- #1
frerelupin
- 4
- 0
I have been pondering but cannot quite resolve the following question:
Imagine two spaceships, separated by 4 light-seconds initially. Spaceship A is traveling at 0.8c and Spaceship B (the one with the lead) is traveling at 0.4c.
Clearly an external observer will see this "chase" last for 10 seconds.
Spaceship A determines that the chase lasts ~6 seconds.
Spaceship B determines that the chase lasts ~9.17 seconds.
Calculating their velocities relative to one another is trivial and will be 0.588c and -0.588c.
Here is my conundrum: I want to be able to show that all frames are relative thus doing Einstein a solid. I feel I should be able to do this just using d=vt if I can answer the following question:
How far does Spaceship B appear to travel from A's perspective, and vice versa.
I can't quite get this to work out, but I feel that Spaceship A should see Spaceship B coming at them for 6 seconds at -0.588c, which means they covered 3.53 light-seconds, and that Spaceship B should see Spaceship A coming at them for 9.17 seconds at 0.588c meaning they covered 5.39 light-seconds.
There should be a manner in which I can determine the distance each appeared to travel using length contraction; that is to say, without using the times and velocities as derived above.
Am I off somewhere? Help!
Imagine two spaceships, separated by 4 light-seconds initially. Spaceship A is traveling at 0.8c and Spaceship B (the one with the lead) is traveling at 0.4c.
Clearly an external observer will see this "chase" last for 10 seconds.
Spaceship A determines that the chase lasts ~6 seconds.
Spaceship B determines that the chase lasts ~9.17 seconds.
Calculating their velocities relative to one another is trivial and will be 0.588c and -0.588c.
Here is my conundrum: I want to be able to show that all frames are relative thus doing Einstein a solid. I feel I should be able to do this just using d=vt if I can answer the following question:
How far does Spaceship B appear to travel from A's perspective, and vice versa.
I can't quite get this to work out, but I feel that Spaceship A should see Spaceship B coming at them for 6 seconds at -0.588c, which means they covered 3.53 light-seconds, and that Spaceship B should see Spaceship A coming at them for 9.17 seconds at 0.588c meaning they covered 5.39 light-seconds.
There should be a manner in which I can determine the distance each appeared to travel using length contraction; that is to say, without using the times and velocities as derived above.
Am I off somewhere? Help!