Doppler dipole ($\Delta T/T_0=(v/c)\cos \theta +O(v^2/c^2)$)

An observer moving through isotropic blackbody radiation sees a direction-dependent temperature. With the sky angle measured toward the velocity apex in the observer frame, $T(\theta )=T_0/[\gamma (1-\beta \cos \theta )]$, where $\beta =v/c$ and $\gamma =(1-{\beta }^2{)}^{-1/2}$. First-order expansion gives the displayed dipole. The forward sky is hotter. The cosmic microwave background dipole is an application.