Answer: GPS Transmission. The GPS (Global Positioning

Chapter 35, Problem 35.46

(choose chapter or problem)

GPS Transmission. The GPS (Global Positioning System) satellites are approximately 5.18 m across and transmit two low-power signals, one of which is at 1575.42 MHz (in the UHF band). In a series of laboratory tests on the satellite, you put two 1575.42-MHz UHF transmitters at opposite ends of the satellite. These broadcast in phase uniformly in all directions. You measure the intensity at points on a circle that is several hundred meters in radius and centered on the satellite. You measure angles on this circle relative to a point that lies along the centerline of the satellite (that is, the perpendicular bisector of a line that extends from one transmitter to the other). At this point on the circle, the measured intensity is \(2.00 \mathrm{\ W} / \mathrm{m}^{2}\). (a) At how many other angles in the range \(0^{\circ}<\theta<90^{\circ}\) is the intensity also \(2.00 \mathrm{\ W} / \mathrm{m}^{2}\)? (b) Find the four smallest angles in the range \(0^{\circ}<\theta<90^{\circ}\) for which the intensity is \(2.00 \mathrm{\ W} / \mathrm{m}^{2}\). (c) What is the intensity at a point on the circle at an angle of \(4.65^{\circ}\) from the centerline?