1. The problem statement, all variables and given/known data
Assume a rocket ship leaves the earth in the year 2100. Castor, one of a set of identical twins born in 2080, remains on earth to work at Mission Control, while the other twin, Pollux, travels in the rocket. Ignore the motion of the earth relative to the fixed stars. The rocket is constructed so that it has an acceleration g in its instantaneous rest frame (making the astronauts feel at home) Suppose the rocket accelerates in a straight line path for 5 years (by its OWN chronometer), decelerates at the same rate for another 5 years (of its own time), turns around (in negligible time), accelerates back for 5 years, decelerates for 5 years, and then lands on earth.

a) How old is Pollux according to his watch?
b) What year is it on Earth?
c) How far away from the earth did the rocket travel?

2. Relevant equations

Relativistic velocity formulas, time formulas, and acceleration formulas.

3. The attempt at a solution

So I've taken a time derivative of the velocity formulas and it matches with my book, but this only gives me accelerations in terms of other reference frames. What I'm having trouble with is calculating the equation of motion for the rocket according to the astronauts. How can I continuously add their velocities (because they are accelerating), to say get their velocity as a function of time in their frame? And once I get that, how can I handle the fact that gamma is changing in the time dilation formula?