Apparent superluminal motion (${\beta }_{\mathrm{app}}=\beta \sin \theta /(1-\beta \cos \theta )$)

A moving feature can have inferred transverse speed ${\beta }_{\mathrm{app}}c$ greater than $c$ because its second signal starts closer to the observer. The light-travel delay gives ${\beta }_{\mathrm{app}}=\beta \sin \theta /(1-\beta \cos \theta )$, whose maximum is $\Gamma \beta$ at $\cos \theta =\beta$. No local material or signal speed exceeds $c$.