The aliens intiated their attack to the earth! They shoot bullets with mass $m$ and speed $v$ from a far-awar planet. To defend, humans built a field $U=\alpha/r$ that can repel the bullets. What regions are safe? The answer turns out to be the interior of a circular paraboloid.
https://ulysseszh.github.io/physics/2023/02/01/defend-aliens.html?
The aliens intiated their attack to the earth! They shoot bullets with mass $m$ and speed $v$ from a far-awar planet. To defend, humans built a field $U=\alpha/r$ that can repel the bullets. What regions are safe? The answer turns out to be the interior of a circular paraboloid.