Circular orbital speed from surface gravity ($v=\sqrt{g_s{R}^2/r}$)

For a spherical central body of radius $R$ with surface gravity $g_s=GM/R^2$, a circular test-particle orbit at radius $r$ has $v=\sqrt{g_s{R}^2/r}$. surface gravity is used to infer $GM$, not incorrectly kept constant at orbital height.