The distance to Planet X from Earth is 1.00 light-year. Part A How long does it

Question

The distance to Planet X from Earth is 1.00 light-year.

Part A How long does it take a spaceship to reach X, according to the pilot of the spaceship, if the speed of the ship is 0.620c relative to X? t1 = ______y

Part B How long does it take the ship to make the trip according to an astronaut already stationed on Planet X? t2 =________ y

Part C Determine the distance between Earth and Planet X according to the pilot. L1 =__________ ly

Part D Determine the distance between Earth and Planet X according to the X-based astronaut. L2 =_________ ly

Explanation / Answer

  To Astronout already based on platerx x the time is
t2 = 1 c-years / 0.62c

= 1.613 years.

To the pilot, this is reduced by dividing by a time dilation factor gamma

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

=1/sqrt (1-(0.62)^2)

=0.7846


Time taken according to the pilot on spaceship,

t1= gamma* 1/ 0.62 years

=1.265 years.

L2 =1 light years.

L1 = 1*gamma = 1*0.7846 = 0.7846 light years.

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