Recoil angle in a two-body elastic collision (${\theta }_2=(\pi -{\theta }^{\ast })/2$)

For a nonrelativistic elastic collision with the target initially at rest, let ${\theta }^{\ast }$ be the outgoing projectile angle in the centre-of-mass frame. The laboratory target velocity is proportional to $(1-\cos {\theta }^{\ast },-\sin {\theta }^{\ast })$. Its unsigned recoil angle is therefore $(\pi -{\theta }^{\ast })/2$, independent of the mass ratio. At zero deflection the target is stationary and its direction is undefined; the right-angle value is a limit.