The starship Enterprise leaves a distant earth colony,which is nearly at rest wi

Question

The starship Enterprise leaves a distant earth colony,which is nearly at rest with respect to the earth. The ship travelsat nearly constant velocity toward earth. When theEnterprise reaches earth 1.08 yhas elapsed, as measured on the ship. Clocks in the earth'sreference frame show that the voyage lasted 2.70 y. How far from earth is the colony, as measuredin the reference frame of the earth?
light years

(b) How far from earth is the colony, as measured in the referenceframe of the ship?
light years
How far from earth is the colony, as measuredin the reference frame of the earth?
light years

(b) How far from earth is the colony, as measured in the referenceframe of the ship?
light years

Explanation / Answer

1 - v2/c2 = (.96/3.06)2
v2/c2 = 1 -(.96/3.06)2 = .9016
v = .949c
1) d = v*t = .949 * .96 = .9115 light years
2) d' = d*sqrt(1-v2/c2) = .2860 lightyears
v2/c2 = 1 -(.96/3.06)2 = .9016
v = .949c
1) d = v*t = .949 * .96 = .9115 light years
2) d' = d*sqrt(1-v2/c2) = .2860 lightyears

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