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How many photons are received per bit transmitted from Voyager 1?
As of 2024, according to https://voyager.jpl.nasa.gov/ , Voyager 1 is around one light·day away from Earth and still in radio contact. When Voyager 1 sends messages to Earth, roughly how many photo...
$\begingroup$For an exact calculation we need to address a few choices: (you can change them, the answer will not be tremendously affected) We'll ignore this here since losses related to illuminators or Cassegrain construction will not even be one order of magnitude, insignificant compared with the rest. B) The beam forming by Voyager's $d=3.7{\rm m}$ dish will direct them predominantly to Earth, with $(\pi d/\lambda)^2$ antenna gain, but still, at the current distance of $R=23.5$ billion kilometers, this only results in $3.4\cdot10^{-22}$ Watt per square meter reaching Earth, so a receiver with a $D=70{\rm m}$ dish will collect only $1.3$ attowatt ($1.3\cdot 10^{-18}{\rm W}$), summarized by: $$ P_{\rm received} = P_{\rm transmit}\ \Big(\frac{\pi d}{\lambda}\Big)^2 \ \frac1{4\pi R^2}\ \frac{\pi D^2}4 $$ Dividing by $E_\phi$ we see that this power then still corresponds to c. $240000$ photons per second, or $1500$ photons per bit.
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