The exact solution of the relativistic orbit equation and some of its consequences are treated. Consideration of the hydrogen atom leads to the determination of the relationship between the four physical forces. Then photonic orbits are investigated and the relation to the Weierstrass theory is given. Algebraic conditions for closed orbits are considered. Eventually, it is shown that the system which compensates the perihel-shift is a particularly good reference system for an observer. This leads to Cartesian ovals as curves of relativistic motion.