Would the Bitcoin network function well over planetary distances? How would miners on Mars be able to contribute blocks if it can take several minutes to send data back and forth?

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If it works within ~10 min blocks, network should still be able to sync, yes?

That's the problem, the delay takes anywhere from 3 to 20 minutes.

Not sure about mining, but even if round trip is too long to use the base chain, lightning channels could be opened up on earth for martians to use possibly. Channels that get unilaterally closed might be an issue

This essay explores the topic, short answer is no.

https://www.unchained.com/blog-tag/bitcoin-astronomy