A spaceship is headed toward Alpha Centauri at 0.999c. According to us, the distance to Alpha Centauri is about 4 light-years. How far away is Alpha Centauri according to the travelers in the ship?

a) also about 4 light-years

b) very slightly more than 4 light-years

c) very slightly less than 4 light-years

d) quite a bit less than 4 light-years

e) quite a bit more than 4 light-years

According to the travellers, Alpha Centauri is c) very slightly less than 4 light-years

Explanation:

For a stationary observer, Alpha Centauri is 4 light-years away but for an observer who is travelling close to the speed of light, Alpha Centauri is very slightly less than 4 light-years. The following expression explains why:

v = d / t

where

v is the speed of the spaceship d is the distance t is the time

Therefore,

d = v * t

d = (0.999 c) (4 light-years)

d = 3.996 light-years

This distance is very slightly less than 4 light-years.