Worked example 6.1.1: GPS L1: field strength and polarisation

Five short calculations tied to the applications. They use only $E/H={\eta }_0$, ${\mathcal{P}}_{av}=|E_0{|}^2/2{\eta }_0$, the polarisation vectors, Malus' law and the two-way Doppler shift, and no new physics. Numerical constants: $c=3\times 10^{8}m/s$, ${\eta }_0=120\pi =377\Omega$. The polarisation match of a wave and an antenna, with unit polarisation vectors written for the same $a_k$, is $|p_w\cdot p_a^{\ast }{|}^2$, with $p=(a_x\mp \mathrm{j}{a}_y)/\sqrt{2}$ for RHCP and LHCP along $+z$. A good way to use them: read the given quantities, produce the formula from the corresponding application or problem yourself, and only then put the numbers in.