= Black-hole sphere of influence
{title2=$r_{\rm inf}\simeq GM_\bullet/\sigma^2$}
The <black-hole sphere of influence> is a characteristic radius where the central <black hole> appreciably changes surrounding stellar dynamics. Equating its <Newtonian gravitational potential> scale $GM_\bullet/r$ to the ambient squared <velocity dispersion> gives $r_{\rm inf}\simeq GM_\bullet/\sigma^2$. Dynamical mass measurements depend on angular resolution $r_{\rm inf}/D$, tracer brightness, and degeneracies in the orbital distribution, not solely on <black hole> mass.
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