You can store a private key at long distances. You just can’t actively participate in the network when that far away. And you can use custodians for transactions in the meantime, like a checking account.

For on-chain transactions it is not a problem. You can still receive blocks, even if they were mined hours or days ago. So sending a transaction to the network and receiving confirmations could just take a long time. For the mining itself the consensus rules could be changed to increase the time between blocks when expanding the network to other planets or other solar systems.

That's such an interesting idea, I've never thought about it that way... Earth is roughly 8 light-minutes from the sun, but Mars gets a maximum distance of 20 light-minutes away from Earth... So I guess a Mars-Earth Bitcoin Blockchain is "kinda" feasible, but once you get out to the Belt, other systems would be needed...