I use Arecibo to illustrate the point I was trying to make about the link power budget. You know, if you do not have a lot of power at the transmit end or you have a LOT OF FREE SPACE LOSS you must have a great receiver (high gain) on the other end. Satellites are space limited and power limited, so obviously you have to calculate the gain at the receiver to support the link. In the case of Hubble the received signal is optical, I.e., light. Arecibo is looking for a radio signal, no? Ditto the radio antenna array out west as seen in the movie Contact. Jodie Fosters SETI group in Contact picked up a radio signal. A radio signal just like a satellite signal, with EIRP. The only difference is the radio waves received by radio telescopes are from astrological sources, not satellites. The received signal are not (visible) light. Which brings us to the dodgy subject of light and electromagnetic waves and photons.