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 Then all communication between the two parties, leaving you with effectively a hard fork. But that doesn’t mean that bitcoin is for earth, only. 
 If you leave earth with earth-level difficulty, you wouldn’t even be able to continue mining elsewhere anyways. You would have to use something else. 
 …for 2016 blocks. 
 You wouldn’t be able to mine a single block, and even if you somehow could grind it out, the difficulty adjustment is capped. It would effectively be stalled. 
 Ah, true. 

Well, looks like we will have to send miners ahead of people. Or build room on the ship for it. Plenty of room to build in space, and plenty of cooling.