Question

A spaceship is built to reach a star system 15 light-years away.

(a) How fast must the spaceship move (in units of c) so that the round trip time experienced by the crew is 20 years?

(b) How much time would the round trip take as measured by observers on earth?

Answer 1

Answer:

a) 0.72c  b) 57.63 years

Explanation:

First you need to know that 1 light year is equivalent to 9.46*10^15m, so 15 light years are 1.374*10^17 m. Now 20 years are equivalent to (20)*(365)*(24)*(60)*(60) seconds = 6.3*10^8 seconds. So dividing the distance by the time you have 2.18*10^8 m/s. And you know that c = 3*10^8, so dividing the velocity by c, you have that the spaceship travels at 0.72c. With the dilation time factor you can calculate (b), the equation is t/sqrt(1-(v^2/c^2)). where t is the time (40 years) and v the velocity (0.72c), so substituting you have 57.63 years, that is the time observed in the earth.