# Copernicus's epicycles from Newton's gravitational force law via linear perturbation theory in geometric algebra

@article{Sugon2008CopernicussEF, title={Copernicus's epicycles from Newton's gravitational force law via linear perturbation theory in geometric algebra}, author={Quirino Sugon and Sarah Bragais and Daniel J. Mcnamara}, journal={arXiv: Space Physics}, year={2008} }

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…

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