τ Ceti is the closest single star that is similar to the Sun. At time t=0, Alice leaves Earth in her starship and travels at a speed of 0.95c to τ Ceti, 11.7 ly away as measured by astronomers on Earth. Her twin brother, Bob, remains at home, at x=0.
(a) According to Bob, what is the interval between Alice's leaving Earth and arriving at τ Ceti?
(b) According to Alice, what is the interval between her leaving Earth and arriving at τ Ceti?
(c) Upon arriving at τ Ceti, Alice immediately turns around and returns to Earth at a speed of 0.95c. (Assume that the actual turnaround takes negligible time.) What was the proper time for Alice during her round trip to τ Ceti?
(d) When she and Bob meet on her return to Earth, how much younger will Alice be than her brother?