The nearest star beyond our solar system is about 4 light years away. A spaceshi

Question

The nearest star beyond our solar system is about 4 light years away. A spaceship can get to the star in 5 years, as measured on Earth.

Part A

How long would the ship's pilot judge the journey to take?

Express your answer using two significant figures.

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Part B

How far from Earth would the pilot find the star to be?

Express your answer using two significant figures.

The nearest star beyond our solar system is about 4 light years away. A spaceship can get to the star in 5 years, as measured on Earth.

Part A

How long would the ship's pilot judge the journey to take?

Express your answer using two significant figures.

t =   y  

SubmitMy AnswersGive Up

Part B

How far from Earth would the pilot find the star to be?

Express your answer using two significant figures.

x =   ly  

Explanation / Answer

distance of the star from the earth is 4 light years = 4*3*10^8*365*24*60*60= 3.78432*10^16 m = 3.78432*10^13 km

time taken to reach the star is t = 5 years = 5*365*24*60*60 = 157680000 s

now velocity of the space ship from earth is v = 3.78432*10^16/157680000 =240000000 m/s= 24000 km/s

now journey time T'= T_0*gamma , gamma = 1/(sqrt(1-v^2/c^2)) = 1/ sqrt((1-(24000000^2/(3*10^8)^2)))

                               = 1.00321

a) T' = T_0*gamma
= 157680000*1.00321=158186152.80 s= 5.01 y

b) distance of the solar system is L'= Lo*gamma= 3.78432*10^16*1.00321= 3.7964676672*10^16 m = 4.01 ly

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