# Special relativity of a rocket

1. May 31, 2009

### vorcil

1)
How fast must a rocket travel on a journey to and from a distant star so that the astronauts age 12.0 years while the Mission Control workers on earth age 130 years ? c

2)
As measured by Mission Control, how far away is the distant star? in light years

my attempt
1)
Time in moving reference frame = (sqrt(1-beta))*time in inertial reference frame

12/130 = sqrt(1-beta)
12/130 ^2 = 1- beta
12/130^2 = Tn
tn = 1-beta
beta = 1-td
beta = v^2/c^2

converting light years to seconds (1ly = 31556296 seconds)
((12*31556926) / (130*31556926))^2 = 8.520*10^-3
1-(8.520*10^-3) = 0.99147 = beta
v^2/c^2 = 0.99147
sqrt(0.99147*c^2) = v
v/c = 0.9957 c which is 0.9957 as a fraction of the speed of light that the rocket has to be traveling
this was correct

2)
not quite sure how to solve the next one

2. Jun 1, 2009

### Staff: Mentor

Good. Note on terminology: Beta usually stands for v/c, not v^2/c^2.

According to Mission Control, how fast was the rocket moving and how long did it take to reach its destination? (Use basic kinematics.)