The equation of motion of an interstellar Bussard ramjet

An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. The velocity of an ideal ramjet (100% efficient hydrogen fusion engine) could, in theory, approach the speed of light in a time of the order of years, or less. The relativistic effects for such a spaceship would be very large. 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, are presented in an analytical form. The nonrelativistic and ultrarelativistic limits are studied. The possibility of using interstellar antimatter as a source of energy is also discussed