Consider a communications satellite that orbits the Earth at a height of about 40,000 kilometers. At this height the orbit period is 24 hours, so that it seems to hang motionless above the Earth,...

Consider a communications satellite that orbits the Earth at a height of about 40,000 kilometers. At this height the orbit

period is 24 hours, so that it seems to hang motionless above the Earth, which turns underneath the satellite once every 24

hours. This is called a “synchronous” satellite. The advantage of such an arrangement is that receiving antennas on the

ground can point at a seemingly fixed location of the satellite in the sky and not have to be steered. You have probably seen

such fixed receiving antennas pointed at the sky.

If the broadcasting antenna on the satellite is 2 meters in diameter and broadcasts at a frequency of 10 gigahertz (f = 10 ×

109 hertz), approximately what is the diameter of the region on the ground where the satellite transmission can be picked

up?