  Relativistic Coulomb systems are studied in velocity space, prompted by the
fact that the study of Newtonian Kepler/Coulomb systems in velocity space
provides a method much simpler (and more elegant) than the familiar analytic
solutions in ordinary space. The key for the simplicity and elegance of the
velocity-space method is the linearity of the velocity equation, which is a
unique feature of $1/r$ interactions for Newtonian and relativistic systems
alike, allowing relatively simple analytic discussion with coherent geometrical
interpretations. Relativistic velocity space is a 3-D hyperboloid ($H^3$)
embedded in a 3+1 pseudo-Euclidean space. The orbits in velocity space for the
various types of possible trajectories are discussed, accompanied with
illustrations.
