A habitable star system is about 12 light years from the Earth. A twin astronaut from earth leaves his sibling behind on a spaceship that very rapidly reaches cruising speed of 12/13c towards the star system, rapidly stops and plants a flag on the planet, then rapidly reaches cruising speed on the return trip to earth, and lands safely back on earth.
a. Determine the Lorentz factor for the relative motions of the spaceship and earth-star system.
b. How far away is the star system according to the astronaut just after initially reaching cruising speed?
c. How long does the astronaut travel according to the earth-bound sibling?
d. How old will the astronaut be when the spaceship returns?