Question

Alpha Proxima with a distance of only 4.233 light years is the star that is closest to our Sun. In the far distant future a spaceship travels from Earth to Alpha Proxima with a constant speed of 0.900c relative to the earth.

a) How much time would elapse during the trip on a clock on board the spaceship?

b) How much time would elapse during the trip on a clock on Earth?

Answer 1

(a)

for observers on spaceship, distance to star will be contracted

L = L_o * sqrt ( 1 - v² / c²)

L = 4.233 * sqrt ( 1 - 0.9² c² / c²)

L = 1.845 light years

so,

time = 1.845 / 0.9

time = 2.05 years

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for observers on earth, clock on spaceship runs slow

so,

t = 2.05 / sqrt ( 1 - 0.9² c² / c²)

t = 2.05 / 0.435

t = 4.7 years