Question

# The starship Enterprise leaves a distant earth colony, which is nearly at rest with respect to...

The starship Enterprise leaves a distant earth colony, which is nearly at rest with respect to the earth. The ship travels at nearly constant velocity toward earth. When the Enterprise reaches earth 1.02 y has elapsed, as measured on the ship. Clocks in the earth's reference frame show that the voyage lasted 2.89 y.

How far from earth is the colony, as measured in the reference frame of the earth?
Unit: light years

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

Unit: light years

By time dilation

more time = gamma *less time

2.79 = gamma * 1.02

gamma = 2.89/1.02 = 2.83333333

and we know

gamma = 1/ sqrt( 1- v^2/c^2)

2.83333333 = 1/ sqrt( 1- v^2/c^2)

v≈0.935646 c

Then the distance from the earth to colony as measured in theframe of reference of earth is

= 2.89y*0.935646 c =2.70401694 ly

B)

And the distance from the earth to colony as measured inthe frame of reference of ship is

= 1.02y* 0.935646c =0.95435892 ly

Goodluck for exams Comment in case any doubt, will reply for sure..

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