= Geometric correction for heliocentric velocity dispersion
{title2=$A(r,R_\odot)$}
For tracers sampled uniformly on a Galactocentric shell of radius $r$, with the Sun at radius $R_\odot$, the correction in the <heliocentric projection of a spherical velocity dispersion> is
$$
A=\frac{r^2+R_\odot^2}{4r^2}
-\frac{(r^2-R_\odot^2)^2}{8r^3R_\odot}
\ln\left|\frac{r+R_\odot}{r-R_\odot}\right|.
$$
The limiting value at $r=R_\odot$ is $1/2$; it tends to $2/3$ as $r/R_\odot\to0$ and to $2R_\odot^2/(3r^2)$ at large radius. Uniform heliocentric <solid angle> at fixed $r>R_\odot$ instead gives $A=2R_\odot^2/(3r^2)$ exactly. Specify the selection measure when applying the correction.
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