= Spherical mass profile for a flat rotation curve
{title2=$M(<r)=v_0^2r/G,\quad\rho(r)=v_0^2/(4\pi Gr^2)$}
In a spherically dominated <Newtonian gravitational field>, the <circular orbit> speed satisfies $v_c^2=GM(<r)/r$. A flat <galaxy rotation curve> therefore implies $M(<r)=v_0^2r/G$. Differentiating the enclosed mass gives $\rho=(4\pi r^2)^{-1}dM/dr$, yielding the inverse-square density profile. This is a halo-region approximation, not a mass inversion for a flattened stellar disk. A flat curve extending to infinite radius would imply infinite mass, so a real halo profile must eventually change or truncate.
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