[camacazio]

I screwed up my chain rule. These derivatives of Length with respect to time needed to be redone. My function for the accelleration of expansion is too messy to type up. For the rate of expansion at a given time, however, is not so difficult.

(L/c)*(vng-(ng)^2*t)/[1-((v-ngt)/c)^2]

The second derivative with respect to time gave me a nasty function. It also continues to not tend towards 0. This function, however, does. It's units are in m^2/s^2 though, which is a huge set-back. I should have units of m/s, since it should be a Length devided by a Time.