Energies and angular momenta of periodic Schwarzschild geodesics

We consider physical parameters of Levin and Perez-Giz's "periodic table of orbits" around the Schwarzschild black hole, where each periodic orbit is classified according to three integers (z, w, v). In particular, we chart its distribution in terms of its angular momenta L and energy E. In the (L, E) -parameter space, the set of all periodic orbits can be partitioned into domains according to their whirl number w, where the limit of infinite w approaches the branch of unstable circular orbits. Within each domain of a given whirl number w, the infinite zoom limit limz ->infinity(z, w, v) converges to the common boundary with the adjacent domain of whirl number w - 1. The distribution of the periodic orbit branches can also be inferred from perturbing stable circular orbits, using the fact that every stable circular orbit is the zero -eccentricity limit of some periodic orbit, or arbitrarily close to one.