According to you, an astronaut\'s trip from Earth to a distant planet takes 24 y

Question

According to you, an astronaut's trip from Earth to a distant planet takes 24 years. The distant planet is in the same frame of reference as the Earth, and the astronaut travels at constant velocity between the two planets.

(a) How long does the trip take, according to the astronaut, if the astronaut's speed with respect to you is 64% of the speed of light?
  years

(b) What is the distance between the planets, according to you?
   light-years

(c) What is the distance between the planets, according to the astronaut?
light-years

Explanation / Answer

(a) given speed of astronaut wrt earth = 0.64c

hence gama = 1/(1-(v/c)^2)^(1/2)

= 1/(1 - 0.4096)^(0.5)

= 1.30

time taken according to astronaut = gama*24 years = 1.30*24 years = 31.2 years

(b) distance of plant according to me = 24 year*0.64c

= 24 year*0.64*1 light year/year = 15.36 light years

(c)  distance of plant according to astronaut = 15.36/gama = 15.36/1.30 gight years = 11.82 light years

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