= Transverse relativistic interception
{title2=$t=\frac{a}{\sqrt{u^2-v^2}}$}
In a station frame, a target begins at $(0,a)$ with <velocity> $(v,0)$, and an interceptor launches from the origin at <speed> u greater than v. Straight-line interception requires its <velocity> components to be $(v,\sqrt{u^2-v^2})$, and takes station time $t=a/\sqrt{u^2-v^2}$. The target-frame coordinate interval is $\gamma_v(t-v\Delta x/c^2)=t/\gamma_v$, since $\Delta x=vt$. This differs from the interceptor's <proper time> $t/\gamma_u$. A symmetric return to the stationary launch point instead has target-frame round-trip coordinate duration $2\gamma_v t$, because its endpoint spatial separation in the station frame is zero.
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