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AlexCdeP
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Homework Statement
Challenge: a rather eccentric group of astronomy students wanted to celebrate the impact of the Shoemaker-Levy comet on Jupiter by holding a party of sufficiently long duration that their celebrations were simultaneous with the impact of the comet in all inertial reference frames.
For how long do they need to party?
How might the party end?
[The distance from the Earth to Jupiter is 8E11m and you may neglect their relative motion]
Homework Equations
The Lorentz transformation formulae
x=γ(x'+vt')
t=γ(t'+vx'/c2)
where γ=(1/(1-v2/c2)1/2 and is the gamma factor.
Where x is the distance in one frame and x' is the distance in another, and t is the time in one frame and t' is the time in the other. v is the velocity relative to one another.
At least I think these are the equations I need. Please correct me if I'm wrong, I may have a fundamental misunderstanding of the situation.
The Attempt at a Solution
OK, I have spent a fair while on this question and although initially I made the mistake of taking the party and Jupiter as being two separate reference frames like an idiot I finally realized that I can in fact consider the two events to be in the same reference frame. Calling x the distance in this reference frame x is now 8E11m and the time difference is of course 0 as they are simultaneous so t=0. However in order for these to be simultaneous in all reference frames I now have four unknowns as i don't know γ x' or t' or v, I can cope with three but not four. Which means that I'm missing a clue in the question here, any ideas?
While I was writing I suddenly thought maybe t is not 0 but t' is 0, is t in fact the length of time it takes light to travel from Jupiter? If that's the case then this is solved. I really like this question! :D Relativity = mind blown
Thanks in advance
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