Relativity problem, or how time flies when you're walking on the bridge of the Starship Enterprise

[ abridged from problem 3.22 on pg 76 of wolfgang rindler's relativity ]

A rocket moves from in an inertial frame S with constant proper acceleration 9.8 m/s^2 (thus giving maximum comfort to its passengers).  Find its Lorentz factor relative to S when its own clock indicates times tau = 1 day, 1 year, 10 years [...] If the rocket accelerates for 10 years of its own time, then decelerates for 10 years, and then repeats the whole maneuver in the reverse direction, what is the total time elapsed in S during the rocket's absence?

[ answer: 44,052 years]