Final answer:
The range of a radio signal is related to the power of the transmitter and follows an inverse square law. Detecting radio signals from intelligent life in other solar systems is extremely challenging due to the great distances and the weakening of radio signals over space.
Step-by-step explanation:
The question pertains to the range of a radio signal and how it can be determined based on the power of the radio transmitter. The strength of a radio signal, which follows an inverse square law, is crucial for determining the range or distance at which a receiver can still detect a signal from a transmitter. To find out at what distance must you be from a 650-kHz radio station with power 50.0 kW for there to be only one photon per second per square meter, one would need to consider factors such as the signal's frequency, power, and the assumption of no reflections and absorption in space. This is directly related to the challenge of detecting intelligent life in other solar systems through their radio broadcasts.
For the second question, if a 60-kW transmitter sends a signal to a satellite 100 km away, and the transmitter's power is increased to 90 kW, we would need to calculate at what distance the signal will have the same maximum field strength. This is determined by the increased power and the inverse square law mentioned earlier.
The implications for detecting intelligent life in other solar systems by detecting their radio broadcasts involve considering the vast distances and the inevitable weakening of signals with distance, making the possibility of detecting such signals a significant challenge.