Equations of motion of a hybrid relativistic rocket and Bussard ramjet

A possible generalization of a Bussard ramjet is a vehicle that carries part of the fuel from the beginning of the journey and collects the other part from the interstellar medium. Its velocity could be controlled by regulating the amount of scooped and ejected mass. In this paper, the motion of such a hybrid spacecraft is analyzed within the framework of special relativity. The results permit to compare the performance of a Bussard ramjet and a standard rocket (which is known to be quite inadequate for interstellar travels). It turns out that even a hybrid ramjet is well outside presently conceivable technology.