A spaceship is headed toward Alpha Centauri at 0.999c. According to us, the distance to Alpha Centauri is about 4 light-years. H
ow 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 <em>c) very slightly less than 4 light-years</em>
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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 <em>very slightly less than 4 light-years. </em>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<em> very slightly less than 4 light-years. </em>
