Question

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

Answer 1

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

Step-by-step 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.