I am in astrology and I have to calculate cosmological distances between things in space and I need help with the math
There is the question
you have to go to a star that is 415 years away traveling at 99700 kmh how many years does it take you
In: Mathematics
I assume that this question is about relativistic time dilation. So I assume the question means that at velocity v you will reach the object in 415 years in Earth’s frame of reference and so how long does this journey take in your frame travelling at v.
Well with a light clock (two mirrors and a beam of light) and a bit of Pythagoras you can derive that in the moving frame (relative to the reference/clock frame) elapsed time just gets gamma factored. So t’ (elapsed time in the reference coordinate system aka Earth I assume) is just t (the moving frame aka you) times the gamma factor 1/[(1-v²/c²)^(½)]. So t’=t×gamma or 415/gamma = t.
But I’m either missing something since with this velocity the gamma factor is practically 1, 99700 km/h isn’t fast enough for special relativity to be a major factor here.
Maybe the question states that the star is 415 light years away and in that case 1 light year = c×1 year = x km distance 415 × x km / km/h = t h amount of time.
Latest Answers