Help with Lorentz transformations

[Nisse]

I'm trying to work out how to use the Lorentz equations but so far I haven't been very successful. It would help if I had an example to let me know what I'm aiming for, so if someone would be kind enough to answer my questions about the fairly simple scenario below I would be very grateful.

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Two space stations A and B are 18.66 light minutes apart and at rest with respect to each other and to an independent observer O. All their clocks are synchronized.

At time T0, A sends a light pulse towards B, while B launches a ship at 0.866c towards A. Observer O should see the light pulse meet the ship after 10 minutes, 8.66 light minutes from B. The ship, of course, should see the light pulse approaching it at speed c.

When the ship meets the light pulse, it immediately (in its frame) decelerates and is at rest with respect to A, B and O.
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All of the following questions relate to the ship's reference frame.

1. At the point of its launch, how far does the ship regard the distance to A?
2. After 1 minute has elapsed, how far is the ship from B, and how far is the light pulse from A?
3. How much time has elapsed when the light pulse meets the ship, and how far is the ship from B at this point?
4. After the ship has stopped and is at rest with respect to O, how far from B does it find itself?

Apologies if these seem like daft questions, but any help is much appreciated!

 

[tiny-tim]

Hi Nisse!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Nisse]

I chose a speed of 0.866c because that gives a length contraction of approx. 0.5 and a time dilation of approx. 2, just to make things easier. Here are the answers I got:

1. At the point of launch, traveling at 0.866c, the ship thinks the distance to A is 9.33 light minutes.

2. After 1 minute the ship is 0.866 light minutes from B. As the gap between the ship and the light pulse is decreasing at speed c, the ship thinks the light pulse is now 0.134 light minutes from A.

3. The ship meets the light pulse after 9.33 seconds, at a distance of 8.08 light minutes from B.

4. After the ship has stopped, it finds itself 16.16 light minutes from B. Observer O sees the ship stop 8.66 minutes after it meets the light pulse.

Is any of this correct, or have I got it completely wrong?

 

[Nisse]

Anyone?

 

[Nisse]

 

[diazona]

Sorry for the lack of attention :-( I think you've got it, though. Assuming that in #3 you meant 9.33 minutes, not seconds. The other thing is that the observer would see the ship stop immediately when it reaches the light pulse, since those are simultaneous, colocated events (same time, same place, so all observers see them as such). Why did you say that O sees the ship stop 8.66 minutes after meeting the light pulse?