A rocket of initial mass, mi, starts at rest and propels itself by an engine ejecting photons backwards. After the rocket has reached a speed of v, it switches off its engine and its final mass is mf. By using four-momenta and three-momenta for the rocket and photon beam, calculate the ratio of the initial to final mass for the rocket as a function of ẞ only.

A rocket of initial mass, mi, starts at rest and propels itself by an engine ejecting photons backwards. After the rocket has reached a speed of v, it switches off its engine and its final mass is mf. By using four-momenta and three-momenta for the rocket and photon beam, calculate the ratio of the initial to final mass for the rocket as a function of ẞ only.