Astronomers discover a planet orbiting around a star similarto our sun that is 2

Question

Astronomers discover a planet orbiting around a star similarto our sun that is 29 light years away.How fast must a rocket ship go if the round trip is to take nolonger than 58 years in time for theastronauts aboard? I got help on this problem earlier and know the solution is v=.707c and that it will take 82 years. Can someone help me understand the steps though? I'm not surehow to solve for Velocity. Astronomers discover a planet orbiting around a star similarto our sun that is 29 light years away.How fast must a rocket ship go if the round trip is to take nolonger than 58 years in time for theastronauts aboard? I got help on this problem earlier and know the solution is v=.707c and that it will take 82 years. Can someone help me understand the steps though? I'm not surehow to solve for Velocity.

Explanation / Answer

displacement d = 2*29 ly, time T = 58 y time t = T/(1 -v2/c2)    (time for theearth) speed v = d/t = d(1 - v2/c2) /T = 58ly(1 - v2/c2) /58 y = c(1 -v2/c2) v/c = (1 - v2/c2) v2/c2 = 1/2 v = c/2 = 0.707 c t = T*2 = 82 years

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