Needless to say, it's quite unlikely that an alien planet will be at rest with respect to Earth. You may remember that we (and our telescope in Arecibo) are whizzing along on a rotating planet which is revolving around the Sun, which in turn is orbiting the center of our Milky Way galaxy, etc. We can assume that our extra-terrestrial friends are likewise situated.
Radio waves emitted from a moving source and/or received by a moving target show a phenomenon called "the Doppler effect." For example, when you hear a car honking as it passes you, the frequencyor pitchof the sound changes as the car passes.
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