Or possible the ship's computer initiated the "SOS" when the suspended animation chambers began to fail. By the time the Enterprise found the ship, a dozen of Khan's people had perished.Khan broadcast a beacon signal, perhaps to lure in ships he could hijack.
The Enterprise first detected the ship on it's scanners, it was only when the Botany Bay was just outside of visual range that Uhura picked up it's signal. The Botany Bay's radio signal might not have possessed much range.It would stretch credibility that Kirk's would be the only ship in Sol's Oort cloud to come close enough to the siren song ...
Well off the beaten trail, who would have pick up the signal?
Depends, was the Botany Bay on a direct line between two destinations, I would imagine (imo) that most civilian traffic in the central Federation is point A to point B.when thousands if not millions of warp sorties must have zoomed through that region in whichever direction.
The corridor linking Sol with Alpha Centauri would be frequently used, but move a quarter light year to one side and it gets empty and lonely.
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