  The Hamilton-Jacobi equation for test particles in the Kerr geometry is
separable. Using action-angle variables, we establish several relations between
various physical quantities that characterize bound timelike geodesic orbits
around a spinning black hole, including the particle's rest mass, energy,
angular momentum, mean redshift and fundamental frequencies. These relations
are explicitly checked to hold true in the particular case of equatorial
circular orbits. An application to the gravitational wave-driven, adiabatic
inspiral of extreme-mass-ratio compact binaries is briefly discussed.
