Polar projectile Coriolis deflection ($d=\Omega u\cos \theta (2u\sin \theta /g{)}^2$)

In a flat uniform-gravity model at the North pole, Earth's rotation is vertical. To first order in angular speed, the horizontal component $u\cos \theta$ gives constant transverse Coriolis acceleration $-2\Omega u\cos \theta$ toward the right of the aiming direction. The return flight time is $2u\sin \theta /g$, proving the displayed miss distance. At the maximum unperturbed range, $\theta =45^{\circ }$, it becomes $\sqrt{2}\Omega u^3/g^2$. curvature, varying gravity, air drag and second-order rotational terms are excluded.