The proposed experiment SLAC E166 intends to generate circularly polarized gamma rays of energy 10 MeV by passing a 50 GeV electron beam through a meter long wiggler with approximately 400 periods. Using an analytic model formulated by Rullier and me, I present calculations of electron trajectories. At this extremely high energy the trajectories are described quite well by the model, and an extremely simple picture emerges, even for trajectories that that fail to encircle the axis of the wiggler. The calculations are successfully compared with standard numerical integration of the Lorentz force equations of motion. In addition, the calculation of the spectrum and angular distribution of the radiated photons is easily carried out.