$32\mathrm{.}43$ CP Global Positioning System $($GPS$).$ The GPS network consists of $24$ satellites, each of which makes two orbits around the earth per day. Each satellite transmits a $50\mathrm{.}0$ W $($or even less$)$ sinusoidal electromagnetic signal at two frequencies, one of which is $1575\mathrm{.}42$ MHz$.$ Assume that a satellite transmits half of its power at each frequency and that the waves travel uniformly in a downward hemisphere. $($a$)$ What average intensity does a GPS receiver on the ground, directly below the satellite, receive? $($Hint: First use Newton$$s laws to find the altitude of the satellite.$)($b$)$ What are the amplitudes of the electric and magnetic fields at the GPS receiver in part $($a$),$ and how long does it take the signal to reach the receiver? $($c$)$ If the receiver is a square panel $1\mathrm{.}50$ cm on a side that absorbs all of the beam, what average pressure does the signal exert on it$?($d$)$ What wavelength must the receiver be tuned to$?$