  We derive Copernicus's epicycles from Newton's gravitational force law by
assuming that a planet's orbit is a perturbed circular orbit, with the
perturbation defined to be co-rotating with the said orbit. We substitute this
orbit expression into Newton's gravitation law and showed that the perturbation
satisfies the linear part of Hill's oscillator equation for lunar motion. We
solve this oscillator equation using an exponential Fourier series and impose
the boundary conditions at the aphelion and perihelion to derive Copernicus's
formulas for the eccentric, deferent, and epicycle. We show that for small
eccetricity, the Copernican orbit expression also leads to Kepler's law of
areas for planetary motion. The formalism we use is the Clifford (geometric)
algebra Cl_{2,0}.
