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But....How does it know it's the earth?

It is billions km away.., is the earth that noisy compare to solar wind and cosmic rays?

>>j16sdi+(OP)
Voyager has a star sensor that is meant to align with the Sun and Canopus (IIRC). If both are properly aligned it means it's pointed in the right direction. At its current distance the beam width is wide enough to cover all of Earth's orbit. So really it just needs to point at the Sun anymore.

The carrier signal from Earth is also powerful on a particular frequency and polarization. While there's definitely noise at the receiver it's looking for a very specific signal so can filter out everything it's not expecting. We do the same thing on the Earth side, filtering out noise to recover the very weak signal received from Voyager.