A Bussard ramjet is a relativistic spacecraft, fueled by fusion energy of cosmic matter that is collected during the flight. We derive the equation of motion of such a spaceship for a given mass density in space and the fusion mass defect. Two ramjet engine scenarios, where the thrust for propulsion is generated by emission of photons or acceleration of matter, are outlined. As long as not all collected matter is transformed into fusion energy, mass engines are superior to photon engines. If the collected matter is stopped by the spacecraft before fusion it may not reach relativistic terminal velocities. For an ideal ramjet, where no matter is stopped for the generation of energy for propulsion, endless acceleration and relativistic velocities may be obtained such that crossing the universe in a human lifespan would be possible. A journey along one space coordinate and the smallest possible radii of curves were evaluated. The results are compared to the plots in the novel “Tau Zero” by Poul Anderson.