Radial Mach number
= Radial Mach number
{title2=$M_r=\widehat r\cdot v/c_0$}
The radial <Mach number> is the source <velocity> projected toward the observer, divided by the <sound speed>. It enters the <moving-surface retarded Jacobian> through $d|x-y(\tau)|/d\tau=-\widehat r\cdot v$. The sign is directional: a source moving toward the observer has positive $M_r$ and compressed arrival times.