Question

On his trip from the sun to Alpha Centauri, bob rests on his coffee break at an interstellar cafe, exactly midway along a line that joins the two stars. Let his break position be x=0 and his break start time =0 (again, he as at rest relative to the stars). Violent explosions occur on both stars, on the sun at position = -2.2ly and time = 0 and on Alpha Centauri at position 2.2ly and time = 0, measured in Bob's frame. Alice passes Bob exactly when her clock reads 0y at the speed 0.998c (she's not doing a coffee break).

a) According to Alice, what is the position and time of the explosions on the Sun and on Alpha Centauri? Answer in ly and y respectively.

b) Assume that Bob stays at the coffee shop for 1 year by his watch (he likes coffee). How long will Alice claim that Bob stayed at the coffee shop? (Alice continues her way to Alpha Centauri at 0.998c without stopping)

Answer 1

1) positions of alpha century w.rt alice is

sp at t=0 c= 2.2 ly and v= 0.998c

so we get

and of sun then

and time of explosion of alpha century w,r,t alice

so at t=0 x=2.2ly

so for sun alice move with -v velocity and x= -2.2ly

so again we get

2)time will be dilated in alice's clock

so

so

so for v= 0.998c we get

as seen by Alice watch