A key premise in many science fiction stories is the idea that radio and TV signals from Earth can travel through space and be received by listeners in another star system. Show that this is a fallacy by calculating the maximum distance from Earth where a signal could be received with a SNR of 0 dB. Specifically, assume TV channel 4, broadcasting at 67 MHz, with a 4 MHz bandwidth, a transmitter power of 1000 W, transmit and receive antenna gains of 4 dB, a cosmic background noise temperature of 4 K, and a perfectly noiseless receiver. How much would this distance decrease if an SNR of 30 dB is required at the receiver? (30 dB is a typical value for good reception of an analog video signal.) Relate these distances to the nearest planet in our solar system