Stellar Orbits
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.