John stays on Earth, and his sister Jane departs on January 1st, 2012 towards a

Question

John stays on Earth, and his sister Jane departs on January 1st, 2012 towards a planet B at a distance 8 light years away (in the frame of the earth). She travels back and forth at a speed of 0.8 c, and assume that she takes no time in accelerating, decelerating. it takes 20 years in the earth system for her to return (returning on January 1st 2032, according to earth calendars), while the calendar in her spaceship will indicate January 1st 2018 upon arrival to planet B, and January 1st 2024 the day she meets again her (now eight years older) brother.

A) Draw a CAREFUL spacetime diagram with axes for the two systems (the one of the earth and the one moving towards B at a speed of 0.8c. labeling carefully the years in both time axes. MAKE SURE THE DIFFERENT AXES HAVE THE
APPROPRIATE SCALES. Show some of the rays ( the photographs they
exchange the day of their birthdays). You should be able to show the one he
sends in 2013 and in 2014, and when do they arrive to her. Also show the rays
she sends him, on the years 2013,2014,2015,2016, 2017, 2018 and when does he
receive them.

B) Now show another spacetime diagram with axes for the two systems (the one form the earth and the one moving to the left during her return trip.) Be careful here because the origins are different. She departs on year 2018, from a place with x-coordinate 8 light years, while he is at that moment in year 2022, and at position x= 0. Show in this case as well a few of his rays ( emitted between the years 2022 and 2032, showing when she receives them) and a few of hers (emitted between the year 2018 and 2024 and when does he receive them).

Explanation / Answer

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