If anyone is interested, I figured out my error.... and it was such a simple one, I'm almost kicking myself for not realizing it. The error was in the sentence quoted above.We can then simply accept v(T0) = aT0
The problem was that I was thinking of the acceleration of the rocket as constant from the point of view of the stationary observer. This would require the rocket continually increase its throttle, as discussed in the thread http://www.sciforums.com/showthread.php?s=&threadid=15271
Instead, the derivation that others provided is that the acceleration is constant from the point of view of a person on the rocket. This means v(T<sub>0</sub>) does not equal aT<sub>0</sub>. v(T<sub>0</sub>) actually equals aT<sub>0</sub> * 1/<font face=symbol>g</font>. This works out to
v = at / sqrt(1 + (at/c)<sup>2</sup>)
and leads to an arcsinh, rather than an arcsin, in the final answer.
I would like to add, though, that if the rocket's acceleration is constant from the point of view of a stationary observer, then my derivation is correct. It's the right answer, just the wrong problem.
- Warren