For detecting the planet Earth we...I mean they:

• Could detect Earth passing in transit across the sun.
• Could detect the emission spectrum of certain chemicals such as chlorophyll, water, methane from biological processes, ect.
• Could detect certain electromagnetic wave emissions (the earliest radio communications were amplitude modulated which tend to be reflected rather than pass through the ionosphere).
• Could detect objects sent away from Earth such as Voyager 1, Voyager 2, Pioneer 10, Pioneer 11, New Horizons and possibly the "phantom cosmonauts" that may or may not have been covered up by the Soviet Union and who may or may not become tasty frozen treats for the more carnivorous aliens of the galaxy.

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