Yes, it is possible to listen to other planets using radio waves. In fact, radio astronomy is a field of science that focuses on studying celestial objects and phenomena using radio waves. Radio waves can be emitted by various astronomical sources, including planets, stars, galaxies, and other cosmic objects.
Regarding attempts to listen to other planets, scientists have conducted experiments and projects aimed at detecting radio signals from extraterrestrial civilizations. These efforts are part of the field known as the Search for Extraterrestrial Intelligence (SETI). The primary goal of SETI is to search for artificial radio signals that could indicate the presence of intelligent life elsewhere in the universe.
To date, however, no definitive evidence of extraterrestrial intelligent life has been found. There have been numerous searches and programs dedicated to this pursuit, such as the SETI Institute's ongoing initiatives, including the Allen Telescope Array and the Breakthrough Listen project.
As for the distance at which we should try listening, there is no specific limit. Radio waves can travel vast distances through space, and we can detect them as long as they are within the range of our receiving equipment and have sufficient strength. Scientists have targeted nearby star systems in their search for extraterrestrial signals, such as the famous Arecibo Message sent to the globular star cluster M13 in 1974.
However, it's important to note that the vastness of space and the limitations of our technology make it a challenging task to detect and interpret potential signals from other planets or civilizations. The search for extraterrestrial intelligence remains an ongoing scientific endeavor, and future advancements in technology may enhance our capabilities in this field.