  We use 57 recently found topological satellites of
Broucke-Hadjidemetriou-Henon's periodic orbits with values of the topological
exponent $k$ ranging from $k$ = 3 to $k$ = 58 to plot the angular momentum $L$
as a function of the period $T$, with both $L$ and $T$ rescaled to energy
$E=-\frac12$. Upon plotting $L(T/k)$ we find that all our solutions fall on a
curve that is virtually indiscernible by naked eye from the $L(T)$ curve for
non-satellite solutions. The standard deviation of the satellite data from the
sixth-order polynomial fit to the progenitor data is $\sigma = 0.13$. This
regularity supports Henon's 1976 conjecture that the linearly stable
Broucke-Hadjidemetriou-Henon orbits are also perpetually, or
Kolmogorov-Arnold-Moser stable.
