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 1.09 yhas elapsed, as measured on the ship. Clocks in the earth'sreference frame show that the voyage lasted 2.77 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

t = / (1 - v2 /c2)      where isthe proper time (frame in which clock is at rest) (1 - v2 / c2) = 1.09/ 2.77 = .394 v = .919 c L = L0 (1 - v2 /c2)   where L0 is the proper length (measurement stick is at rest - earthframe) L0 = v t = .919 c * 2.77 y = 2.55light-years   as measured on earth L = .394 * 2.55 = 1 L-y as measured on ship Check:     .919 c * 1.09 years = 1L-y      speed of ship * time measured onship

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