Natural units of star clusters angular momentum and energy I'm calculating the total angular momentum of a bunch of theoretical stars of a few solar masses, separated by a few light years, moving at velocities of about a few dozens of km / sec.

Mechanical angular momentum relative to an arbitrary origin (the cluster's center of mass is a good choice) is this :
\begin{equation}
\vec{L} = \sum_i \vec{r}_i \times m_i \, \vec{v}_i,
\end{equation}
so the SI units are $\mathrm{kg} \cdot \mathrm{m}^2 / \mathrm{sec}$.  But in real astronomy, what should be the most simple/natural units for star clusters ?  $M_{\odot} \cdot (\mathrm{ly})^2 / \mathrm{year} \equiv M_{\odot} \, c^2 \cdot \mathrm{year}$ ?

What are the angular momentum units used by astronomers ?

And what about energy units for a cluster of stars ?  I'm interested in kinematical energy and gravitationnal potential energy of the whole cluster.  Certainly not joules !?  And $M_{\odot} \, c^2$ would certainly be too much, I suppose !
Using unit analysis, I've found that a natural unit of angular momentum should be
\begin{equation}\tag{1}
L_0 = \frac{G M_{\odot}}{c} \approx 8.816 \times 10^{41} \, \text{kg} \, \text{m}^2/\text{s}.
\end{equation}

In the case of a bounded system of two equal masses, circularly moving around their center of mass, the total angular momentum (relative to the center of mass) is
\begin{equation}\tag{2}
L_{\text{bound}} = 2 M \, v \, r = \frac{2M \, v^2 \, r}{v}.
\end{equation}
Now, using Newton's equation and the gravitationnal force, we have
\begin{equation}
M \, v^2 = \frac{G M^2}{4 \, r}.
\end{equation}
Thus, equation (2) becomes :
\begin{equation}\tag{3}
L_{\text{bound}} = \frac{G M^2}{2 \, v}.
\end{equation}
The classical theory cannot be trusted when $v \sim c$, and since $v &lt; c$ (forgetting the 2 factor) :
\begin{equation}\tag{4}
L_{\text{bound}} \approx \frac{G M^2}{v} &gt; \frac{G M^2}{c} \equiv L_0.
\end{equation}
So $L_0$ appears to be a good unit.  When $L \sim L_0$, we then need relativity.  We're in a classical regime when $L \gg L_0$.

The system isn't bounded when $L \gg L_{\text{bound}}$, which implies $L \ggg L_0$.

I don't know if this is a good way to introduce the $L_0$ unit defined by (1).  Any opinion/suggestions/comments on this ?

Do astronomers use $G M^2 / c$ as natural unit of angular momentum, when they study star clusters and globulars ?