Theory for the Measurement of the Earth's Velocity through the 3°K Cosmic Radiation

The intensity of radiation for an observer moving through thermal radiation is described by an anisotropic temperature $T\left(\theta \right)=T{(1+\beta cos\theta )}^{-1\mathrm{}}$ or $\left(\frac{h{\nu }^3}{c^2}\right)d\Omega d\nu {[\exp \frac{h\nu }{kT\left(\theta \right)}-1]}^{-1\mathrm{}}$, where $\beta =\frac{v}{c}$. Temperature-measuring antennas measure $T\left(\theta \right)$. Intensity measurements give an anisotropy between radiation along $\pi +\theta$ and $\theta$ of $\beta cos\theta$ for $\left(\frac{h\nu }{\mathrm{kT}}\right)\ll 1$ (the same as the temperature anisotropy), and $\left(\frac{h\nu }{\mathrm{kT}}\right)\beta cos\theta$ for $\left(\frac{h\nu }{\mathrm{kT}}\right)\gg 1$. Examples of moving detectors and surfaces in the laboratory and in space are discussed.