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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.

Observer motion produces the cosmic microwave background dipole: to first order in $\beta =v/c$,The direction of motion is hotter and the opposite direction cooler. Its full-sky pattern has one broad positive hemisphere and one broad negative hemisphere; it is not concentrated in the galactic plane.