Question

1. You and your twin just born, and your Dad decided to take you on a trip to show you a planet X. Your starship passes Earth with a relative speed of 0.999 c and maintains the same speed for the entire trip. After traveling 1 year (your time), you and your Dad stop at planet X, turn and then travel back to Earth with the same relative speed (assuming you and your Dad can stop and go like star-track without losing much time). The trip back to Earth takes another year (your time), (a) What is the value of the Lorentz factor γ? (b) How long does the round trip take according to you? (c) How long does the round trip take according to measurement made on Earth by your mother? (d) How old is your twin when you get back on Earth? Which twin is older?

Answer 1

A. The Lorentz factor = 1/ sqrt( 1- v^2/c^2 ) = 1/sqrt ( 1- 0.999^2) =22.37

B. Acoording to the person in startship the time is 2 years as stated in the question also the time spent on the star is negligible compared to the total time is its 2 years for the round trip.

C. Using Time dilation relationship t in moving frame= t on earth /lorentz factor

so the time taken for the trip from the earth t on earth = 22.37*2= 44.73 years

d. So when you return you are two years old while your twin on earth is 44.73 years old. So the kid on Earth is older.