Mining Bitcoin on Mars is totally infeasible, as almost all blocks mined on Mars will be orphaned by the time they reach Earth. I have talked about a solution before:
Each planet will have its own locally-mined cryptocurrency (Marscoin, etc), which each have a floating exchange rate to the original Earth-based Bitcoin. Marscoins and bitcoins can be directly traded for each other in order to settle interplanetary trade balances, the only issue is the speed-of-light delay for confirmations (which is unavoidable no matter what). Naturally Bitcoin can't be mined on Mars and Marscoin can't be mined on Earth, but that's not important.
An interplanetary coin with a block target of several Earth days (to allow interplanetary mining) is also a possibility for interplanetary trade or as a solar-system-wide reserve currency, but probably not necessary as long as the planetary coins can be freely traded, in which case it's likely that Bitcoin will become the solar-system-wide reserve currency (making all previous price predictions seem hopelessly pessimistic).