Consider a communications satellite that orbits the Earth at a height of about 40,000 km. At this height the orbit period is 24 h, so that it seems to hang motionless above the Earth, which turns underneath the satellite once every 24 h. 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 m in diameter and broadcasts at a frequency of 10 GHz (f= 10 × 109 Hz), approximately what is the diameter of the region on the ground where the satellite transmission can be picked up?

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Consider a communications satellite that orbits the Earth at a height of about 40,000 km. At this height the orbit period is 24 h, so that it seems to hang motionless above the Earth, which turns underneath the satellite once every 24 h. 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 m in diameter and broadcasts at a frequency of 10 GHz (f= 10 × 109 Hz), approximately what is the diameter of the region on the ground where the satellite transmission can be picked up?
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