  Action-angle coordinates are a tool commonly used in celestial mechanics to
systematically parametrize and store general solutions of the equations of
motion of astrophysical bodies. I perturbatively construct action-angle
coordinates for bound test particle motion in static, spherically symmetric
space-times using a post-circular expansion. Then I specialise the expressions
to the motion in the gravitational fields of Schwarzschild black holes and give
explicit formulas for the Hamiltonian to the 10th power in the radial action
(20th power in eccentricity), and the transformation to angle coordinates up to
the 8th harmonic with respect to a relativistic orbital anomaly. The results
provide a closed-form perturbative solution for the orbital motion parametrized
by coordinate time that will find applications in the modelling of compact
binary inspirals and other fields of astrophysics.
