= Common Doppler scaling of spectral-line separations
{title2=$\Delta\lambda_{\rm obs}=D\,\Delta\lambda_{\rm emit}$}
If two <spectral lines> come from the same uniformly moving source along the same line of sight, each <wavelength> is multiplied by the same longitudinal <Doppler factor> $D$. Subtracting $\lambda_{2,\rm obs}=D\lambda_{2,\rm emit}$ and $\lambda_{1,\rm obs}=D\lambda_{1,\rm emit}$ proves the displayed identity. Recession has $D>1$ and approach has $D<1$. Defining positive radial velocity for recession gives $\beta=(D^2-1)/(D^2+1)$. A measured increase in wavelength separation therefore cannot be reconciled with strictly approaching longitudinal motion merely by changing the speed's magnitude.
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