The distance from earth to the galactic centre is 23000 ly. What constant speed would be required to make the journey in 30 y of an astronaut's lifetime?

I know the answer should be 0.99999915c but don't know how to get there with time dilation or length contraction

1 answer

1ly = 9.454254*10^15 m
1y = 3.1536*10^7 s
c = 2.99792*10^8 m/s

23000ly/30y
= (2.3*10^4 * 9.454254*10^15)/(30*3.1536*10^7)
= 2.298409*10^11 m/s

see what the Lorentz factor is for 0.99999915c and I'm sure it will work out.