Aspaceship 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

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.

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