In this paper the non relativistic theory of UFT413 is extended to the relativistic, ECE2 covariant, level and the orbit equations obtained from the kinematics and the Lagrangian, giving exact agreement. A triple cross check is completed with the relativistic hamiltonian. The results are two simultaneous relativistic equations which are solved numerically using computational methods developed by co author Horst Eckardt. The orbit equations are transformed into a rotating frame to define the spin connection and vacuum force on the relativistic level. The relevant infinitesimal line element is solved to give the Einstein energy equation and shown to be the line element of a free relativistic particle. The orbit equation of this particle is obtained in two different ways, giving precise agreement. The next step in UFT415 will be to develop the theory in the most general spherically symmetric space, giving m theory. In a previous UFT paper, UFT190, it has been shown that m theory gives a shrinking orbit. It will be interesting to find whether the relativistic rotating frame theory is enough to give a shrinking orbit, or whether additional input from m theory is needed. In UFT413 it was shown that the classical limit gives a lot of important new information: precession, retrograde orbits and so on, but not a shrinking orbit.

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