1. The problem statement, all variables and given/known data I've done the first part, I'm just posting it for completeness A rocket at rest in deep space has a body of mass m and carries an initial mass M of fuel, which is ejected at non-relativistic speed v0 relative to the rocket. Show that the speed of the rocket vf after all the fuel is ejected is given by vf = v0 ln(1 + M/m) Now consider the case of a relativistic rocket, where matter/antimatter fuel is annihilated and expelled from the rocket as photons. Show that the final speed of this rocket is given by 1 + M/m = [(c + vf)/(c - vf)]^0.5 2. Relevant equations 3. The attempt at a solution So for the second bit: I called the mass at any instant n, and attempted to conserve momentum: y1(n + &n)v = y2(v + &v)n - p Where y1 is the gamme for the velocity before the emission of a small fuel element &n (the & is supposed to be a delta), and y2 is the gamme for the velocity of the rocket after emission. y1(n - dn)v = y2(v + dv)n - E Where E is the energy of the emitted photon(s). Here's where I get stuck. Is E = &nc^2 or E = y1 &nc^2 or something else?