  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
$\lim_{z\rightarrow\infty}(z,w,v)$ 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.
