Solution
= Solution
The total ring <mass> is $M=2\pi r\lambda_m=1.257\times10^7\,\mathrm{kg}$. For the <axial gravitational field of a uniform ring>, transverse <force> components cancel by symmetry; each axial component has projection factor $z/\sqrt{r^2+z^2}$. Thus
$$
\boxed{\mathbf F=-\frac{GMm z}{(r^2+z^2)^{3/2}}\,\hat{\mathbf z},
\qquad |\mathbf F|=3.04\times10^{-10}\,\mathrm N.}
$$
The <force> points towards the ring's centre along its axis.