observing rocket travel from point B to point C at speed near light speed. Can he calculate the speed of rocket using v = L / TimeA?
Yes, that's how he can determine that "rocket travel from point B to point C at speed near light speed". It's very important to note here that both L and TimeA are measured in the same frame of reference, that of A.
In rocket at point B here are passenger with clock. He knows distance L between points B and C. After arrival in point C he calculates time it took to travel from point B to point C for him. Can he calculate the speed of rocket using v = L / TimeB?
Here you are making a common mistake, you are mixing up measurements from different frames. In the reference frame of the passenger the distance between B and C is not L. It would be ok to calculate the speed of B-C (not of the rocket, which is at rest in this frame) that way by using a correct distance in that frame. It would come up to the same v as calculated by A, just in the opposite direction.

#### Azaravicius

So, distance isn't absolute but it depends at the speed of observer who makes measurements?

#### Ibix

Science Advisor
Yes. Usually the phenomenon is called "length contraction". There's a fairly subtle interplay between that, time dilation, and the relativity of simultaneity. Your best bet is to study the Lorentz transforms, and I strongly recommend looking up Minkowski diagrams too.

Thanks.

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