The star Alpha goes supernova. 10yrslater and 100 light years away, as measure b

Question

   The star Alpha goes supernova. 10yrslater and 100 light years away, as measure by astronomers in thegalaxy, star Beta explodes.    B) An alien spacecraft passing through thegalaxy finds that the distance between the two explosions is 120lys. According to the aliens, what is the time between theexplosions? I thought you would just use: t= d/v      or    t= x/v     = 120-100/3.00*10^8 m/s this does not give the correctanswer of::: 67.1yrs    The star Alpha goes supernova. 10yrslater and 100 light years away, as measure by astronomers in thegalaxy, star Beta explodes.    B) An alien spacecraft passing through thegalaxy finds that the distance between the two explosions is 120lys. According to the aliens, what is the time between theexplosions? I thought you would just use: t= d/v      or    t= x/v     = 120-100/3.00*10^8 m/s this does not give the correctanswer of::: 67.1yrs

Explanation / Answer

Using Minowski's equation, the square of total displacement in four-dimensionalspace is constant, r2 - c2t2 =r'2 - c2t'2 So, (100ly)2 - (10 ly)2 = (120ly)2 - c2t'2 So, t' = 67.082 years ˜ 67.1 years So, t' = 67.082 years ˜ 67.1 years

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