= Solution
For a steady, spherically symmetric radial inflow, <conservation of mass> makes the <mass accretion rate> independent of radius:
$$
\dot M=4\pi r^2\rho |v_r|.
$$
Atomic <hydrogen> gives $\rho\simeq m_Hn$. The Newtonian <free-fall speed> from rest at infinity is $|v_r|=\sqrt{2GM/r}$, obtained by setting the specific mechanical <energy> $v_r^2/2-GM/r$ to zero. Hence the <spherical free-fall accretion rate> is
$$
\boxed{\dot M=4\pi m_Hn\sqrt{2GM}\,r^{3/2}.}
$$
Using the given values gives $\rho\simeq1.67\times10^{-21}\,\mathrm{kg\,m^{-3}}$, $|v_r|\simeq2.98\times10^5\,\mathrm{m\,s^{-1}}$, and
$$
\boxed{\dot M\simeq5.65\times10^{18}\,\mathrm{kg\,s^{-1}}
\simeq8.96\times10^{-5}\,M_\odot\,\mathrm{yr^{-1}}.}
$$
The area factor assumes a full spherical inflow with negligible angular momentum. With only a local <number density> and speed, an arbitrary nonspherical inflow's total rate is not fixed; one instead integrates $-\rho\mathbf v\cdot d\mathbf S$ over the inflow surface. This is a flux estimate, rather than the pressure-selected <Bondi accretion> solution.
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