Short answer: no!

They'd be far better off with creating their own chain. The fact is that even should they generate a block, the time to send it back to earth would be far longer than the 10 minute timeframe. Probably someone on earth would have generated a block and other would already be chewing on build on that block before anybody's ever heard of yours coming from mars (http://www.wolframalpha.com/input/?i=Distance+between+earth+and+mars)

P.S.: which doesn't mean that bitcoin is not applicable, you'd just have exchange rates between Earth Bitcoins and Mars Bitcoins

Basically yes, it's because the network has to agree on a consistent state, and the smaller group will eventually be overtaken by the larger one and all incompatible blocks are lost (Bitcoins generated in those blocks will no longer be accepted by the network).

It's not really a vulnerability, you'd be free to keep on working on the smaller chain, resulting in a network fork, but you'd have to convince people to (a) accept your coins and (b) join your network.

As long as network splits are short I don't see a big problem, but should for example china decide to drop all bitcoin connections to the outside world we'd end up with a Bitcoin block chain for China and one for the rest of the world. I guess we'll see it sooner or later. But "Don't Panic"

If the person that generated the bitcoins joins the network before any other has found the bitcoins, it should be fine. First to notify the network the discover is the one that gets the bitcoins.

1. Create a stable wormhole big enough to carry information from one side to another.
2. Wire it up.
3. Viola, an internet connection to Earth.
4. Setup bitcoin...and you're DONE!

Quantum entanglement does not allow FTL communication.

In other star and planetary systems it is really better to create a separate block chain.
But what about nearby objects: Moon, Mars? Can we use DTN or something like that?

It takes just 1.28 seconds for light to reach the Moon's surface from the Earth's surface.

384,467,001 m 299,792,458 mps = 1.282,443,873 s

From 3 to 22 minutes depending on the position of Mars. But we should keep in mind
that Mars is not always visible from Earth - so that requires a system of repeaters.

Approximate calculations for the minimum and the maximum distances:
55,750,000,000 m 299,792,458 mps = 185.961,983,073 s = 3.099,366,385 min
401,000,000,000 m 299,792,458 mps = 1,337.859,778,937 s = 22.297,662,982 min

To summarize. It seems that it is safer to use separate block chains for each planet.
However, I do not see any problems in the use of a single chain for natural satellites.

Actually, the vaccum sucks for cooling things.