•First-order Epicyclic theory (yes, epicycles!)
•Just an overview here for context
•Work with nearly circular orbits in a flattened axisymmetric gravitational potential. Write down the equations of motion in polar coordinates, using a Taylor series.
•Basically just looking at the linear deviation from circular orbits.
You wind up with equations that solve for the radial excursions and the precession of the orbit in terms of “epicycles” of
frequency κ.