s1133 - , t = t 2-sinh( ) / , x = x 2-[cosh( )-1] / . With...

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ADVANCED DYNAMICS — PHY 4241/5227 SOLUTIONS – SET 10 Problem 31: In units with c = 1 and time, distance in years: Always t news = t - x . In the first 5 years (time unit years, distance unit light years): ζ = α τ , α = g/c , 0 τ 5 y (accelerating away from earth , t = sinh( ζ ) /α , x = [cosh( ζ ) - 1] /α . With τ 1 = 5 y , ζ 1 = α τ 1 , t 1 = t ( ζ 1 ) and x 1 = x ( ζ 1 ) we have in the next five years ζ = ζ 1 - α ( τ - τ 1 ) , 5 τ 10 y (slowing down) , t = t 1 + [ t 1 - sinh( ζ ) ] , x = x 1 + { x 1 - [cosh( ζ ) - 1] } . With τ 2 = 2 τ 1 , t 2 = 2 t 1 and x 2 = 2 x 1 we have in the next five years ζ = α ( τ 2 - τ ) , 10 τ 15 y (accelerating towards earth)
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Unformatted text preview: , t = t 2-sinh( ) / , x = x 2-[cosh( )-1] / . With 3 = 3 1 , and t 3 = 3 t 1 we have in the nal ve years ( 3 = 1 , x 3 = x 1 ) = 1 + ( - 3 ) , 15 20 y (slowing down) , t = t 3 + t 1 + sinh( ) / , x = x 1-[cosh( )-1] / . Remark: News from the spaceship, sent of at speed of light at its time , reaches earth at time t to earth = t + x ....
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