In a system for determining the position of a spacecraft based on vector determinations, a direction vector is measured in a body-fixed coordinate system; a reference direction vector is determined within a reference coordinate system based on the path position of the spacecraft and an orbit model; the overall spin vector of the spacecraft is determined within the body-fixed coordinate system; and a reference overall spin vector of the spacecraft is determined within a reference coordinate system by time propagation of known initial values of the overall spin of the spacecraft or by time tracking of a reference model. The position of the spacecraft is determined based on the four vectors.