= Finite normalization of an energy-only Kepler distribution
{title2=$N=(2\pi)^3\int_0^\infty L^2F(-\mu^2/(2L^2))\,dL$}
For bound <Kepler orbits> with gravitational parameter $\mu$, integrating the <Delaunay variables> over $0<G<L$, $-G<H<G$ and their three full angle periods gives the displayed population. A globally defined <thermal eccentricity distribution> requires this integral to converge, or an explicit finite action range. Merely having finite $F(E)$ at every energy does not suffice: $F=1$ yields an infinite integral at large $L$. At each fixed energy, or on every finite normalized action band, the cumulative eccentricity fraction remains $e^2$.
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