TL;DR: Whatever block interval one employs, another planet with greater mining power will eventually overtake the local blockchain. It would only be possible to lock other miners out by adding low-depth checkpoints.
Gedankenexperiment:
MarsCoin starts a new blockchain with a 2 minute block interval, they have one Unit of Mining Power [UMP] at their disposal with a new MarsCoin specific mining algorithm.
Some traders from Earth start using MarsCoin for their transactions with Mars colonists. They get blocks with a 20 minute delay (as proposed in the question). After a while they realize that the MarsCoin mining rewards are quite juicy and technology is much cheaper on Earth than in the underdeveloped colony: They create mining equipment with 2 UMP, allowing them to find blocks twice as fast than on Mars.
- -20 minutes: Mars is at Block X and broadcasts it to Earth.
- …
- 0 minutes: Earth receives Block X from Mars, and starts their own mining effort. The difficulty has not increased yet, so they can mine one block per minute for the time being. Mars is at Block X+10.
- 2 minutes: Earth receives Block X+1 from Mars, but Earth is already on Block X+2 on their own chain. Earth subsequently outperforms Mars and continues mining on their own chain. Mars is at Block X+11.
- …
- 21 minutes: Mars receives the first block Block X+1 from Earth and discards it, because Mars found Block X+20 at 20 minutes. Earth is at Block X+21, and received Block X+10 last from Mars.
- …
- 61 minutes: Mars receives Block X+41 from Earth, Mars is at Block X+40. Earth's chain's total proof of work is greater than Mars' chain's. Mars' chain is discarded in favor for Earth's. Mars' miners lose the mining reward of the last 40 blocks. Earth is at Block X+61.
Conclusion:
Neither distance, nor block interval are sufficiently prohibitive. As long as the other planet has more mining power it will eventually overtake the local blockchain.
Addendum: Short block interval with checkpoints at low depth
When I just read this question again, I thought of another thing. If one was hellbent to keep non-martian mining efforts from bearing fruits, one could introduce a sliding checkpoint scheme. In my above example, where I was prescribing a block interval of two minutes and terrestrian mining was twice as fast as martian mining, it would take a reorganization of more than forty blocks for the terrestrian chain to replace the martian.
If the community of Mars agreed upon forbidding chain reorganizations of more than 15 blocks (which at two minute intervals is less time than that of a radio wave roundtrip) by adding every block with 15 confirmations to the checkpoint list, terrestrian miners would be able to fork themselves from the Marscoin chain, but would never be able to take over the martian mining.
People on Mars could use a different mining algorithm. – Luca Matteis – 2014-08-12T19:13:13.267
I think that would lessen the risk of having another planet taking over, but I don't think that eliminates the risk. – user18953 – 2014-08-12T20:30:52.823
Will this even be necessary in the future? I believe by the time we have terraformed and colonized Mars, Quantum Entanglement will be the primary method to instantaneously transmit data... – ManeBit – 2015-01-06T17:01:46.627
http://physics.stackexchange.com/a/78130 – Nick ODell – 2015-01-06T17:04:18.433
There are a few technical issues with your statements, however, using theoretical quantum links for data transfer will be instantaneous. – Willtech – 2018-05-10T10:16:25.240