Equation of motion of an interstellar Bussard ramjet with radiation loss

An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In a recent paper, it was shown that the relativistic equation of motion of an ideal ramjet (100% efficient hydrogen fusion engine) is analytical. When a radiation loss appears, the speed of the ramjet is limited. But, the parametric equations, in terms of the ramjet's speed, for the position of the ramjet in the inertial frame of the interstellar medium, the time in this frame, and the proper time indicated by the clocks on board the spaceship, can still be obtained in an analytical form. The nonrelativistic motion and the motion near the limit speed are studied.