If hashes are cheap on Earth, you want them exported to Mars to improve the security of the Martian block chain. Exporting hashes is easy to do in the stateless manner we expect from decentralized Bitcoin technology.

Each block on a block chain is protected against modification by the proof of work it shows and by the proof of work shown by the blocks that follow it. This proof of work is communicable---the work done in one chain can be applied to another chain.

So, for example, we have Marscoin and Bitcoin. Bitcoin (still focused on and near Earth) is by far the stronger chain. Marscoin is great for local transactions on Mars, but nobody trusts it for serious savings because its network difficulty is much lower than Bitcoin.

However, some people on Earth start to include hashes of recent Marscoin block headers in their transaction outputs (maybe using ContractHashTool to do this as a part of their regular transactions).

Following a soft fork of Marscoin, Marscoin full nodes download both the Bitcoin block chain and the Marscoin block chain. Looking at the Bitcoin block chain, they find the first Marscoin header hash encoded in an output and look at how much proof of work is protecting that transaction on the Bitcoin block chain. They add that proof of work to the corresponding block on the Marscoin block chain---now that block is protected by the combined hash rate of two planets! For example:

Bitcoin Block 10,000,000 Confirmed 100 times

Protected by proof of work equal to 10^72 hashes

Has a transaction that references Marscoin block 50,000 Marscoin Block 50,000 Confirmed 200 times

Protected by native proof of work equal to 10^48 hashes

External proof of work adds an extra 10^72 hashes

The Marscoin full nodes perform the same calculation for any other Marscoin header hashes found in the Bitcoin block chain. Now attacking all but the most recent Marscoin blocks requires attacking Bitcoin at the same time.

To prevent denial-of-service attacks against recent blocks, methods like Gavin Andresen's require-priority idea can ensure high-priority Martian transactions get through even if malcontents try using cheap Terran hash rate in short-chain 51% attacks.

Now Terrans and Martians can live in peace and harmony---all thanks to Bitcoin. :-)