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> Hence the huge receiving dishes, and apparently one 100 foot dish alone does not collect enough energy to reconstruct the signal

Around 30k photons a second.

  You have: ((23W/(pi*astronomicalunit^2)) * (pi(50ft)^2)) / (6.626e-34J/Hz * 10GHz)
  You want: 
        Definition: 36024.297 / s
…I don't know if that's a lot, or where the noise floor is.


As a comparison of unlike but related units:

> For example, the data rate used from Jupiter was about 115,000 bits per second

And I think it affects the calculation slightly that Voyager's downlink transmits at about 8.4 GHz (X-band).

Good stuff here: https://www.allaboutcircuits.com/news/voyager-mission-annive...




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