I apologize for any confusion. It seems there might be a misunderstanding. The calculations I provided earlier were unrelated to receiving a radio wave from a specific distance.
In terms of receiving radio signals, the factors that affect signal strength and reception can vary depending on several factors, including the frequency of the radio wave, the power of the transmitter, the presence of obstacles or interference, and the sensitivity of the receiving equipment. Distance alone is not the sole determinant of whether you can receive a radio signal or not.
Receiving a radio signal from a specific source, such as a radio station, involves several factors such as the transmitting power of the station, the terrain, buildings, and other obstructions that can attenuate or block the signal, and the quality and location of the receiving equipment (e.g., the antenna and the radio receiver). Even for signals transmitted relatively close by, reception can be affected by these factors.
On the other hand, detecting and studying radio waves from astronomical sources, such as distant stars or galaxies, involves specialized equipment, sensitive receivers, and complex data analysis techniques. Scientists employ sophisticated instruments like radio telescopes and utilize advanced techniques to amplify and analyze weak signals from space.
Receiving a radio signal from a radio station that is relatively close but experiencing difficulty can be influenced by specific local factors, while the detection and study of radio waves from astronomical sources involve different considerations and advanced scientific methodologies.