Corrected entry: Given how close the Enterprise and Vengeance were to Earth, the fact that Uhura can get a communications signal to New Vulcan to reach Spock Prime but not one to Starfleet Command which is literally outside their viewscreen window is preposterous.
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Correction: At no point does anyone say that they can't get a signal to Starfleet Command. Spock chooses to try to contact Spock Prime because he may be able to offer valuable advice on dealing with Khan. On the other hand, Spock is probably reluctant to contact Starfleet Command at this point because he doesn't know what Marcus (who is, remember, in charge of Starfleet) has told them about the situation (remember, Marcus' story is that the Enterprise crew 'went rogue in league with Khan, leaving him no choice but to destroy them'). Right now Starfleet Command will almost certainly take Marcus's side, and Spock doesn't have the time to persuade them to side with him instead.
Aerinah