Equal-rate rocket burning and accretion ($v(t)=u(1-e^{-\alpha t/M_0})$)

If stationary mass arrives at the same constant time rate as fuel is ejected, total rocket mass stays fixed. The rocket equation with stationary mass accretion is then $M_0\dot{v}+\alpha v=\alpha u$. For initial rest, speed approaches the relative exhaust speed exponentially with relaxation time $M_0/\alpha$. This is the regular equal-rate limit of the unequal-rate mass-power formula.