  We show the traditional rocket problem, where the ejecta velocity is assumed
constant, can be reduced to an integral quadrature of which the completely
non-relativistic equation of Tsiolkovsky, as well as the fully relativistic
equation derived by Ackeret, are limiting cases. By expanding this quadrature
in series, it is shown explicitly how relativistic corrections to the mass
ratio equation as the rocket transitions from the Newtonian to the relativistic
regime can be represented as products of exponential functions of the rocket
velocity, ejecta velocity, and the speed of light. We find that even low order
correction products approximate the traditional relativistic equation to a high
accuracy in flight regimes up to $0.5c$ while retaining a clear distinction
between the non-relativistic base-case and relativistic corrections. We
furthermore use the results developed to consider the case where the rocket is
not moving relativistically but the ejecta stream is, and where the ejecta
stream is massless.
