Right up my alley. I've out lived the National Space Society life membership system. I have moon, Mars and asteroid base designs up my sleeve. I'm also a traveller fan they have week long waits in the traveller RPG and that's only the solar system next door. It gets to be 18 month in the Imperium centre to edge. 5 years spinward to coreward, ~3000 light years.
First there would be very few time sensitive transactions. Who cares if the payroll to the NASA hard drive on Mars takes an hour. Payday will be the next morning anyway. Most transactions would be local.
Secondly just maintaining a buffer account on earth with a few BTC padding it out would work in most cases. Major Tom buys a gift for his wife. The transaction goes to earth but references the wallet on earth not mars. The transaction clears locally on earth. Tom wont know that for 20 minutes but it does not matter since he wont/ can't do a transaction to double spend. Very few opportunities will exist for Tom to get a BTC on mars or earth and spend it immediately. If that is likely then the buffer is spent instead and he's asked to refill a half a minute later.
The bitcoin mining protocols are time independent. They only know if something is newer than something else not what timezone either the transaction or the mining occured in. Mars base time will just be another time zone to those buts of software that check time. It has an extra hour in the day but that wont have much effect. When space colonisation gets going big time there will be a hundred new time zones and delays out to 8 hours, Saturns moons. But most thinks traded on the ships and stations will be purely local. If they were paid for, probably with big crowd funding appeals, then that would again be all local on earth or where- ever. All trade is limited by the speed of information. You can not trade, bargain, bid or promise, when you can't communicate. Not even information can be traded faster than light so the speed of bitcoin communication is not a problem.
